This function performs multiple-group item calibration (Bock & Zimowski, 1997) using marginal maximum likelihood estimation via the expectation-maximization (MMLE-EM) algorithm (Bock & Aitkin, 1981). It also supports multiple-group fixed item parameter calibration (MG-FIPC; e.g., Kim & Kolen, 2016), which extends the single-group FIPC method (Kim, 2006) to multiple-group settings. For dichotomous items, the function supports one-, two-, and three-parameter logistic IRT models. For polytomous items, the graded response model (GRM) and the (generalized) partial credit model (GPCM) are available.
Usage
est_mg(
x = NULL,
data,
group.name = NULL,
D = 1,
model = NULL,
cats = NULL,
item.id = NULL,
free.group = NULL,
fix.a.1pl = FALSE,
fix.a.gpcm = FALSE,
fix.g = FALSE,
a.val.1pl = 1,
a.val.gpcm = 1,
g.val = 0.2,
use.aprior = FALSE,
use.bprior = FALSE,
use.gprior = TRUE,
aprior = list(dist = "lnorm", params = c(0, 0.5)),
bprior = list(dist = "norm", params = c(0, 1)),
gprior = list(dist = "beta", params = c(5, 16)),
missing = NA,
Quadrature = c(49, 6),
weights = NULL,
group.mean = 0,
group.var = 1,
EmpHist = FALSE,
use.startval = FALSE,
Etol = 0.001,
MaxE = 500,
control = list(eval.max = 500, iter.max = 200, x.tol = 1e-04),
fipc = FALSE,
fipc.method = "MEM",
fix.loc = NULL,
fix.id = NULL,
se = TRUE,
verbose = TRUE
)Arguments
- x
A list containing item metadata for all groups to be analyzed. For example, if five groups are analyzed, the list should contain five elements, each representing the item metadata for one group. The order of the elements in the list must match the order of group names specified in the
group.nameargument.Each group's item metadata includes essential information for each item (e.g., number of score categories, IRT model type, etc.) required for calibration. See
est_irt()orsimdat()for more details about the item metadata.When
use.startval = TRUE, the item parameters specified in the metadata will be used as starting values for parameter estimation. Ifx = NULL, bothmodelandcatsarguments must be specified. Note that whenfipc = TRUEto implement MG-FIPC, thexargument must be specified and cannot be NULL. Default isNULL.- data
A list containing item response matrices for all groups to be analyzed. For example, if five groups are analyzed, the list should include five elements, each representing the response data matrix for one group. The elements in the list must be ordered to match the group names specified in the
group.nameargument. Each matrix contains examinees' item responses corresponding to the item metadata for that group. In each matrix, rows represent examinees and columns represent items.- group.name
A character vector indicating the names of the groups. For example, if five groups are analyzed, use
group.name = c("G1", "G2", "G3", "G4", "G5"). Group names can be any valid character strings.- D
A scaling constant used in IRT models to make the logistic function closely approximate the normal ogive function. A value of 1.7 is commonly used for this purpose. Default is 1.
- model
A list containing character vectors specifying the IRT models used to calibrate items across all groups. For example, if five groups are analyzed, the list should contain five elements, each being a character vector of IRT model names for one group. The elements in the list must be ordered to match the group names specified in the
group.nameargument.Available IRT models include:
"1PLM","2PLM","3PLM","DRM"for dichotomous items"GRM","GPCM"for polytomous items
Here,
"GRM"denotes the graded response model and"GPCM"the (generalized) partial credit model. Note that"DRM"serves as a general label covering all three dichotomous IRT models.If a single model name is provided in any element of the list, it will be recycled across all items within that group.This argument is used only when
x = NULLandfipc = FALSE. Default isNULL.- cats
A list containing numeric vectors specifying the number of score categories for items in each group. For example, if five groups are analyzed, the list should contain five numeric vectors corresponding to the five groups. The elements in the list must be ordered consistently with the group names specified in the
group.nameargument.If a single numeric value is specified in any element of the list, it will be recycled across all items in the corresponding group. If
cats = NULLand all models specified in themodelargument are dichotomous (i.e., "1PLM", "2PLM", "3PLM", or "DRM"), the function assumes that all items have two score categories across all groups.This argument is used only when
x = NULLandfipc = FALSE. Default isNULL.- item.id
A list containing character vectors of item IDs for each group to be analyzed. For example, if five groups are analyzed, the list should contain five character vectors corresponding to the five groups. The elements in the list must be ordered consistently with the group names specified in the
group.nameargument.When
fipc = TRUEand item IDs are provided via theitem.idargument, the item IDs in thexargument will be overridden. Default isNULL.- free.group
A numeric or character vector indicating the groups for which the scales (i.e., mean and standard deviation) of the latent ability distributions are freely estimated. The scales of the remaining groups (those not specified in this argument) are fixed using the values provided in the
group.meanandgroup.vararguments, or from theweightsargument.For example, suppose that five groups are analyzed with group names "G1", "G2", "G3", "G4", and "G5". To freely estimate the scales for groups 2 through 5, set
free.group = c(2, 3, 4, 5)orfree.group = c("G2", "G3", "G4", "G5"). In this case, the first group ("G1") will have a fixed scale (e.g., a mean of 0 and variance of 1 whengroup.mean = 0,group.var = 1, andweights = NULL).- fix.a.1pl
Logical. If
TRUE, the slope parameters of all 1PLM items are fixed toa.val.1pl; otherwise, they are constrained to be equal and estimated. Default isFALSE.- fix.a.gpcm
Logical. If
TRUE, GPCM items are calibrated as PCM with slopes fixed toa.val.gpcm; otherwise, each item's slope is estimated. Default isFALSE.- fix.g
Logical. If
TRUE, all 3PLM guessing parameters are fixed tog.val; otherwise, each guessing parameter is estimated. Default isFALSE.- a.val.1pl
Numeric. Value to which the slope parameters of 1PLM items are fixed when
fix.a.1pl = TRUE. Default is 1.- a.val.gpcm
Numeric. Value to which the slope parameters of GPCM items are fixed when
fix.a.gpcm = TRUE. Default is 1.- g.val
Numeric. Value to which the guessing parameters of 3PLM items are fixed when
fix.g = TRUE. Default is 0.2.- use.aprior
Logical. If
TRUE, applies a prior distribution to all item discrimination (slope) parameters during calibration. Default isFALSE.- use.bprior
Logical. If
TRUE, applies a prior distribution to all item difficulty (or threshold) parameters during calibration. Default isFALSE.- use.gprior
Logical. If
TRUE, applies a prior distribution to all 3PLM guessing parameters during calibration. Default isTRUE.- aprior, bprior, gprior
A list specifying the prior distribution for all item discrimination (slope), difficulty (or threshold), guessing parameters. Three distributions are supported: Beta, Log-normal, and Normal. The list must have two elements:
dist: A character string, one of"beta","lnorm", or"norm".params: A numeric vector of length two giving the distribution’s parameters. For details on each parameterization, seestats::dbeta(),stats::dlnorm(), andstats::dnorm().
Defaults are:
aprior = list(dist = "lnorm", params = c(0.0, 0.5))bprior = list(dist = "norm", params = c(0.0, 1.0))gprior = list(dist = "beta", params = c(5, 16))
for discrimination, difficulty, and guessing parameters, respectively.
- missing
A value indicating missing responses in the data set. Default is
NA.- Quadrature
A numeric vector of length two:
first element: number of quadrature points
second element: symmetric bound (absolute value) for those points For example,
c(49, 6)specifies 49 evenly spaced points from –6 to 6. These points are used in the E-step of the EM algorithm. Default isc(49, 6).
- weights
A two-column matrix or data frame containing the quadrature points (in the first column) and the corresponding weights (in the second column) for the latent ability prior distribution. If not
NULL, the latent ability distributions for the groups not specified in thefree.groupargument are fixed to match the scale defined by the provided quadrature points and weights. The weights and points can be conveniently generated using the functiongen.weight().If
NULL, a normal prior density is used instead, based on the information provided in theQuadrature,group.mean, andgroup.vararguments. Default isNULL.- group.mean
A numeric value specifying the mean of the latent variable prior distribution when
weights = NULL. Default is 0. For groups not specified in thefree.groupargument, their distribution means are fixed to this value in order to resolve the indeterminacy of the item parameter scale.- group.var
A positive numeric value specifying the variance of the latent variable prior distribution when
weights = NULL. Default is 1. For groups not specified in thefree.groupargument, their distribution variances are fixed to this value in order to resolve the indeterminacy of the item parameter scale.- EmpHist
Logical. If
TRUE, the empirical histograms of the latent ability prior distributions across all groups are estimated simultaneously with the item parameters using the approach proposed by Woods (2007). Item calibration is then performed relative to the estimated empirical priors.- use.startval
Logical. If
TRUE, the item parameters provided in the item metadata (i.e., thexargument) are used as starting values for item parameter estimation. Otherwise, internally generated starting values are used. Default isFALSE.- Etol
A positive numeric value specifying the convergence criterion for the E-step of the EM algorithm. Default is 1e-3. Specifically, the EM algorithm terminates when the largest absolute difference in item parameter estimates between consecutive iterations is smaller than this value.
- MaxE
A positive integer specifying the maximum number of iterations for the E-step in the EM algorithm. Default is
500.- control
A named list of options passed directly to
stats::nlminb()in each M‑step optimization of the EM algorithm. By default:control = list(eval.max = 500, iter.max = 200, x.tol = 1e-4), whereeval.max= 500 limits the number of function evaluationsiter.max= 200 caps the number of internal optimizer iterationsx.tol= 1e‑4 sets the absolute change threshold in parameter values below whichstats::nlminb()considers the solution to have converged Users may additionally supply othernlminb()control options (such asabs.tol,rel.tol,trace, etc.) as needed.
- fipc
Logical. If
TRUE, multiple-group fixed item parameter calibration (MG-FIPC) is applied during item parameter estimation. Whenfipc = TRUE, the information on which items are fixed must be provided via eitherfix.locorfix.id. See below for details.- fipc.method
A character string specifying the FIPC method. Available options are:
"OEM": No Prior Weights Updating and One EM Cycle (NWU-OEM; Wainer & Mislevy, 1990)"MEM": Multiple Prior Weights Updating and Multiple EM Cycles (MWU-MEM; Kim, 2006) Whenfipc.method = "OEM", the maximum number of E-steps is automatically set to 1, regardless of the value specified inMaxE.
- fix.loc
A list of positive integer vectors. Each internal vector specifies the positions of the items to be fixed in the item metadata (i.e.,
x) for each group when MG-FIPC is implemented (i.e.,fipc = TRUE). The internal objects in the list must follow the same order as the group names provided in thegroup.nameargument.For example, suppose three groups are analyzed. In the first group, the 1st, 3rd, and 5th items are fixed; in the second group, the 2nd, 3rd, 4th, and 7th items are fixed; and in the third group, the 1st, 2nd, and 6th items are fixed. Then
fix.loc = list(c(1, 3, 5), c(2, 3, 4, 7), c(1, 2, 6)). Note that if thefix.idargument is not NULL, the information infix.locwill be ignored. See below for details.- fix.id
A vector of character strings specifying the IDs of items to be fixed when MG-FIPC is implemented (i.e.,
fipc = TRUE).For example, suppose that three groups are analyzed. In the first group, three items with IDs G1I1, C1I1, and C1I2 are fixed. In the second group, four items with IDs C1I1, C1I2, C2I1, and C2I2 are fixed. In the third group, three items with IDs C2I1, C2I2, and G3I1 are fixed.
In this case, there are six unique items fixed across the groups—namely, G1I1, C1I1, C1I2, C2I1, C2I2, and G3I1, because C1I1 and C1I2 appear in both the first and second groups, while C2I1 and C2I2 appear in both the second and third groups. Thus, you should specify
fix.id = c("G1I1", "C1I1", "C1I2", "C2I1", "C2I2", "G3I1"). Note that if thefix.idargument is not NULL, the information provided infix.locis ignored. See below for details.- se
Logical. If
FALSE, standard errors of the item parameter estimates are not computed. Default isTRUE.- verbose
Logical. If
FALSE, all progress messages, including information about the EM algorithm process, are suppressed. Default isTRUE.
Value
This function returns an object of class est_irt. The returned
object contains the following components:
- estimates
A list containing two internal elements:
overallandgroup. Theoverallelement is a data frame with item parameter estimates and their standard errors, computed from the combined data across all groups. This data frame includes only the unique items across all groups. Thegroupelement is a list of group-specific data frames, each containing item parameter estimates and standard errors for that particular group.- par.est
A list with the same structure as
estimates, containing only the item parameter estimates (excluding standard errors), formatted according to the item metadata structure.- se.est
A list with the same structure as
estimates, but containing only the standard errors of the item parameter estimates. Note that the standard errors are calculated using the cross-product approximation method (Meilijson, 1989).- pos.par
A data frame indicating the position index of each estimated item parameter. This index is based on the combined data set across all groups (i.e., the first internal object of
estimates). The position information is useful for interpreting the variance-covariance matrix of item parameter estimates.- covariance
A variance-covariance matrix of the item parameter estimates, based on the combined data set across all groups (i.e., the first internal object of
estimates).- loglikelihood
A list containing two internal objects (i.e., overall and group) of marginal log-likelihood values based on the observed data. The structure of the list matches that of
estimates. Specifically, theoverallcomponent contains the total log-likelihood summed across all unique items from all groups, while thegroupcomponent provides group-specific log-likelihood values.- aic
A model fit statistic based on the Akaike Information Criterion (AIC), calculated from the log-likelihood of all unique items.
- bic
A model fit statistic based on the Bayesian Information Criterion (BIC), calculated from the log-likelihood of all unique items.
- group.par
A list containing summary statistics (i.e., mean, variance, and standard deviation) of the latent variable prior distributions across all groups.
- weights
A list of two-column data frames, where the first column contains quadrature points and the second column contains the corresponding weights of the (updated) latent variable prior distributions for each group.
- posterior.dist
A matrix of normalized posterior densities for all response patterns at each quadrature point. Rows and columns represent response patterns and quadrature points, respectively.
- data
A list containing two internal objects (i.e., overall and group) representing the examinees' response data sets. The structure of this list matches that of the
estimatescomponent.- scale.D
The scaling factor used in the IRT model.
- ncase
A list containing two internal objects (i.e., overall and group) representing the total number of response patterns. The structure of this list matches that of the
estimatescomponent.- nitem
A list containing two internal objects (i.e., overall and group) representing the total number of items included in the response data. The structure of this list matches that of the
estimatescomponent.- Etol
The convergence criterion for the E-step of the EM algorithm.
- MaxE
The maximum number of E-steps allowed in the EM algorithm.
- aprior
A list describing the prior distribution used for discrimination parameters.
- bprior
A list describing the prior distribution used for difficulty parameters.
- gprior
A list describing the prior distribution used for guessing parameters.
- npar.est
The total number of parameters estimated across all unique items.
- niter
The number of completed EM cycles.
- maxpar.diff
The maximum absolute change in parameter estimates at convergence.
- EMtime
Time (in seconds) spent on EM cycles.
- SEtime
Time (in seconds) spent computing standard errors.
- TotalTime
Total computation time (in seconds).
- test.1
First-order test result indicating whether the gradient sufficiently vanished for solution stability.
- test.2
Second-order test result indicating whether the information matrix is positive definite, a necessary condition for identifying a local maximum.
- var.note
A note indicating whether the variance-covariance matrix was successfully obtained from the information matrix.
- fipc
Logical. Indicates whether FIPC was used.
- fipc.method
The method used for FIPC.
- fix.loc
A list containing two internal objects (i.e., overall and group) indicating the locations of fixed items when FIPC is applied. The structure of the list matches that of the 'estimates' component.
Note that you can easily extract components from the output using the
getirt() function.
Details
Multiple-group (MG) item calibration (Bock & Zimowski, 1996) provides a unified framework for handling testing scenarios involving multiple groups, such as nonequivalent groups equating, vertical scaling, and the identification of differential item functioning (DIF). In such applications, examinees from different groups typically respond to either the same test form or to different forms that share common (anchor) items.
The goal of MG item calibration is to estimate both item parameters and
latent ability distributions for all groups simultaneously (Bock & Zimowski, 1996).
The irtQ package implements MG calibration via the est_mg() function,
which uses marginal maximum likelihood estimation through the
expectation-maximization (MMLE-EM) algorithm (Bock & Aitkin, 1981).
In addition, the function supports multiple-group fixed item parameter
calibration (MG-FIPC; e.g., Kim & Kolen, 2016), which allows the parameters
of specific items to be fixed across groups.
In MG IRT analyses, it is common for multiple groups' test forms to share
some common (anchor) items. By default, the est_mg() function
automatically constrains items with identical item IDs across groups
to share the same parameter estimates.
Most of the features of the est_mg() function are similar to those of the
est_irt() function. The main difference is that several arguments in
est_mg() accept list objects containing elements for each group to be
analyzed. These arguments include x, data, model, cats,
item.id, fix.loc and fix.id.
Additionally, est_mg() introduces two new arguments: group.name
and free.group. The group.name argument is required to assign a unique
identifier to each group. The order of the list elements provided in
x, data, model, cats, item.id, fix.loc and fix.id
must match the order of group names specified in the group.name argument.
The free.group argument is required to indicate which groups have their
latent ability distribution scales (i.e., mean and standard deviation)
freely estimated. When no item parameters are fixed (i.e., fipc = FALSE),
at least one group must have a fixed latent ability scale (e.g., mean = 0 and
variance = 1) among the multiple groups sharing common items, in order to
resolve the scale indeterminacy inherent in IRT estimation. By specifying
the groups in the free.group argument, the scales for those groups will be
freely estimated, while the scales for all other groups not included in
free.group will be fixed using the values provided in the group.mean and
group.var arguments or from the weights argument.
Situations requiring the implementation of MG-FIPC typically arise when new latent ability scales from multiple-group (MG) test data need to be linked to an established scale (e.g., that of an existing item bank). In a single run of the MG-FIPC procedure, the parameters of non-fixed (freed) items across multiple test forms, as well as the latent ability distributions for multiple groups, can be estimated on the same scale as the fixed items (Kim & Kolen, 2016).
For example, suppose that three different test forms—Form 1, Form 2, and Form 3—are administered to three nonequivalent groups: Group1, Group2, and Group3. Form 1 and Form 2 share 12 common items (C1I1 to C1I12), while Form 2 and Form 3 share 10 common items (C2I1 to C2I10). There are no common items between Form 1 and Form 3. Also, assume that all unique items in Form 1 are from an existing item bank and have already been calibrated on the item bank's scale.
In this case, the goal of MG-FIPC is to estimate the parameters of all items across the three test forms—except the unique items in Form 1— and the latent ability distributions of the three groups, all on the same scale as the item bank. To achieve this, the unique items in Form 1 must be fixed during MG-FIPC to link the current MG test data to the item bank scale.
The est_mg() function can implement MG-FIPC by setting
fipc = TRUE. In this case, the information on which items to fix must be
provided through either the fix.loc or fix.id argument. When using
fix.loc, you must supply a list of item positions (locations)
to be fixed in each group’s test form. For example, suppose that the test
data from the three groups above are analyzed. In the first group,
the 1st, 3rd, and 5th items are fixed; in the second group, the 2nd, 3rd,
4th, and 7th items are fixed; and in the third group, the 1st, 2nd, and
6th items are fixed. In this case, you would specify:
fix.loc = list(c(1, 3, 5), c(2, 3, 4, 7), c(1, 2, 6)).
Alternatively, you can use fix.id to specify a character vector of item IDs
to be fixed across groups. In the first group, the items with IDs G1I1, C1I1,
and C1I2 are fixed; in the second group, the items with IDs C1I1, C1I2,
C2I1, and C2I2 are fixed; and in the third group, the items with IDs C2I1,
C2I2, and G3I1 are fixed. In this case, there are six unique items to be
fixed across all groups: G1I1, C1I1, C1I2, C2I1, C2I2, and G3I1. You would
then specify:
fix.id = c("G1I1", "C1I1", "C1I2", "C2I1", "C2I2", "G3I1").
Note that when both fix.loc and fix.id are provided, the information
in fix.id takes precedence and overrides fix.loc.
References
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
Bock, R. D., & Zimowski, M. F. (1997). Multiple group IRT. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory (pp. 433-448). New York: Springer.
Kim, S. (2006). A comparative study of IRT fixed parameter calibration methods. Journal of Educational Measurement, 43(4), 355-381.
Kim, S., & Kolen, M. J. (2016). Multiple group IRT fixed-parameter estimation for maintaining an established ability scale. Center for Advanced Studies in Measurement and Assessment Report, 49.
Meilijson, I. (1989). A fast improvement to the EM algorithm on its own terms. Journal of the Royal Statistical Society: Series B (Methodological), 51, 127-138.
Woods, C. M. (2007). Empirical histograms in item response theory with ordinal data. Educational and Psychological Measurement, 67(1), 73-87.
Author
Hwanggyu Lim hglim83@gmail.com
Examples
# \donttest{
## ------------------------------------------------------------------------------
# 1. MG calibration using the simMG data
# - Details:
# (a) Constrain common items between groups to have
# identical item parameters (i.e., items C1I1–C1I12 between
# Groups 1 and 2, and items C2I1–C2I10 between Groups 2 and 3).
# (b) Freely estimate the means and variances of the ability
# distributions for all groups except the reference group,
# where the mean and variance are fixed to 0 and 1, respectively.
## ------------------------------------------------------------------------------
# 1-(1). Freely estimate the means and variances of Groups 2 and 3
# Import the true item metadata for the three groups
x <- simMG$item.prm
# Extract model, score category, and item ID information
# from the item metadata for the three groups
model <- list(x$Group1$model, x$Group2$model, x$Group3$model)
cats <- list(x$Group1$cats, x$Group2$cats, x$Group3$cats)
item.id <- list(x$Group1$id, x$Group2$id, x$Group3$id)
# Import the simulated response data sets for the three groups
data <- simMG$res.dat
# Import the group names for the three groups
group.name <- simMG$group.name
# Specify Groups 2 and 3 as the free groups where the scale
# of the ability distributions will be freely estimated.
# Group 1 will serve as the reference group, where the scale
# of the ability distribution is fixed to the values specified
# via the 'group.mean' and 'group.var' arguments
free.group <- c(2, 3) # or use 'free.group <- group.name[2:3]'
# Estimate IRT parameters:
# As long as common items across groups share the same item IDs,
# their item parameters will be constrained to be equal across groups
# unless FIPC is implemented.
fit.1 <-
est_mg(
data = data, group.name = group.name, model = model,
cats = cats, item.id = item.id, D = 1, free.group = free.group,
use.gprior = TRUE, gprior = list(dist = "beta", params = c(5, 16)),
group.mean = 0, group.var = 1, EmpHist = TRUE, Etol = 0.001, MaxE = 500
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -184619.3757, Max-Change: 2.188782
EM iteration: 2, Loglike: -159724.2438, Max-Change: 0.42374
EM iteration: 3, Loglike: -159631.0877, Max-Change: 0.166346
EM iteration: 4, Loglike: -159617.3743, Max-Change: 0.083614
EM iteration: 5, Loglike: -159611.4702, Max-Change: 0.052115
EM iteration: 6, Loglike: -159608.0480, Max-Change: 0.038966
EM iteration: 7, Loglike: -159605.7836, Max-Change: 0.032285
EM iteration: 8, Loglike: -159604.1351, Max-Change: 0.027248
EM iteration: 9, Loglike: -159602.8431, Max-Change: 0.023166
EM iteration: 10, Loglike: -159601.7733, Max-Change: 0.01977
EM iteration: 11, Loglike: -159600.8519, Max-Change: 0.016922
EM iteration: 12, Loglike: -159600.0358, Max-Change: 0.014527
EM iteration: 13, Loglike: -159599.2989, Max-Change: 0.012509
EM iteration: 14, Loglike: -159598.6241, Max-Change: 0.010869
EM iteration: 15, Loglike: -159597.9998, Max-Change: 0.009797
EM iteration: 16, Loglike: -159597.4177, Max-Change: 0.00890
EM iteration: 17, Loglike: -159596.8716, Max-Change: 0.008145
EM iteration: 18, Loglike: -159596.3569, Max-Change: 0.007856
EM iteration: 19, Loglike: -159595.8700, Max-Change: 0.007658
EM iteration: 20, Loglike: -159595.4080, Max-Change: 0.00744
EM iteration: 21, Loglike: -159594.9687, Max-Change: 0.007208
EM iteration: 22, Loglike: -159594.5501, Max-Change: 0.006968
EM iteration: 23, Loglike: -159594.1507, Max-Change: 0.006723
EM iteration: 24, Loglike: -159593.7692, Max-Change: 0.006477
EM iteration: 25, Loglike: -159593.4043, Max-Change: 0.006232
EM iteration: 26, Loglike: -159593.0551, Max-Change: 0.00599
EM iteration: 27, Loglike: -159592.7206, Max-Change: 0.005753
EM iteration: 28, Loglike: -159592.4000, Max-Change: 0.005522
EM iteration: 29, Loglike: -159592.0925, Max-Change: 0.005298
EM iteration: 30, Loglike: -159591.7975, Max-Change: 0.005081
EM iteration: 31, Loglike: -159591.5143, Max-Change: 0.004871
EM iteration: 32, Loglike: -159591.2423, Max-Change: 0.00467
EM iteration: 33, Loglike: -159590.9808, Max-Change: 0.004476
EM iteration: 34, Loglike: -159590.7295, Max-Change: 0.00429
EM iteration: 35, Loglike: -159590.4879, Max-Change: 0.004112
EM iteration: 36, Loglike: -159590.2553, Max-Change: 0.003942
EM iteration: 37, Loglike: -159590.0316, Max-Change: 0.003779
EM iteration: 38, Loglike: -159589.8161, Max-Change: 0.003624
EM iteration: 39, Loglike: -159589.6086, Max-Change: 0.003475
EM iteration: 40, Loglike: -159589.4087, Max-Change: 0.003333
EM iteration: 41, Loglike: -159589.2160, Max-Change: 0.003198
EM iteration: 42, Loglike: -159589.0303, Max-Change: 0.003068
EM iteration: 43, Loglike: -159588.8512, Max-Change: 0.002945
EM iteration: 44, Loglike: -159588.6785, Max-Change: 0.002827
EM iteration: 45, Loglike: -159588.5119, Max-Change: 0.002715
EM iteration: 46, Loglike: -159588.3511, Max-Change: 0.002607
EM iteration: 47, Loglike: -159588.1959, Max-Change: 0.002505
EM iteration: 48, Loglike: -159588.0460, Max-Change: 0.002407
EM iteration: 49, Loglike: -159587.9013, Max-Change: 0.002313
EM iteration: 50, Loglike: -159587.7616, Max-Change: 0.002228
EM iteration: 51, Loglike: -159587.6266, Max-Change: 0.002156
EM iteration: 52, Loglike: -159587.4961, Max-Change: 0.002086
EM iteration: 53, Loglike: -159587.3700, Max-Change: 0.002019
EM iteration: 54, Loglike: -159587.2481, Max-Change: 0.001955
EM iteration: 55, Loglike: -159587.1302, Max-Change: 0.001893
EM iteration: 56, Loglike: -159587.0163, Max-Change: 0.001833
EM iteration: 57, Loglike: -159586.9060, Max-Change: 0.001776
EM iteration: 58, Loglike: -159586.7993, Max-Change: 0.001721
EM iteration: 59, Loglike: -159586.6961, Max-Change: 0.001667
EM iteration: 60, Loglike: -159586.5962, Max-Change: 0.001616
EM iteration: 61, Loglike: -159586.4995, Max-Change: 0.001566
EM iteration: 62, Loglike: -159586.4058, Max-Change: 0.001519
EM iteration: 63, Loglike: -159586.3151, Max-Change: 0.001473
EM iteration: 64, Loglike: -159586.2272, Max-Change: 0.001429
EM iteration: 65, Loglike: -159586.1421, Max-Change: 0.001386
EM iteration: 66, Loglike: -159586.0596, Max-Change: 0.001358
EM iteration: 67, Loglike: -159585.9796, Max-Change: 0.001334
EM iteration: 68, Loglike: -159585.9021, Max-Change: 0.00131
EM iteration: 69, Loglike: -159585.8269, Max-Change: 0.001287
EM iteration: 70, Loglike: -159585.7540, Max-Change: 0.001264
EM iteration: 71, Loglike: -159585.6832, Max-Change: 0.001241
EM iteration: 72, Loglike: -159585.6146, Max-Change: 0.001219
EM iteration: 73, Loglike: -159585.5479, Max-Change: 0.001197
EM iteration: 74, Loglike: -159585.4832, Max-Change: 0.001175
EM iteration: 75, Loglike: -159585.4204, Max-Change: 0.001153
EM iteration: 76, Loglike: -159585.3593, Max-Change: 0.001132
EM iteration: 77, Loglike: -159585.3000, Max-Change: 0.001111
EM iteration: 78, Loglike: -159585.2424, Max-Change: 0.001091
EM iteration: 79, Loglike: -159585.1864, Max-Change: 0.00107
EM iteration: 80, Loglike: -159585.1319, Max-Change: 0.00105
EM iteration: 81, Loglike: -159585.0790, Max-Change: 0.001031
EM iteration: 82, Loglike: -159585.0274, Max-Change: 0.001011
EM iteration: 83, Loglike: -159584.9773, Max-Change: 0.000992
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 15.48 seconds.
# Summary of the estimation
summary(fit.1)
#>
#> Call:
#> est_mg(data = data, group.name = group.name, D = 1, model = model,
#> cats = cats, item.id = item.id, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), group.mean = 0, group.var = 1, EmpHist = TRUE,
#> Etol = 0.001, MaxE = 500)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 362
#> Number of fixed items:
#> Overall: 0
#> By group: 0(Group1), 0(Group2), 0(Group3)
#> Number of E-step cycles completed: 83
#> Maximum parameter change: 0.0009920582
#>
#> Processing time (in seconds)
#> EM algorithm: 14.57
#> Standard error computation: 0.2
#> Total computation: 15.48
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are satisfied.
#> Second-order test: Solution is a possible local maximum.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates is obtainable.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 319169.9
#> By group: 120347.958(Group1), 113944.899(Group2), 84877.056(Group3)
#>
#> Akaike Information Criterion (AIC): 319893.9
#> Bayesian Information Criterion (BIC): 322319.1
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 C1I1 2 3PLM 0.90 0.18 1.36 0.16 0.28 0.05 NA NA
#> 2 C1I2 2 3PLM 2.12 0.15 -0.99 0.10 0.18 0.06 NA NA
#> 3 C1I3 2 3PLM 1.05 0.12 0.61 0.13 0.18 0.05 NA NA
#> 4 C1I4 2 3PLM 1.08 0.13 -0.17 0.22 0.28 0.07 NA NA
#> 5 C1I5 2 3PLM 0.87 0.09 -0.15 0.22 0.18 0.07 NA NA
#> 6 C1I6 2 3PLM 1.91 0.13 0.60 0.04 0.09 0.02 NA NA
#> 7 C1I7 2 3PLM 1.10 0.13 1.10 0.09 0.15 0.03 NA NA
#> 8 C1I8 2 3PLM 0.94 0.12 0.89 0.14 0.16 0.05 NA NA
#> 9 C1I9 2 3PLM 0.89 0.12 0.63 0.18 0.21 0.06 NA NA
#> 10 C1I10 2 3PLM 1.49 0.12 0.13 0.08 0.15 0.04 NA NA
#> 11 G1I1 2 3PLM 0.96 0.11 -0.46 0.20 0.16 0.07 NA NA
#> 12 G1I2 2 3PLM 0.90 0.14 1.20 0.14 0.11 0.04 NA NA
#> 13 G1I3 2 3PLM 1.54 0.26 1.30 0.09 0.19 0.03 NA NA
#> 14 G1I4 2 3PLM 1.57 0.22 0.28 0.12 0.30 0.04 NA NA
#> 15 G1I5 2 3PLM 1.35 0.14 -0.17 0.13 0.16 0.05 NA NA
#> 16 G1I6 2 3PLM 2.17 0.18 0.02 0.06 0.09 0.03 NA NA
#> 17 G1I7 2 3PLM 1.47 0.16 -0.06 0.12 0.20 0.05 NA NA
#> 18 G1I8 2 3PLM 2.53 0.47 1.17 0.07 0.32 0.02 NA NA
#> 19 G1I9 2 3PLM 2.40 0.27 -0.93 0.11 0.24 0.06 NA NA
#> 20 G1I10 2 3PLM 1.26 0.13 -1.76 0.23 0.23 0.10 NA NA
#> 21 G1I11 2 3PLM 1.55 0.15 -1.11 0.16 0.21 0.08 NA NA
#> 22 G1I12 2 3PLM 0.76 0.09 -0.80 0.31 0.20 0.08 NA NA
#> 23 G1I13 2 3PLM 1.05 0.14 -0.12 0.21 0.21 0.07 NA NA
#> 24 G1I14 2 3PLM 1.51 0.38 1.74 0.15 0.30 0.02 NA NA
#> 25 G1I15 2 3PLM 0.87 0.10 -1.43 0.30 0.21 0.09 NA NA
#> 26 G1I16 2 3PLM 1.05 0.11 -1.94 0.27 0.23 0.10 NA NA
#> 27 G1I17 2 3PLM 1.06 0.13 0.26 0.15 0.16 0.05 NA NA
#> 28 G1I18 2 3PLM 2.11 0.21 -0.08 0.08 0.24 0.04 NA NA
#> 29 G1I19 2 3PLM 1.32 0.13 -1.39 0.19 0.20 0.08 NA NA
#> 30 G1I20 2 3PLM 1.03 0.18 0.52 0.19 0.23 0.06 NA NA
#> 31 G1I21 2 3PLM 0.92 0.13 0.76 0.15 0.13 0.05 NA NA
#> 32 G1I22 2 3PLM 1.79 0.22 -0.63 0.16 0.36 0.06 NA NA
#> 33 G1I23 2 3PLM 1.31 0.15 -1.16 0.23 0.26 0.09 NA NA
#> 34 G1I24 2 3PLM 1.66 0.20 0.32 0.09 0.23 0.04 NA NA
#> 35 G1I25 2 3PLM 1.60 0.18 -0.12 0.12 0.25 0.05 NA NA
#> 36 G1I26 2 3PLM 1.91 0.26 0.66 0.08 0.25 0.03 NA NA
#> 37 G1I27 2 3PLM 1.62 0.18 -1.55 0.20 0.27 0.10 NA NA
#> 38 G1I28 2 3PLM 1.35 0.17 0.57 0.10 0.15 0.04 NA NA
#> 39 G1I29 2 3PLM 0.92 0.09 -0.37 0.17 0.12 0.06 NA NA
#> 40 G1I30 2 3PLM 1.06 0.29 2.24 0.25 0.17 0.03 NA NA
#> 41 G1I31 2 3PLM 2.45 0.49 1.62 0.09 0.18 0.01 NA NA
#> 42 G1I32 2 3PLM 1.11 0.12 -0.07 0.15 0.15 0.05 NA NA
#> 43 G1I33 2 3PLM 1.62 0.18 0.18 0.09 0.16 0.04 NA NA
#> 44 G1I34 2 3PLM 1.34 0.14 0.24 0.09 0.11 0.04 NA NA
#> 45 G1I35 2 3PLM 1.35 0.17 1.28 0.08 0.07 0.02 NA NA
#> 46 G1I36 2 3PLM 1.44 0.15 -1.23 0.19 0.22 0.09 NA NA
#> 47 G1I37 2 3PLM 1.06 0.15 -0.58 0.27 0.27 0.09 NA NA
#> 48 G1I38 5 GRM 1.06 0.06 -0.37 0.05 0.21 0.05 0.86 0.06
#> 49 C1I11 5 GRM 1.19 0.05 -2.21 0.09 -1.45 0.07 -0.75 0.05
#> 50 C1I12 5 GRM 0.91 0.04 -0.69 0.06 0.03 0.04 0.68 0.04
#> 51 G2I1 2 3PLM 1.76 0.19 -0.86 0.18 0.24 0.10 NA NA
#> 52 G2I2 2 3PLM 0.84 0.11 -0.44 0.31 0.21 0.09 NA NA
#> 53 G2I3 2 3PLM 1.09 0.14 0.09 0.20 0.18 0.08 NA NA
#> 54 G2I4 2 3PLM 1.51 0.29 1.45 0.09 0.18 0.04 NA NA
#> 55 G2I5 2 3PLM 0.71 0.10 -1.66 0.40 0.20 0.09 NA NA
#> 56 G2I6 2 3PLM 1.09 0.15 -1.60 0.30 0.22 0.10 NA NA
#> 57 G2I7 2 3PLM 1.33 0.14 0.26 0.12 0.13 0.05 NA NA
#> 58 G2I8 2 3PLM 2.22 0.19 -0.09 0.08 0.14 0.05 NA NA
#> 59 G2I9 2 3PLM 1.08 0.13 -1.56 0.28 0.21 0.09 NA NA
#> 60 G2I10 2 3PLM 1.65 0.28 0.88 0.11 0.29 0.05 NA NA
#> 61 G2I11 2 3PLM 0.96 0.13 0.86 0.14 0.11 0.05 NA NA
#> 62 G2I12 2 3PLM 1.68 0.19 -0.68 0.19 0.26 0.10 NA NA
#> 63 G2I13 2 3PLM 1.17 0.13 -1.30 0.24 0.21 0.09 NA NA
#> 64 G2I14 2 3PLM 1.43 0.14 0.22 0.11 0.13 0.05 NA NA
#> 65 G2I15 2 3PLM 1.58 0.21 0.05 0.17 0.27 0.08 NA NA
#> 66 G2I16 2 3PLM 1.77 0.24 0.74 0.09 0.22 0.05 NA NA
#> 67 G2I17 2 3PLM 2.11 0.22 -1.21 0.15 0.20 0.09 NA NA
#> 68 G2I18 2 3PLM 1.79 0.21 0.63 0.08 0.14 0.04 NA NA
#> 69 G2I19 2 3PLM 1.12 0.15 0.05 0.22 0.21 0.08 NA NA
#> 70 G2I20 2 3PLM 1.70 0.47 2.16 0.18 0.16 0.02 NA NA
#> 71 G2I21 2 3PLM 2.49 0.38 1.53 0.06 0.12 0.02 NA NA
#> 72 G2I22 2 3PLM 1.50 0.19 0.24 0.15 0.22 0.07 NA NA
#> 73 G2I23 2 3PLM 2.19 0.28 0.45 0.09 0.28 0.05 NA NA
#> 74 G2I24 2 3PLM 1.43 0.12 0.36 0.07 0.07 0.03 NA NA
#> 75 G2I25 2 3PLM 1.80 0.23 1.37 0.06 0.07 0.02 NA NA
#> 76 G2I26 2 3PLM 1.90 0.20 -0.88 0.17 0.25 0.10 NA NA
#> 77 G2I27 2 3PLM 0.99 0.12 -0.58 0.25 0.20 0.09 NA NA
#> 78 G2I28 5 GRM 1.14 0.07 -0.37 0.07 0.14 0.05 0.78 0.05
#> 79 C2I1 2 3PLM 1.07 0.08 -0.29 0.11 0.13 0.04 NA NA
#> 80 C2I2 2 3PLM 1.00 0.09 1.23 0.07 0.06 0.02 NA NA
#> 81 C2I3 2 3PLM 1.63 0.16 1.37 0.05 0.13 0.01 NA NA
#> 82 C2I4 2 3PLM 1.55 0.11 0.24 0.06 0.18 0.02 NA NA
#> 83 C2I5 2 3PLM 1.43 0.10 -0.07 0.07 0.12 0.03 NA NA
#> 84 C2I6 2 3PLM 2.04 0.10 -0.06 0.04 0.05 0.01 NA NA
#> 85 C2I7 2 3PLM 1.56 0.11 0.00 0.07 0.18 0.02 NA NA
#> 86 C2I8 2 3PLM 1.53 0.15 1.27 0.06 0.19 0.02 NA NA
#> 87 C2I9 2 3PLM 2.17 0.13 -1.01 0.07 0.14 0.03 NA NA
#> 88 C2I10 2 3PLM 1.58 0.12 -1.35 0.14 0.26 0.05 NA NA
#> 89 G3I1 2 3PLM 1.52 0.14 -1.10 0.13 0.16 0.05 NA NA
#> 90 G3I2 2 3PLM 0.77 0.10 -0.60 0.27 0.19 0.07 NA NA
#> 91 G3I3 2 3PLM 1.15 0.12 0.08 0.12 0.17 0.03 NA NA
#> 92 G3I4 2 3PLM 1.31 0.24 1.71 0.12 0.22 0.02 NA NA
#> 93 G3I5 2 3PLM 0.79 0.11 -1.00 0.36 0.29 0.08 NA NA
#> 94 G3I6 2 3PLM 1.18 0.15 -1.30 0.25 0.33 0.07 NA NA
#> 95 G3I7 2 3PLM 1.37 0.13 0.26 0.09 0.14 0.03 NA NA
#> 96 G3I8 2 3PLM 1.92 0.18 -0.08 0.07 0.15 0.02 NA NA
#> 97 G3I9 2 3PLM 1.13 0.12 -1.20 0.21 0.21 0.06 NA NA
#> 98 G3I10 2 3PLM 1.51 0.21 0.97 0.09 0.29 0.02 NA NA
#> 99 G3I11 2 3PLM 0.90 0.10 0.80 0.11 0.08 0.03 NA NA
#> 100 G3I12 2 3PLM 1.42 0.17 -0.78 0.15 0.26 0.05 NA NA
#> 101 G3I13 2 3PLM 1.11 0.13 -1.10 0.22 0.24 0.06 NA NA
#> 102 G3I14 2 3PLM 1.38 0.14 0.30 0.09 0.17 0.03 NA NA
#> 103 G3I15 2 3PLM 1.29 0.13 -0.06 0.11 0.19 0.03 NA NA
#> 104 G3I16 2 3PLM 1.58 0.18 0.74 0.08 0.20 0.02 NA NA
#> 105 G3I17 2 3PLM 1.61 0.16 -1.55 0.15 0.19 0.06 NA NA
#> 106 G3I18 2 3PLM 1.38 0.14 0.71 0.08 0.12 0.02 NA NA
#> 107 G3I19 2 3PLM 0.99 0.11 0.09 0.14 0.17 0.04 NA NA
#> 108 G3I20 2 3PLM 1.16 0.24 2.27 0.20 0.12 0.02 NA NA
#> 109 G3I21 2 3PLM 3.06 0.57 1.63 0.06 0.14 0.01 NA NA
#> 110 G3I22 2 3PLM 1.17 0.11 0.09 0.10 0.10 0.03 NA NA
#> 111 G3I23 2 3PLM 1.79 0.17 0.32 0.06 0.15 0.02 NA NA
#> 112 G3I24 2 3PLM 1.13 0.09 0.32 0.08 0.05 0.02 NA NA
#> 113 G3I25 2 3PLM 1.38 0.15 1.35 0.08 0.05 0.01 NA NA
#> 114 G3I26 2 3PLM 1.66 0.17 -1.00 0.12 0.22 0.04 NA NA
#> 115 G3I27 2 3PLM 0.92 0.10 -0.62 0.21 0.18 0.06 NA NA
#> 116 G3I28 5 GRM 0.94 0.05 -0.38 0.06 0.15 0.06 0.81 0.07
#> par.5 se.5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 NA NA
#> 5 NA NA
#> 6 NA NA
#> 7 NA NA
#> 8 NA NA
#> 9 NA NA
#> 10 NA NA
#> 11 NA NA
#> 12 NA NA
#> 13 NA NA
#> 14 NA NA
#> 15 NA NA
#> 16 NA NA
#> 17 NA NA
#> 18 NA NA
#> 19 NA NA
#> 20 NA NA
#> 21 NA NA
#> 22 NA NA
#> 23 NA NA
#> 24 NA NA
#> 25 NA NA
#> 26 NA NA
#> 27 NA NA
#> 28 NA NA
#> 29 NA NA
#> 30 NA NA
#> 31 NA NA
#> 32 NA NA
#> 33 NA NA
#> 34 NA NA
#> 35 NA NA
#> 36 NA NA
#> 37 NA NA
#> 38 NA NA
#> 39 NA NA
#> 40 NA NA
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 1.42 0.08
#> 49 -0.12 0.03
#> 50 1.25 0.06
#> 51 NA NA
#> 52 NA NA
#> 53 NA NA
#> 54 NA NA
#> 55 NA NA
#> 56 NA NA
#> 57 NA NA
#> 58 NA NA
#> 59 NA NA
#> 60 NA NA
#> 61 NA NA
#> 62 NA NA
#> 63 NA NA
#> 64 NA NA
#> 65 NA NA
#> 66 NA NA
#> 67 NA NA
#> 68 NA NA
#> 69 NA NA
#> 70 NA NA
#> 71 NA NA
#> 72 NA NA
#> 73 NA NA
#> 74 NA NA
#> 75 NA NA
#> 76 NA NA
#> 77 NA NA
#> 78 1.44 0.07
#> 79 NA NA
#> 80 NA NA
#> 81 NA NA
#> 82 NA NA
#> 83 NA NA
#> 84 NA NA
#> 85 NA NA
#> 86 NA NA
#> 87 NA NA
#> 88 NA NA
#> 89 NA NA
#> 90 NA NA
#> 91 NA NA
#> 92 NA NA
#> 93 NA NA
#> 94 NA NA
#> 95 NA NA
#> 96 NA NA
#> 97 NA NA
#> 98 NA NA
#> 99 NA NA
#> 100 NA NA
#> 101 NA NA
#> 102 NA NA
#> 103 NA NA
#> 104 NA NA
#> 105 NA NA
#> 106 NA NA
#> 107 NA NA
#> 108 NA NA
#> 109 NA NA
#> 110 NA NA
#> 111 NA NA
#> 112 NA NA
#> 113 NA NA
#> 114 NA NA
#> 115 NA NA
#> 116 1.55 0.09
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) 0.00 1.00 1.00
#> se(Group1) NA NA NA
#> estimate(Group2) 0.49 0.56 0.75
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.37 1.95 1.40
#> se(Group3) 0.03 0.06 0.02
#>
# Extract the item parameter estimates
getirt(fit.1, what = "par.est")
#> $overall
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.9002993 1.3630996576 0.27971247 NA NA
#> 2 C1I2 2 3PLM 2.1246417 -0.9940070191 0.18249617 NA NA
#> 3 C1I3 2 3PLM 1.0541278 0.6086911591 0.18187156 NA NA
#> 4 C1I4 2 3PLM 1.0789640 -0.1731865978 0.28172552 NA NA
#> 5 C1I5 2 3PLM 0.8731636 -0.1539491078 0.18023951 NA NA
#> 6 C1I6 2 3PLM 1.9100015 0.5956052553 0.08680994 NA NA
#> 7 C1I7 2 3PLM 1.1042207 1.1038327947 0.15045515 NA NA
#> 8 C1I8 2 3PLM 0.9407054 0.8862776984 0.15890193 NA NA
#> 9 C1I9 2 3PLM 0.8926878 0.6255808127 0.20799520 NA NA
#> 10 C1I10 2 3PLM 1.4872042 0.1323954152 0.15372172 NA NA
#> 11 G1I1 2 3PLM 0.9648995 -0.4558711256 0.15992372 NA NA
#> 12 G1I2 2 3PLM 0.8982317 1.2036385734 0.10668307 NA NA
#> 13 G1I3 2 3PLM 1.5352805 1.2976450244 0.18624929 NA NA
#> 14 G1I4 2 3PLM 1.5653523 0.2810572501 0.30326526 NA NA
#> 15 G1I5 2 3PLM 1.3511034 -0.1735122324 0.16083579 NA NA
#> 16 G1I6 2 3PLM 2.1741319 0.0170068932 0.08620387 NA NA
#> 17 G1I7 2 3PLM 1.4655950 -0.0639529914 0.20160863 NA NA
#> 18 G1I8 2 3PLM 2.5274624 1.1707732480 0.32453925 NA NA
#> 19 G1I9 2 3PLM 2.3986360 -0.9296897943 0.24418284 NA NA
#> 20 G1I10 2 3PLM 1.2585300 -1.7572134104 0.23391662 NA NA
#> 21 G1I11 2 3PLM 1.5470937 -1.1118172631 0.20751568 NA NA
#> 22 G1I12 2 3PLM 0.7556135 -0.8038513481 0.19656034 NA NA
#> 23 G1I13 2 3PLM 1.0527888 -0.1185472914 0.20738601 NA NA
#> 24 G1I14 2 3PLM 1.5102932 1.7406214138 0.29709350 NA NA
#> 25 G1I15 2 3PLM 0.8664971 -1.4323893987 0.21465862 NA NA
#> 26 G1I16 2 3PLM 1.0542506 -1.9446624563 0.22812622 NA NA
#> 27 G1I17 2 3PLM 1.0571687 0.2574260233 0.15670798 NA NA
#> 28 G1I18 2 3PLM 2.1077524 -0.0802270386 0.24053595 NA NA
#> 29 G1I19 2 3PLM 1.3243225 -1.3873897669 0.20073972 NA NA
#> 30 G1I20 2 3PLM 1.0303144 0.5198099412 0.22883325 NA NA
#> 31 G1I21 2 3PLM 0.9230319 0.7599364214 0.13215608 NA NA
#> 32 G1I22 2 3PLM 1.7870120 -0.6306797460 0.36010326 NA NA
#> 33 G1I23 2 3PLM 1.3094006 -1.1637343305 0.25562388 NA NA
#> 34 G1I24 2 3PLM 1.6645514 0.3233691790 0.23193826 NA NA
#> 35 G1I25 2 3PLM 1.5989408 -0.1175965323 0.25385326 NA NA
#> 36 G1I26 2 3PLM 1.9085326 0.6574101909 0.25475783 NA NA
#> 37 G1I27 2 3PLM 1.6232889 -1.5482047548 0.26787427 NA NA
#> 38 G1I28 2 3PLM 1.3497743 0.5653525105 0.15089732 NA NA
#> 39 G1I29 2 3PLM 0.9229732 -0.3681170374 0.12451485 NA NA
#> 40 G1I30 2 3PLM 1.0636199 2.2379302348 0.17259660 NA NA
#> 41 G1I31 2 3PLM 2.4508248 1.6191425518 0.18202915 NA NA
#> 42 G1I32 2 3PLM 1.1137113 -0.0722062408 0.14770787 NA NA
#> 43 G1I33 2 3PLM 1.6242308 0.1841468639 0.16019712 NA NA
#> 44 G1I34 2 3PLM 1.3396394 0.2438713584 0.10954369 NA NA
#> 45 G1I35 2 3PLM 1.3498016 1.2826823306 0.06760955 NA NA
#> 46 G1I36 2 3PLM 1.4377572 -1.2263600168 0.22297804 NA NA
#> 47 G1I37 2 3PLM 1.0646367 -0.5799937856 0.27097889 NA NA
#> 48 G1I38 5 GRM 1.0649768 -0.3653605941 0.21365349 0.8571501 1.4220840
#> 49 C1I11 5 GRM 1.1892683 -2.2080814019 -1.44963215 -0.7471002 -0.1188008
#> 50 C1I12 5 GRM 0.9141155 -0.6885203551 0.02631147 0.6789189 1.2487151
#> 51 G2I1 2 3PLM 1.7609541 -0.8578505772 0.24035894 NA NA
#> 52 G2I2 2 3PLM 0.8436960 -0.4382789597 0.21438678 NA NA
#> 53 G2I3 2 3PLM 1.0886052 0.0911696948 0.18458253 NA NA
#> 54 G2I4 2 3PLM 1.5129142 1.4502930939 0.18027120 NA NA
#> 55 G2I5 2 3PLM 0.7139700 -1.6581797024 0.19781812 NA NA
#> 56 G2I6 2 3PLM 1.0919249 -1.5999033276 0.21671254 NA NA
#> 57 G2I7 2 3PLM 1.3325688 0.2633001080 0.13036039 NA NA
#> 58 G2I8 2 3PLM 2.2199875 -0.0891740329 0.13780823 NA NA
#> 59 G2I9 2 3PLM 1.0832071 -1.5619697271 0.20682223 NA NA
#> 60 G2I10 2 3PLM 1.6525972 0.8838581722 0.29075920 NA NA
#> 61 G2I11 2 3PLM 0.9630202 0.8571579301 0.11294805 NA NA
#> 62 G2I12 2 3PLM 1.6845080 -0.6793797278 0.25993819 NA NA
#> 63 G2I13 2 3PLM 1.1744864 -1.3046157584 0.20979661 NA NA
#> 64 G2I14 2 3PLM 1.4329862 0.2158522635 0.12986846 NA NA
#> 65 G2I15 2 3PLM 1.5763766 0.0515443553 0.27114790 NA NA
#> 66 G2I16 2 3PLM 1.7692947 0.7418363902 0.21979684 NA NA
#> 67 G2I17 2 3PLM 2.1059175 -1.2085830261 0.20089939 NA NA
#> 68 G2I18 2 3PLM 1.7861465 0.6306602725 0.14248762 NA NA
#> 69 G2I19 2 3PLM 1.1236963 0.0462753631 0.21071941 NA NA
#> 70 G2I20 2 3PLM 1.6957930 2.1576947264 0.16005055 NA NA
#> 71 G2I21 2 3PLM 2.4882719 1.5329597738 0.11756098 NA NA
#> 72 G2I22 2 3PLM 1.4964966 0.2397808194 0.21725633 NA NA
#> 73 G2I23 2 3PLM 2.1906673 0.4452744274 0.28388427 NA NA
#> 74 G2I24 2 3PLM 1.4315517 0.3567207426 0.07277537 NA NA
#> 75 G2I25 2 3PLM 1.8049099 1.3706377058 0.07249339 NA NA
#> 76 G2I26 2 3PLM 1.8993430 -0.8763222592 0.24753546 NA NA
#> 77 G2I27 2 3PLM 0.9922602 -0.5809395819 0.20058057 NA NA
#> 78 G2I28 5 GRM 1.1428941 -0.3726286563 0.13986303 0.7760909 1.4399545
#> 79 C2I1 2 3PLM 1.0724788 -0.2925185566 0.12706645 NA NA
#> 80 C2I2 2 3PLM 1.0026458 1.2329410898 0.06038371 NA NA
#> 81 C2I3 2 3PLM 1.6298126 1.3717691197 0.12593191 NA NA
#> 82 C2I4 2 3PLM 1.5539481 0.2386833730 0.18401402 NA NA
#> 83 C2I5 2 3PLM 1.4284843 -0.0690446133 0.11886473 NA NA
#> 84 C2I6 2 3PLM 2.0356386 -0.0609918393 0.04627366 NA NA
#> 85 C2I7 2 3PLM 1.5601571 0.0009650233 0.17678863 NA NA
#> 86 C2I8 2 3PLM 1.5324423 1.2675649742 0.18822170 NA NA
#> 87 C2I9 2 3PLM 2.1652174 -1.0147828257 0.14241930 NA NA
#> 88 C2I10 2 3PLM 1.5756487 -1.3546338577 0.26239714 NA NA
#> 89 G3I1 2 3PLM 1.5177028 -1.1012930873 0.16029848 NA NA
#> 90 G3I2 2 3PLM 0.7684745 -0.5958229704 0.19239503 NA NA
#> 91 G3I3 2 3PLM 1.1511024 0.0760256821 0.16953254 NA NA
#> 92 G3I4 2 3PLM 1.3078975 1.7075770992 0.22441977 NA NA
#> 93 G3I5 2 3PLM 0.7934450 -1.0028686375 0.28801113 NA NA
#> 94 G3I6 2 3PLM 1.1835586 -1.2995355425 0.32753494 NA NA
#> 95 G3I7 2 3PLM 1.3696476 0.2557793125 0.14270858 NA NA
#> 96 G3I8 2 3PLM 1.9236418 -0.0843458754 0.14793716 NA NA
#> 97 G3I9 2 3PLM 1.1300723 -1.1978738763 0.21206463 NA NA
#> 98 G3I10 2 3PLM 1.5126694 0.9703312346 0.29033962 NA NA
#> 99 G3I11 2 3PLM 0.9021794 0.7968831684 0.08388012 NA NA
#> 100 G3I12 2 3PLM 1.4214420 -0.7766765567 0.25975672 NA NA
#> 101 G3I13 2 3PLM 1.1082496 -1.0983147685 0.23504140 NA NA
#> 102 G3I14 2 3PLM 1.3797649 0.3022772312 0.16690037 NA NA
#> 103 G3I15 2 3PLM 1.2876135 -0.0573943526 0.19245588 NA NA
#> 104 G3I16 2 3PLM 1.5824294 0.7372872340 0.20217816 NA NA
#> 105 G3I17 2 3PLM 1.6058953 -1.5522762073 0.18645088 NA NA
#> 106 G3I18 2 3PLM 1.3800007 0.7080448815 0.11881653 NA NA
#> 107 G3I19 2 3PLM 0.9933705 0.0911167343 0.16557109 NA NA
#> 108 G3I20 2 3PLM 1.1645170 2.2678742087 0.11821851 NA NA
#> 109 G3I21 2 3PLM 3.0616274 1.6301700618 0.14040136 NA NA
#> 110 G3I22 2 3PLM 1.1712500 0.0856353360 0.10276551 NA NA
#> 111 G3I23 2 3PLM 1.7915979 0.3172563764 0.15045425 NA NA
#> 112 G3I24 2 3PLM 1.1259988 0.3187456984 0.05486984 NA NA
#> 113 G3I25 2 3PLM 1.3848088 1.3476897615 0.05145709 NA NA
#> 114 G3I26 2 3PLM 1.6627860 -0.9983631680 0.21786458 NA NA
#> 115 G3I27 2 3PLM 0.9242740 -0.6199576215 0.18433956 NA NA
#> 116 G3I28 5 GRM 0.9426521 -0.3795334512 0.14801722 0.8117698 1.5515925
#>
#> $group
#> $group$Group1
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.9002993 1.36309966 0.27971247 NA NA
#> 2 C1I2 2 3PLM 2.1246417 -0.99400702 0.18249617 NA NA
#> 3 C1I3 2 3PLM 1.0541278 0.60869116 0.18187156 NA NA
#> 4 C1I4 2 3PLM 1.0789640 -0.17318660 0.28172552 NA NA
#> 5 C1I5 2 3PLM 0.8731636 -0.15394911 0.18023951 NA NA
#> 6 C1I6 2 3PLM 1.9100015 0.59560526 0.08680994 NA NA
#> 7 C1I7 2 3PLM 1.1042207 1.10383279 0.15045515 NA NA
#> 8 C1I8 2 3PLM 0.9407054 0.88627770 0.15890193 NA NA
#> 9 C1I9 2 3PLM 0.8926878 0.62558081 0.20799520 NA NA
#> 10 C1I10 2 3PLM 1.4872042 0.13239542 0.15372172 NA NA
#> 11 G1I1 2 3PLM 0.9648995 -0.45587113 0.15992372 NA NA
#> 12 G1I2 2 3PLM 0.8982317 1.20363857 0.10668307 NA NA
#> 13 G1I3 2 3PLM 1.5352805 1.29764502 0.18624929 NA NA
#> 14 G1I4 2 3PLM 1.5653523 0.28105725 0.30326526 NA NA
#> 15 G1I5 2 3PLM 1.3511034 -0.17351223 0.16083579 NA NA
#> 16 G1I6 2 3PLM 2.1741319 0.01700689 0.08620387 NA NA
#> 17 G1I7 2 3PLM 1.4655950 -0.06395299 0.20160863 NA NA
#> 18 G1I8 2 3PLM 2.5274624 1.17077325 0.32453925 NA NA
#> 19 G1I9 2 3PLM 2.3986360 -0.92968979 0.24418284 NA NA
#> 20 G1I10 2 3PLM 1.2585300 -1.75721341 0.23391662 NA NA
#> 21 G1I11 2 3PLM 1.5470937 -1.11181726 0.20751568 NA NA
#> 22 G1I12 2 3PLM 0.7556135 -0.80385135 0.19656034 NA NA
#> 23 G1I13 2 3PLM 1.0527888 -0.11854729 0.20738601 NA NA
#> 24 G1I14 2 3PLM 1.5102932 1.74062141 0.29709350 NA NA
#> 25 G1I15 2 3PLM 0.8664971 -1.43238940 0.21465862 NA NA
#> 26 G1I16 2 3PLM 1.0542506 -1.94466246 0.22812622 NA NA
#> 27 G1I17 2 3PLM 1.0571687 0.25742602 0.15670798 NA NA
#> 28 G1I18 2 3PLM 2.1077524 -0.08022704 0.24053595 NA NA
#> 29 G1I19 2 3PLM 1.3243225 -1.38738977 0.20073972 NA NA
#> 30 G1I20 2 3PLM 1.0303144 0.51980994 0.22883325 NA NA
#> 31 G1I21 2 3PLM 0.9230319 0.75993642 0.13215608 NA NA
#> 32 G1I22 2 3PLM 1.7870120 -0.63067975 0.36010326 NA NA
#> 33 G1I23 2 3PLM 1.3094006 -1.16373433 0.25562388 NA NA
#> 34 G1I24 2 3PLM 1.6645514 0.32336918 0.23193826 NA NA
#> 35 G1I25 2 3PLM 1.5989408 -0.11759653 0.25385326 NA NA
#> 36 G1I26 2 3PLM 1.9085326 0.65741019 0.25475783 NA NA
#> 37 G1I27 2 3PLM 1.6232889 -1.54820475 0.26787427 NA NA
#> 38 G1I28 2 3PLM 1.3497743 0.56535251 0.15089732 NA NA
#> 39 G1I29 2 3PLM 0.9229732 -0.36811704 0.12451485 NA NA
#> 40 G1I30 2 3PLM 1.0636199 2.23793023 0.17259660 NA NA
#> 41 G1I31 2 3PLM 2.4508248 1.61914255 0.18202915 NA NA
#> 42 G1I32 2 3PLM 1.1137113 -0.07220624 0.14770787 NA NA
#> 43 G1I33 2 3PLM 1.6242308 0.18414686 0.16019712 NA NA
#> 44 G1I34 2 3PLM 1.3396394 0.24387136 0.10954369 NA NA
#> 45 G1I35 2 3PLM 1.3498016 1.28268233 0.06760955 NA NA
#> 46 G1I36 2 3PLM 1.4377572 -1.22636002 0.22297804 NA NA
#> 47 G1I37 2 3PLM 1.0646367 -0.57999379 0.27097889 NA NA
#> 48 G1I38 5 GRM 1.0649768 -0.36536059 0.21365349 0.8571501 1.4220840
#> 49 C1I11 5 GRM 1.1892683 -2.20808140 -1.44963215 -0.7471002 -0.1188008
#> 50 C1I12 5 GRM 0.9141155 -0.68852036 0.02631147 0.6789189 1.2487151
#>
#> $group$Group2
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.9002993 1.3630996576 0.27971247 NA NA
#> 2 C1I2 2 3PLM 2.1246417 -0.9940070191 0.18249617 NA NA
#> 3 C1I3 2 3PLM 1.0541278 0.6086911591 0.18187156 NA NA
#> 4 C1I4 2 3PLM 1.0789640 -0.1731865978 0.28172552 NA NA
#> 5 C1I5 2 3PLM 0.8731636 -0.1539491078 0.18023951 NA NA
#> 6 C1I6 2 3PLM 1.9100015 0.5956052553 0.08680994 NA NA
#> 7 C1I7 2 3PLM 1.1042207 1.1038327947 0.15045515 NA NA
#> 8 C1I8 2 3PLM 0.9407054 0.8862776984 0.15890193 NA NA
#> 9 C1I9 2 3PLM 0.8926878 0.6255808127 0.20799520 NA NA
#> 10 C1I10 2 3PLM 1.4872042 0.1323954152 0.15372172 NA NA
#> 11 C1I11 5 GRM 1.1892683 -2.2080814019 -1.44963215 -0.7471002 -0.1188008
#> 12 C1I12 5 GRM 0.9141155 -0.6885203551 0.02631147 0.6789189 1.2487151
#> 13 G2I1 2 3PLM 1.7609541 -0.8578505772 0.24035894 NA NA
#> 14 G2I2 2 3PLM 0.8436960 -0.4382789597 0.21438678 NA NA
#> 15 G2I3 2 3PLM 1.0886052 0.0911696948 0.18458253 NA NA
#> 16 G2I4 2 3PLM 1.5129142 1.4502930939 0.18027120 NA NA
#> 17 G2I5 2 3PLM 0.7139700 -1.6581797024 0.19781812 NA NA
#> 18 G2I6 2 3PLM 1.0919249 -1.5999033276 0.21671254 NA NA
#> 19 G2I7 2 3PLM 1.3325688 0.2633001080 0.13036039 NA NA
#> 20 G2I8 2 3PLM 2.2199875 -0.0891740329 0.13780823 NA NA
#> 21 G2I9 2 3PLM 1.0832071 -1.5619697271 0.20682223 NA NA
#> 22 G2I10 2 3PLM 1.6525972 0.8838581722 0.29075920 NA NA
#> 23 G2I11 2 3PLM 0.9630202 0.8571579301 0.11294805 NA NA
#> 24 G2I12 2 3PLM 1.6845080 -0.6793797278 0.25993819 NA NA
#> 25 G2I13 2 3PLM 1.1744864 -1.3046157584 0.20979661 NA NA
#> 26 G2I14 2 3PLM 1.4329862 0.2158522635 0.12986846 NA NA
#> 27 G2I15 2 3PLM 1.5763766 0.0515443553 0.27114790 NA NA
#> 28 G2I16 2 3PLM 1.7692947 0.7418363902 0.21979684 NA NA
#> 29 G2I17 2 3PLM 2.1059175 -1.2085830261 0.20089939 NA NA
#> 30 G2I18 2 3PLM 1.7861465 0.6306602725 0.14248762 NA NA
#> 31 G2I19 2 3PLM 1.1236963 0.0462753631 0.21071941 NA NA
#> 32 G2I20 2 3PLM 1.6957930 2.1576947264 0.16005055 NA NA
#> 33 G2I21 2 3PLM 2.4882719 1.5329597738 0.11756098 NA NA
#> 34 G2I22 2 3PLM 1.4964966 0.2397808194 0.21725633 NA NA
#> 35 G2I23 2 3PLM 2.1906673 0.4452744274 0.28388427 NA NA
#> 36 G2I24 2 3PLM 1.4315517 0.3567207426 0.07277537 NA NA
#> 37 G2I25 2 3PLM 1.8049099 1.3706377058 0.07249339 NA NA
#> 38 G2I26 2 3PLM 1.8993430 -0.8763222592 0.24753546 NA NA
#> 39 G2I27 2 3PLM 0.9922602 -0.5809395819 0.20058057 NA NA
#> 40 G2I28 5 GRM 1.1428941 -0.3726286563 0.13986303 0.7760909 1.4399545
#> 41 C2I1 2 3PLM 1.0724788 -0.2925185566 0.12706645 NA NA
#> 42 C2I2 2 3PLM 1.0026458 1.2329410898 0.06038371 NA NA
#> 43 C2I3 2 3PLM 1.6298126 1.3717691197 0.12593191 NA NA
#> 44 C2I4 2 3PLM 1.5539481 0.2386833730 0.18401402 NA NA
#> 45 C2I5 2 3PLM 1.4284843 -0.0690446133 0.11886473 NA NA
#> 46 C2I6 2 3PLM 2.0356386 -0.0609918393 0.04627366 NA NA
#> 47 C2I7 2 3PLM 1.5601571 0.0009650233 0.17678863 NA NA
#> 48 C2I8 2 3PLM 1.5324423 1.2675649742 0.18822170 NA NA
#> 49 C2I9 2 3PLM 2.1652174 -1.0147828257 0.14241930 NA NA
#> 50 C2I10 2 3PLM 1.5756487 -1.3546338577 0.26239714 NA NA
#>
#> $group$Group3
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C2I1 2 3PLM 1.0724788 -0.2925185566 0.12706645 NA NA
#> 2 C2I2 2 3PLM 1.0026458 1.2329410898 0.06038371 NA NA
#> 3 C2I3 2 3PLM 1.6298126 1.3717691197 0.12593191 NA NA
#> 4 C2I4 2 3PLM 1.5539481 0.2386833730 0.18401402 NA NA
#> 5 C2I5 2 3PLM 1.4284843 -0.0690446133 0.11886473 NA NA
#> 6 C2I6 2 3PLM 2.0356386 -0.0609918393 0.04627366 NA NA
#> 7 C2I7 2 3PLM 1.5601571 0.0009650233 0.17678863 NA NA
#> 8 C2I8 2 3PLM 1.5324423 1.2675649742 0.18822170 NA NA
#> 9 C2I9 2 3PLM 2.1652174 -1.0147828257 0.14241930 NA NA
#> 10 C2I10 2 3PLM 1.5756487 -1.3546338577 0.26239714 NA NA
#> 11 G3I1 2 3PLM 1.5177028 -1.1012930873 0.16029848 NA NA
#> 12 G3I2 2 3PLM 0.7684745 -0.5958229704 0.19239503 NA NA
#> 13 G3I3 2 3PLM 1.1511024 0.0760256821 0.16953254 NA NA
#> 14 G3I4 2 3PLM 1.3078975 1.7075770992 0.22441977 NA NA
#> 15 G3I5 2 3PLM 0.7934450 -1.0028686375 0.28801113 NA NA
#> 16 G3I6 2 3PLM 1.1835586 -1.2995355425 0.32753494 NA NA
#> 17 G3I7 2 3PLM 1.3696476 0.2557793125 0.14270858 NA NA
#> 18 G3I8 2 3PLM 1.9236418 -0.0843458754 0.14793716 NA NA
#> 19 G3I9 2 3PLM 1.1300723 -1.1978738763 0.21206463 NA NA
#> 20 G3I10 2 3PLM 1.5126694 0.9703312346 0.29033962 NA NA
#> 21 G3I11 2 3PLM 0.9021794 0.7968831684 0.08388012 NA NA
#> 22 G3I12 2 3PLM 1.4214420 -0.7766765567 0.25975672 NA NA
#> 23 G3I13 2 3PLM 1.1082496 -1.0983147685 0.23504140 NA NA
#> 24 G3I14 2 3PLM 1.3797649 0.3022772312 0.16690037 NA NA
#> 25 G3I15 2 3PLM 1.2876135 -0.0573943526 0.19245588 NA NA
#> 26 G3I16 2 3PLM 1.5824294 0.7372872340 0.20217816 NA NA
#> 27 G3I17 2 3PLM 1.6058953 -1.5522762073 0.18645088 NA NA
#> 28 G3I18 2 3PLM 1.3800007 0.7080448815 0.11881653 NA NA
#> 29 G3I19 2 3PLM 0.9933705 0.0911167343 0.16557109 NA NA
#> 30 G3I20 2 3PLM 1.1645170 2.2678742087 0.11821851 NA NA
#> 31 G3I21 2 3PLM 3.0616274 1.6301700618 0.14040136 NA NA
#> 32 G3I22 2 3PLM 1.1712500 0.0856353360 0.10276551 NA NA
#> 33 G3I23 2 3PLM 1.7915979 0.3172563764 0.15045425 NA NA
#> 34 G3I24 2 3PLM 1.1259988 0.3187456984 0.05486984 NA NA
#> 35 G3I25 2 3PLM 1.3848088 1.3476897615 0.05145709 NA NA
#> 36 G3I26 2 3PLM 1.6627860 -0.9983631680 0.21786458 NA NA
#> 37 G3I27 2 3PLM 0.9242740 -0.6199576215 0.18433956 NA NA
#> 38 G3I28 5 GRM 0.9426521 -0.3795334512 0.14801722 0.8117698 1.551592
#>
#>
# Extract the standard error estimates
getirt(fit.1, what = "se.est")
#> $overall
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.17989519 0.16035224 0.04893744 NA NA
#> 2 C1I2 2 3PLM 0.14509575 0.09689007 0.05855244 NA NA
#> 3 C1I3 2 3PLM 0.12333025 0.13013772 0.04568686 NA NA
#> 4 C1I4 2 3PLM 0.12539952 0.21610221 0.06984577 NA NA
#> 5 C1I5 2 3PLM 0.09159813 0.22015093 0.06797074 NA NA
#> 6 C1I6 2 3PLM 0.13215821 0.04030740 0.01860230 NA NA
#> 7 C1I7 2 3PLM 0.13398772 0.08891913 0.03307573 NA NA
#> 8 C1I8 2 3PLM 0.12334991 0.13614025 0.04646945 NA NA
#> 9 C1I9 2 3PLM 0.12236592 0.18495675 0.05639681 NA NA
#> 10 C1I10 2 3PLM 0.11760294 0.08417251 0.03717477 NA NA
#> 11 G1I1 2 3PLM 0.10655826 0.20217054 0.06672572 NA NA
#> 12 G1I2 2 3PLM 0.13694638 0.13626565 0.03909387 NA NA
#> 13 G1I3 2 3PLM 0.26266869 0.09156215 0.02556423 NA NA
#> 14 G1I4 2 3PLM 0.21896209 0.11821220 0.04253288 NA NA
#> 15 G1I5 2 3PLM 0.14227648 0.12915817 0.05186212 NA NA
#> 16 G1I6 2 3PLM 0.18452247 0.05538028 0.02621436 NA NA
#> 17 G1I7 2 3PLM 0.16049350 0.12171798 0.04882272 NA NA
#> 18 G1I8 2 3PLM 0.46550649 0.06951993 0.01895467 NA NA
#> 19 G1I9 2 3PLM 0.26711886 0.11407326 0.06322653 NA NA
#> 20 G1I10 2 3PLM 0.12545580 0.22750745 0.09762660 NA NA
#> 21 G1I11 2 3PLM 0.15057675 0.16486816 0.07867466 NA NA
#> 22 G1I12 2 3PLM 0.09367336 0.31303395 0.08422275 NA NA
#> 23 G1I13 2 3PLM 0.14115709 0.20788070 0.06872976 NA NA
#> 24 G1I14 2 3PLM 0.38235203 0.15053141 0.02485445 NA NA
#> 25 G1I15 2 3PLM 0.09621277 0.29800051 0.09181670 NA NA
#> 26 G1I16 2 3PLM 0.11062833 0.26571952 0.09735725 NA NA
#> 27 G1I17 2 3PLM 0.13151860 0.15421189 0.05197027 NA NA
#> 28 G1I18 2 3PLM 0.20611213 0.08024248 0.03657769 NA NA
#> 29 G1I19 2 3PLM 0.12685072 0.19375886 0.08485688 NA NA
#> 30 G1I20 2 3PLM 0.18089581 0.18707909 0.05966072 NA NA
#> 31 G1I21 2 3PLM 0.13455458 0.14996962 0.04703101 NA NA
#> 32 G1I22 2 3PLM 0.21911500 0.15737913 0.06424983 NA NA
#> 33 G1I23 2 3PLM 0.15053755 0.22982042 0.09322036 NA NA
#> 34 G1I24 2 3PLM 0.19679685 0.09411360 0.03689301 NA NA
#> 35 G1I25 2 3PLM 0.18243227 0.12257416 0.04913825 NA NA
#> 36 G1I26 2 3PLM 0.25542584 0.07703704 0.02893084 NA NA
#> 37 G1I27 2 3PLM 0.17691915 0.20386267 0.10127163 NA NA
#> 38 G1I28 2 3PLM 0.16553187 0.09754762 0.03666743 NA NA
#> 39 G1I29 2 3PLM 0.09087413 0.17161992 0.05512983 NA NA
#> 40 G1I30 2 3PLM 0.28799644 0.24787264 0.02955840 NA NA
#> 41 G1I31 2 3PLM 0.48866407 0.09220125 0.01439037 NA NA
#> 42 G1I32 2 3PLM 0.12263290 0.15178218 0.05400259 NA NA
#> 43 G1I33 2 3PLM 0.17530464 0.08877908 0.03732072 NA NA
#> 44 G1I34 2 3PLM 0.13610866 0.09412723 0.03674769 NA NA
#> 45 G1I35 2 3PLM 0.17137910 0.08344182 0.02039465 NA NA
#> 46 G1I36 2 3PLM 0.14523548 0.19046168 0.08649362 NA NA
#> 47 G1I37 2 3PLM 0.14678991 0.27080023 0.08750606 NA NA
#> 48 G1I38 5 GRM 0.05824336 0.05464783 0.05036679 0.06337710 0.08439014
#> 49 C1I11 5 GRM 0.04768216 0.09429091 0.06737581 0.04635165 0.03448717
#> 50 C1I12 5 GRM 0.04132681 0.05629429 0.04082063 0.04311500 0.05653026
#> 51 G2I1 2 3PLM 0.19350221 0.17643375 0.09757730 NA NA
#> 52 G2I2 2 3PLM 0.11489091 0.30524136 0.09207477 NA NA
#> 53 G2I3 2 3PLM 0.13653157 0.20117207 0.07586750 NA NA
#> 54 G2I4 2 3PLM 0.29245623 0.09333564 0.03808894 NA NA
#> 55 G2I5 2 3PLM 0.10481807 0.39787167 0.08903051 NA NA
#> 56 G2I6 2 3PLM 0.14518031 0.29678044 0.09513691 NA NA
#> 57 G2I7 2 3PLM 0.13785758 0.12130037 0.05478446 NA NA
#> 58 G2I8 2 3PLM 0.19269491 0.08072746 0.05145801 NA NA
#> 59 G2I9 2 3PLM 0.13251099 0.27721615 0.09193314 NA NA
#> 60 G2I10 2 3PLM 0.28338383 0.11486665 0.05004309 NA NA
#> 61 G2I11 2 3PLM 0.12959812 0.14260521 0.05017878 NA NA
#> 62 G2I12 2 3PLM 0.19165147 0.18551525 0.09840785 NA NA
#> 63 G2I13 2 3PLM 0.13361413 0.24090086 0.09247457 NA NA
#> 64 G2I14 2 3PLM 0.14344036 0.11234266 0.05306700 NA NA
#> 65 G2I15 2 3PLM 0.20783033 0.17092977 0.07863958 NA NA
#> 66 G2I16 2 3PLM 0.24141540 0.09487270 0.04614521 NA NA
#> 67 G2I17 2 3PLM 0.21812356 0.14792918 0.08902957 NA NA
#> 68 G2I18 2 3PLM 0.20825056 0.08176892 0.04319252 NA NA
#> 69 G2I19 2 3PLM 0.14974281 0.21807451 0.08279427 NA NA
#> 70 G2I20 2 3PLM 0.47112164 0.18433168 0.02351512 NA NA
#> 71 G2I21 2 3PLM 0.37699918 0.05953101 0.01720186 NA NA
#> 72 G2I22 2 3PLM 0.18888770 0.14944483 0.06872351 NA NA
#> 73 G2I23 2 3PLM 0.28077865 0.09153703 0.04827635 NA NA
#> 74 G2I24 2 3PLM 0.12130175 0.07457793 0.03386516 NA NA
#> 75 G2I25 2 3PLM 0.22582407 0.06157614 0.02227878 NA NA
#> 76 G2I26 2 3PLM 0.20134542 0.16552101 0.09828502 NA NA
#> 77 G2I27 2 3PLM 0.11980495 0.24841774 0.08769248 NA NA
#> 78 G2I28 5 GRM 0.07259152 0.06782688 0.04972658 0.04738506 0.07009125
#> 79 C2I1 2 3PLM 0.07967461 0.10986098 0.03524967 NA NA
#> 80 C2I2 2 3PLM 0.08692171 0.06717781 0.01809171 NA NA
#> 81 C2I3 2 3PLM 0.15623585 0.05282304 0.01408261 NA NA
#> 82 C2I4 2 3PLM 0.11189913 0.06186328 0.02306786 NA NA
#> 83 C2I5 2 3PLM 0.09565798 0.06810561 0.02521438 NA NA
#> 84 C2I6 2 3PLM 0.10326422 0.03696659 0.01351802 NA NA
#> 85 C2I7 2 3PLM 0.10574626 0.06606876 0.02489720 NA NA
#> 86 C2I8 2 3PLM 0.15231896 0.05723105 0.01673332 NA NA
#> 87 C2I9 2 3PLM 0.13437617 0.07069516 0.03095926 NA NA
#> 88 C2I10 2 3PLM 0.12209895 0.14135303 0.05284333 NA NA
#> 89 G3I1 2 3PLM 0.14295950 0.12757467 0.04598806 NA NA
#> 90 G3I2 2 3PLM 0.09806822 0.27491495 0.06605199 NA NA
#> 91 G3I3 2 3PLM 0.12223986 0.11810373 0.03455361 NA NA
#> 92 G3I4 2 3PLM 0.23674338 0.12489657 0.02042690 NA NA
#> 93 G3I5 2 3PLM 0.11027073 0.35844706 0.08124875 NA NA
#> 94 G3I6 2 3PLM 0.15212744 0.25219492 0.07173387 NA NA
#> 95 G3I7 2 3PLM 0.13192537 0.08582984 0.02599794 NA NA
#> 96 G3I8 2 3PLM 0.17753632 0.06568100 0.02302363 NA NA
#> 97 G3I9 2 3PLM 0.12073992 0.20628990 0.06412558 NA NA
#> 98 G3I10 2 3PLM 0.21325449 0.09460878 0.02268460 NA NA
#> 99 G3I11 2 3PLM 0.10223560 0.11256805 0.02810817 NA NA
#> 100 G3I12 2 3PLM 0.16809784 0.14982785 0.04805076 NA NA
#> 101 G3I13 2 3PLM 0.12969261 0.21859906 0.06476116 NA NA
#> 102 G3I14 2 3PLM 0.14184270 0.08769788 0.02633227 NA NA
#> 103 G3I15 2 3PLM 0.13462872 0.11103389 0.03394777 NA NA
#> 104 G3I16 2 3PLM 0.17691571 0.07758799 0.02083063 NA NA
#> 105 G3I17 2 3PLM 0.15688465 0.15428884 0.05926460 NA NA
#> 106 G3I18 2 3PLM 0.14382506 0.07697407 0.02111022 NA NA
#> 107 G3I19 2 3PLM 0.11393846 0.14464817 0.04000362 NA NA
#> 108 G3I20 2 3PLM 0.23541976 0.19741351 0.01684581 NA NA
#> 109 G3I21 2 3PLM 0.57479199 0.06270311 0.01022201 NA NA
#> 110 G3I22 2 3PLM 0.11463786 0.09814469 0.02978440 NA NA
#> 111 G3I23 2 3PLM 0.16694784 0.06445158 0.01994484 NA NA
#> 112 G3I24 2 3PLM 0.09417036 0.07931539 0.02063766 NA NA
#> 113 G3I25 2 3PLM 0.14627533 0.07996861 0.01264067 NA NA
#> 114 G3I26 2 3PLM 0.16594755 0.12414916 0.04434197 NA NA
#> 115 G3I27 2 3PLM 0.10437934 0.20932778 0.05657496 NA NA
#> 116 G3I28 5 GRM 0.04771674 0.05965450 0.05957007 0.07120741 0.09365933
#>
#> $group
#> $group$Group1
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.17989519 0.16035224 0.04893744 NA NA
#> 2 C1I2 2 3PLM 0.14509575 0.09689007 0.05855244 NA NA
#> 3 C1I3 2 3PLM 0.12333025 0.13013772 0.04568686 NA NA
#> 4 C1I4 2 3PLM 0.12539952 0.21610221 0.06984577 NA NA
#> 5 C1I5 2 3PLM 0.09159813 0.22015093 0.06797074 NA NA
#> 6 C1I6 2 3PLM 0.13215821 0.04030740 0.01860230 NA NA
#> 7 C1I7 2 3PLM 0.13398772 0.08891913 0.03307573 NA NA
#> 8 C1I8 2 3PLM 0.12334991 0.13614025 0.04646945 NA NA
#> 9 C1I9 2 3PLM 0.12236592 0.18495675 0.05639681 NA NA
#> 10 C1I10 2 3PLM 0.11760294 0.08417251 0.03717477 NA NA
#> 11 G1I1 2 3PLM 0.10655826 0.20217054 0.06672572 NA NA
#> 12 G1I2 2 3PLM 0.13694638 0.13626565 0.03909387 NA NA
#> 13 G1I3 2 3PLM 0.26266869 0.09156215 0.02556423 NA NA
#> 14 G1I4 2 3PLM 0.21896209 0.11821220 0.04253288 NA NA
#> 15 G1I5 2 3PLM 0.14227648 0.12915817 0.05186212 NA NA
#> 16 G1I6 2 3PLM 0.18452247 0.05538028 0.02621436 NA NA
#> 17 G1I7 2 3PLM 0.16049350 0.12171798 0.04882272 NA NA
#> 18 G1I8 2 3PLM 0.46550649 0.06951993 0.01895467 NA NA
#> 19 G1I9 2 3PLM 0.26711886 0.11407326 0.06322653 NA NA
#> 20 G1I10 2 3PLM 0.12545580 0.22750745 0.09762660 NA NA
#> 21 G1I11 2 3PLM 0.15057675 0.16486816 0.07867466 NA NA
#> 22 G1I12 2 3PLM 0.09367336 0.31303395 0.08422275 NA NA
#> 23 G1I13 2 3PLM 0.14115709 0.20788070 0.06872976 NA NA
#> 24 G1I14 2 3PLM 0.38235203 0.15053141 0.02485445 NA NA
#> 25 G1I15 2 3PLM 0.09621277 0.29800051 0.09181670 NA NA
#> 26 G1I16 2 3PLM 0.11062833 0.26571952 0.09735725 NA NA
#> 27 G1I17 2 3PLM 0.13151860 0.15421189 0.05197027 NA NA
#> 28 G1I18 2 3PLM 0.20611213 0.08024248 0.03657769 NA NA
#> 29 G1I19 2 3PLM 0.12685072 0.19375886 0.08485688 NA NA
#> 30 G1I20 2 3PLM 0.18089581 0.18707909 0.05966072 NA NA
#> 31 G1I21 2 3PLM 0.13455458 0.14996962 0.04703101 NA NA
#> 32 G1I22 2 3PLM 0.21911500 0.15737913 0.06424983 NA NA
#> 33 G1I23 2 3PLM 0.15053755 0.22982042 0.09322036 NA NA
#> 34 G1I24 2 3PLM 0.19679685 0.09411360 0.03689301 NA NA
#> 35 G1I25 2 3PLM 0.18243227 0.12257416 0.04913825 NA NA
#> 36 G1I26 2 3PLM 0.25542584 0.07703704 0.02893084 NA NA
#> 37 G1I27 2 3PLM 0.17691915 0.20386267 0.10127163 NA NA
#> 38 G1I28 2 3PLM 0.16553187 0.09754762 0.03666743 NA NA
#> 39 G1I29 2 3PLM 0.09087413 0.17161992 0.05512983 NA NA
#> 40 G1I30 2 3PLM 0.28799644 0.24787264 0.02955840 NA NA
#> 41 G1I31 2 3PLM 0.48866407 0.09220125 0.01439037 NA NA
#> 42 G1I32 2 3PLM 0.12263290 0.15178218 0.05400259 NA NA
#> 43 G1I33 2 3PLM 0.17530464 0.08877908 0.03732072 NA NA
#> 44 G1I34 2 3PLM 0.13610866 0.09412723 0.03674769 NA NA
#> 45 G1I35 2 3PLM 0.17137910 0.08344182 0.02039465 NA NA
#> 46 G1I36 2 3PLM 0.14523548 0.19046168 0.08649362 NA NA
#> 47 G1I37 2 3PLM 0.14678991 0.27080023 0.08750606 NA NA
#> 48 G1I38 5 GRM 0.05824336 0.05464783 0.05036679 0.06337710 0.08439014
#> 49 C1I11 5 GRM 0.04768216 0.09429091 0.06737581 0.04635165 0.03448717
#> 50 C1I12 5 GRM 0.04132681 0.05629429 0.04082063 0.04311500 0.05653026
#>
#> $group$Group2
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.17989519 0.16035224 0.04893744 NA NA
#> 2 C1I2 2 3PLM 0.14509575 0.09689007 0.05855244 NA NA
#> 3 C1I3 2 3PLM 0.12333025 0.13013772 0.04568686 NA NA
#> 4 C1I4 2 3PLM 0.12539952 0.21610221 0.06984577 NA NA
#> 5 C1I5 2 3PLM 0.09159813 0.22015093 0.06797074 NA NA
#> 6 C1I6 2 3PLM 0.13215821 0.04030740 0.01860230 NA NA
#> 7 C1I7 2 3PLM 0.13398772 0.08891913 0.03307573 NA NA
#> 8 C1I8 2 3PLM 0.12334991 0.13614025 0.04646945 NA NA
#> 9 C1I9 2 3PLM 0.12236592 0.18495675 0.05639681 NA NA
#> 10 C1I10 2 3PLM 0.11760294 0.08417251 0.03717477 NA NA
#> 11 C1I11 5 GRM 0.04768216 0.09429091 0.06737581 0.04635165 0.03448717
#> 12 C1I12 5 GRM 0.04132681 0.05629429 0.04082063 0.04311500 0.05653026
#> 13 G2I1 2 3PLM 0.19350221 0.17643375 0.09757730 NA NA
#> 14 G2I2 2 3PLM 0.11489091 0.30524136 0.09207477 NA NA
#> 15 G2I3 2 3PLM 0.13653157 0.20117207 0.07586750 NA NA
#> 16 G2I4 2 3PLM 0.29245623 0.09333564 0.03808894 NA NA
#> 17 G2I5 2 3PLM 0.10481807 0.39787167 0.08903051 NA NA
#> 18 G2I6 2 3PLM 0.14518031 0.29678044 0.09513691 NA NA
#> 19 G2I7 2 3PLM 0.13785758 0.12130037 0.05478446 NA NA
#> 20 G2I8 2 3PLM 0.19269491 0.08072746 0.05145801 NA NA
#> 21 G2I9 2 3PLM 0.13251099 0.27721615 0.09193314 NA NA
#> 22 G2I10 2 3PLM 0.28338383 0.11486665 0.05004309 NA NA
#> 23 G2I11 2 3PLM 0.12959812 0.14260521 0.05017878 NA NA
#> 24 G2I12 2 3PLM 0.19165147 0.18551525 0.09840785 NA NA
#> 25 G2I13 2 3PLM 0.13361413 0.24090086 0.09247457 NA NA
#> 26 G2I14 2 3PLM 0.14344036 0.11234266 0.05306700 NA NA
#> 27 G2I15 2 3PLM 0.20783033 0.17092977 0.07863958 NA NA
#> 28 G2I16 2 3PLM 0.24141540 0.09487270 0.04614521 NA NA
#> 29 G2I17 2 3PLM 0.21812356 0.14792918 0.08902957 NA NA
#> 30 G2I18 2 3PLM 0.20825056 0.08176892 0.04319252 NA NA
#> 31 G2I19 2 3PLM 0.14974281 0.21807451 0.08279427 NA NA
#> 32 G2I20 2 3PLM 0.47112164 0.18433168 0.02351512 NA NA
#> 33 G2I21 2 3PLM 0.37699918 0.05953101 0.01720186 NA NA
#> 34 G2I22 2 3PLM 0.18888770 0.14944483 0.06872351 NA NA
#> 35 G2I23 2 3PLM 0.28077865 0.09153703 0.04827635 NA NA
#> 36 G2I24 2 3PLM 0.12130175 0.07457793 0.03386516 NA NA
#> 37 G2I25 2 3PLM 0.22582407 0.06157614 0.02227878 NA NA
#> 38 G2I26 2 3PLM 0.20134542 0.16552101 0.09828502 NA NA
#> 39 G2I27 2 3PLM 0.11980495 0.24841774 0.08769248 NA NA
#> 40 G2I28 5 GRM 0.07259152 0.06782688 0.04972658 0.04738506 0.07009125
#> 41 C2I1 2 3PLM 0.07967461 0.10986098 0.03524967 NA NA
#> 42 C2I2 2 3PLM 0.08692171 0.06717781 0.01809171 NA NA
#> 43 C2I3 2 3PLM 0.15623585 0.05282304 0.01408261 NA NA
#> 44 C2I4 2 3PLM 0.11189913 0.06186328 0.02306786 NA NA
#> 45 C2I5 2 3PLM 0.09565798 0.06810561 0.02521438 NA NA
#> 46 C2I6 2 3PLM 0.10326422 0.03696659 0.01351802 NA NA
#> 47 C2I7 2 3PLM 0.10574626 0.06606876 0.02489720 NA NA
#> 48 C2I8 2 3PLM 0.15231896 0.05723105 0.01673332 NA NA
#> 49 C2I9 2 3PLM 0.13437617 0.07069516 0.03095926 NA NA
#> 50 C2I10 2 3PLM 0.12209895 0.14135303 0.05284333 NA NA
#>
#> $group$Group3
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C2I1 2 3PLM 0.07967461 0.10986098 0.03524967 NA NA
#> 2 C2I2 2 3PLM 0.08692171 0.06717781 0.01809171 NA NA
#> 3 C2I3 2 3PLM 0.15623585 0.05282304 0.01408261 NA NA
#> 4 C2I4 2 3PLM 0.11189913 0.06186328 0.02306786 NA NA
#> 5 C2I5 2 3PLM 0.09565798 0.06810561 0.02521438 NA NA
#> 6 C2I6 2 3PLM 0.10326422 0.03696659 0.01351802 NA NA
#> 7 C2I7 2 3PLM 0.10574626 0.06606876 0.02489720 NA NA
#> 8 C2I8 2 3PLM 0.15231896 0.05723105 0.01673332 NA NA
#> 9 C2I9 2 3PLM 0.13437617 0.07069516 0.03095926 NA NA
#> 10 C2I10 2 3PLM 0.12209895 0.14135303 0.05284333 NA NA
#> 11 G3I1 2 3PLM 0.14295950 0.12757467 0.04598806 NA NA
#> 12 G3I2 2 3PLM 0.09806822 0.27491495 0.06605199 NA NA
#> 13 G3I3 2 3PLM 0.12223986 0.11810373 0.03455361 NA NA
#> 14 G3I4 2 3PLM 0.23674338 0.12489657 0.02042690 NA NA
#> 15 G3I5 2 3PLM 0.11027073 0.35844706 0.08124875 NA NA
#> 16 G3I6 2 3PLM 0.15212744 0.25219492 0.07173387 NA NA
#> 17 G3I7 2 3PLM 0.13192537 0.08582984 0.02599794 NA NA
#> 18 G3I8 2 3PLM 0.17753632 0.06568100 0.02302363 NA NA
#> 19 G3I9 2 3PLM 0.12073992 0.20628990 0.06412558 NA NA
#> 20 G3I10 2 3PLM 0.21325449 0.09460878 0.02268460 NA NA
#> 21 G3I11 2 3PLM 0.10223560 0.11256805 0.02810817 NA NA
#> 22 G3I12 2 3PLM 0.16809784 0.14982785 0.04805076 NA NA
#> 23 G3I13 2 3PLM 0.12969261 0.21859906 0.06476116 NA NA
#> 24 G3I14 2 3PLM 0.14184270 0.08769788 0.02633227 NA NA
#> 25 G3I15 2 3PLM 0.13462872 0.11103389 0.03394777 NA NA
#> 26 G3I16 2 3PLM 0.17691571 0.07758799 0.02083063 NA NA
#> 27 G3I17 2 3PLM 0.15688465 0.15428884 0.05926460 NA NA
#> 28 G3I18 2 3PLM 0.14382506 0.07697407 0.02111022 NA NA
#> 29 G3I19 2 3PLM 0.11393846 0.14464817 0.04000362 NA NA
#> 30 G3I20 2 3PLM 0.23541976 0.19741351 0.01684581 NA NA
#> 31 G3I21 2 3PLM 0.57479199 0.06270311 0.01022201 NA NA
#> 32 G3I22 2 3PLM 0.11463786 0.09814469 0.02978440 NA NA
#> 33 G3I23 2 3PLM 0.16694784 0.06445158 0.01994484 NA NA
#> 34 G3I24 2 3PLM 0.09417036 0.07931539 0.02063766 NA NA
#> 35 G3I25 2 3PLM 0.14627533 0.07996861 0.01264067 NA NA
#> 36 G3I26 2 3PLM 0.16594755 0.12414916 0.04434197 NA NA
#> 37 G3I27 2 3PLM 0.10437934 0.20932778 0.05657496 NA NA
#> 38 G3I28 5 GRM 0.04771674 0.05965450 0.05957007 0.07120741 0.09365933
#>
#>
# Extract the group-level parameter estimates (i.e., scale parameters)
getirt(fit.1, what = "group.par")
#> $Group1
#> mu sigma2 sigma
#> estimates 0 1 1
#> se NA NA NA
#>
#> $Group2
#> mu sigma2 sigma
#> estimates 0.48545465 0.5575252 0.74667607
#> se 0.01669618 0.0176349 0.01180894
#>
#> $Group3
#> mu sigma2 sigma
#> estimates -0.36960845 1.95177274 1.39705860
#> se 0.03123918 0.06173591 0.02209496
#>
# Extract the posterior latent ability distributions for each group
getirt(fit.1, what = "weights")
#> $Group1
#> theta weight
#> 1 -6.00 2.596404e-24
#> 2 -5.75 6.661462e-12
#> 3 -5.50 6.687304e-11
#> 4 -5.25 3.455143e-10
#> 5 -5.00 1.240179e-09
#> 6 -4.75 3.547688e-09
#> 7 -4.50 8.892961e-09
#> 8 -4.25 2.132090e-08
#> 9 -4.00 5.399524e-08
#> 10 -3.75 1.635844e-07
#> 11 -3.50 6.878012e-07
#> 12 -3.25 4.538677e-06
#> 13 -3.00 4.536928e-05
#> 14 -2.75 4.969458e-04
#> 15 -2.50 3.578851e-03
#> 16 -2.25 1.233388e-02
#> 17 -2.00 2.221829e-02
#> 18 -1.75 2.756719e-02
#> 19 -1.50 3.067494e-02
#> 20 -1.25 3.699025e-02
#> 21 -1.00 5.137755e-02
#> 22 -0.75 7.176369e-02
#> 23 -0.50 8.884787e-02
#> 24 -0.25 1.006945e-01
#> 25 0.00 1.009843e-01
#> 26 0.25 9.093334e-02
#> 27 0.50 8.369774e-02
#> 28 0.75 8.097105e-02
#> 29 1.00 7.169684e-02
#> 30 1.25 5.091446e-02
#> 31 1.50 3.038547e-02
#> 32 1.75 1.784466e-02
#> 33 2.00 1.099557e-02
#> 34 2.25 6.559709e-03
#> 35 2.50 3.586983e-03
#> 36 2.75 1.890639e-03
#> 37 3.00 1.057103e-03
#> 38 3.25 6.683050e-04
#> 39 3.50 4.688643e-04
#> 40 3.75 3.327412e-04
#> 41 4.00 2.150724e-04
#> 42 4.25 1.183608e-04
#> 43 4.50 5.413395e-05
#> 44 4.75 2.065077e-05
#> 45 5.00 6.683841e-06
#> 46 5.25 1.876663e-06
#> 47 5.50 4.678457e-07
#> 48 5.75 1.058922e-07
#> 49 6.00 2.221172e-08
#>
#> $Group2
#> theta weight
#> 1 -6.00 4.462701e-59
#> 2 -5.75 5.478200e-57
#> 3 -5.50 1.250041e-54
#> 4 -5.25 5.639732e-52
#> 5 -5.00 5.211160e-49
#> 6 -4.75 9.838327e-46
#> 7 -4.50 3.615813e-42
#> 8 -4.25 2.347660e-38
#> 9 -4.00 2.341231e-34
#> 10 -3.75 3.033389e-30
#> 11 -3.50 4.296681e-26
#> 12 -3.25 5.685725e-22
#> 13 -3.00 6.113539e-18
#> 14 -2.75 4.561112e-14
#> 15 -2.50 1.824133e-10
#> 16 -2.25 2.490398e-07
#> 17 -2.00 6.146622e-05
#> 18 -1.75 1.684078e-03
#> 19 -1.50 7.306548e-03
#> 20 -1.25 1.587374e-02
#> 21 -1.00 2.333185e-02
#> 22 -0.75 1.961168e-02
#> 23 -0.50 3.881370e-02
#> 24 -0.25 1.156738e-01
#> 25 0.00 8.052857e-02
#> 26 0.25 8.668950e-02
#> 27 0.50 1.901804e-01
#> 28 0.75 1.359231e-01
#> 29 1.00 8.624615e-02
#> 30 1.25 8.381817e-02
#> 31 1.50 5.935414e-02
#> 32 1.75 3.231143e-02
#> 33 2.00 1.436083e-02
#> 34 2.25 3.834694e-03
#> 35 2.50 1.089214e-03
#> 36 2.75 7.241950e-04
#> 37 3.00 9.441983e-04
#> 38 3.25 1.046937e-03
#> 39 3.50 5.018765e-04
#> 40 3.75 8.379032e-05
#> 41 4.00 5.539575e-06
#> 42 4.25 1.915245e-07
#> 43 4.50 4.643638e-09
#> 44 4.75 1.007048e-10
#> 45 5.00 2.322071e-12
#> 46 5.25 6.327049e-14
#> 47 5.50 2.144754e-15
#> 48 5.75 9.160692e-17
#> 49 6.00 4.870649e-18
#>
#> $Group3
#> theta weight
#> 1 -6.00 7.731298e-07
#> 2 -5.75 3.145368e-06
#> 3 -5.50 1.179526e-05
#> 4 -5.25 4.054836e-05
#> 5 -5.00 1.268999e-04
#> 6 -4.75 3.584830e-04
#> 7 -4.50 9.049299e-04
#> 8 -4.25 2.018717e-03
#> 9 -4.00 3.937687e-03
#> 10 -3.75 6.669793e-03
#> 11 -3.50 9.833099e-03
#> 12 -3.25 1.285721e-02
#> 13 -3.00 1.552609e-02
#> 14 -2.75 1.830649e-02
#> 15 -2.50 2.198421e-02
#> 16 -2.25 2.658226e-02
#> 17 -2.00 3.040018e-02
#> 18 -1.75 3.230747e-02
#> 19 -1.50 3.635519e-02
#> 20 -1.25 5.077580e-02
#> 21 -1.00 7.272466e-02
#> 22 -0.75 6.898185e-02
#> 23 -0.50 5.513930e-02
#> 24 -0.25 6.620643e-02
#> 25 0.00 8.981610e-02
#> 26 0.25 8.120609e-02
#> 27 0.50 5.730756e-02
#> 28 0.75 4.971849e-02
#> 29 1.00 4.623885e-02
#> 30 1.25 3.634235e-02
#> 31 1.50 3.452349e-02
#> 32 1.75 3.537759e-02
#> 33 2.00 2.023739e-02
#> 34 2.25 7.344692e-03
#> 35 2.50 2.991667e-03
#> 36 2.75 1.765572e-03
#> 37 3.00 1.415897e-03
#> 38 3.25 1.272697e-03
#> 39 3.50 1.056410e-03
#> 40 3.75 7.149887e-04
#> 41 4.00 3.785780e-04
#> 42 4.25 1.595304e-04
#> 43 4.50 5.584698e-05
#> 44 4.75 1.699530e-05
#> 45 5.00 4.664197e-06
#> 46 5.25 1.184031e-06
#> 47 5.50 2.823534e-07
#> 48 5.75 6.377004e-08
#> 49 6.00 1.368772e-08
#>
# 1-(2). Alternatively, the same parameter estimation can be performed by
# inserting a list of item metadata for the groups into the 'x' argument.
# If the item metadata contains item parameters to be used as starting values,
# set 'use.startval = TRUE'.
# Also, specify the groups in which the ability distribution scales
# will be freely estimated using their group names.
free.group <- group.name[2:3]
fit.2 <-
est_mg(
x = x, data = data, group.name = group.name, D = 1,
free.group = free.group, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)),
group.mean = 0, group.var = 1, EmpHist = TRUE, use.startval = TRUE,
Etol = 0.001, MaxE = 500
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -159736.5073, Max-Change: 0.400714
EM iteration: 2, Loglike: -159610.2190, Max-Change: 0.165418
EM iteration: 3, Loglike: -159601.3164, Max-Change: 0.088375
EM iteration: 4, Loglike: -159596.5635, Max-Change: 0.054733
EM iteration: 5, Loglike: -159593.6124, Max-Change: 0.040346
EM iteration: 6, Loglike: -159591.6852, Max-Change: 0.035828
EM iteration: 7, Loglike: -159590.3654, Max-Change: 0.030999
EM iteration: 8, Loglike: -159589.4215, Max-Change: 0.026538
EM iteration: 9, Loglike: -159588.7193, Max-Change: 0.022633
EM iteration: 10, Loglike: -159588.1782, Max-Change: 0.019291
EM iteration: 11, Loglike: -159587.7475, Max-Change: 0.016548
EM iteration: 12, Loglike: -159587.3947, Max-Change: 0.014582
EM iteration: 13, Loglike: -159587.0984, Max-Change: 0.012898
EM iteration: 14, Loglike: -159586.8441, Max-Change: 0.011459
EM iteration: 15, Loglike: -159586.6218, Max-Change: 0.010231
EM iteration: 16, Loglike: -159586.4248, Max-Change: 0.009182
EM iteration: 17, Loglike: -159586.2479, Max-Change: 0.008283
EM iteration: 18, Loglike: -159586.0876, Max-Change: 0.007509
EM iteration: 19, Loglike: -159585.9412, Max-Change: 0.006838
EM iteration: 20, Loglike: -159585.8067, Max-Change: 0.006252
EM iteration: 21, Loglike: -159585.6824, Max-Change: 0.005735
EM iteration: 22, Loglike: -159585.5673, Max-Change: 0.005275
EM iteration: 23, Loglike: -159585.4607, Max-Change: 0.004862
EM iteration: 24, Loglike: -159585.3616, Max-Change: 0.004488
EM iteration: 25, Loglike: -159585.2689, Max-Change: 0.004146
EM iteration: 26, Loglike: -159585.1819, Max-Change: 0.003832
EM iteration: 27, Loglike: -159585.0999, Max-Change: 0.003542
EM iteration: 28, Loglike: -159585.0226, Max-Change: 0.003272
EM iteration: 29, Loglike: -159584.9497, Max-Change: 0.00302
EM iteration: 30, Loglike: -159584.8808, Max-Change: 0.002784
EM iteration: 31, Loglike: -159584.8156, Max-Change: 0.002563
EM iteration: 32, Loglike: -159584.7538, Max-Change: 0.002355
EM iteration: 33, Loglike: -159584.6951, Max-Change: 0.00216
EM iteration: 34, Loglike: -159584.6391, Max-Change: 0.001976
EM iteration: 35, Loglike: -159584.5858, Max-Change: 0.001804
EM iteration: 36, Loglike: -159584.5348, Max-Change: 0.001641
EM iteration: 37, Loglike: -159584.4860, Max-Change: 0.001489
EM iteration: 38, Loglike: -159584.4392, Max-Change: 0.001351
EM iteration: 39, Loglike: -159584.3942, Max-Change: 0.00126
EM iteration: 40, Loglike: -159584.3510, Max-Change: 0.001174
EM iteration: 41, Loglike: -159584.3092, Max-Change: 0.001092
EM iteration: 42, Loglike: -159584.2690, Max-Change: 0.001015
EM iteration: 43, Loglike: -159584.2300, Max-Change: 0.000942
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 8.88 seconds.
# Summary of the estimation
summary(fit.2)
#>
#> Call:
#> est_mg(x = x, data = data, group.name = group.name, D = 1, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), group.mean = 0, group.var = 1, EmpHist = TRUE,
#> use.startval = TRUE, Etol = 0.001, MaxE = 500)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 362
#> Number of fixed items:
#> Overall: 0
#> By group: 0(Group1), 0(Group2), 0(Group3)
#> Number of E-step cycles completed: 43
#> Maximum parameter change: 0.0009420884
#>
#> Processing time (in seconds)
#> EM algorithm: 8.01
#> Standard error computation: 0.43
#> Total computation: 8.88
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are satisfied.
#> Second-order test: Solution is a possible local maximum.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates is obtainable.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 319168.5
#> By group: 120345.77(Group1), 113945.748(Group2), 84876.941(Group3)
#>
#> Akaike Information Criterion (AIC): 319892.5
#> Bayesian Information Criterion (BIC): 322317.7
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 C1I1 2 3PLM 0.91 0.18 1.38 0.16 0.28 0.05 NA NA
#> 2 C1I2 2 3PLM 2.14 0.15 -0.95 0.10 0.19 0.06 NA NA
#> 3 C1I3 2 3PLM 1.07 0.12 0.63 0.13 0.18 0.04 NA NA
#> 4 C1I4 2 3PLM 1.09 0.13 -0.14 0.21 0.29 0.07 NA NA
#> 5 C1I5 2 3PLM 0.88 0.09 -0.12 0.22 0.18 0.07 NA NA
#> 6 C1I6 2 3PLM 1.93 0.13 0.61 0.04 0.09 0.02 NA NA
#> 7 C1I7 2 3PLM 1.12 0.14 1.12 0.09 0.15 0.03 NA NA
#> 8 C1I8 2 3PLM 0.95 0.12 0.90 0.13 0.16 0.05 NA NA
#> 9 C1I9 2 3PLM 0.91 0.13 0.66 0.18 0.21 0.06 NA NA
#> 10 C1I10 2 3PLM 1.50 0.12 0.16 0.08 0.16 0.04 NA NA
#> 11 G1I1 2 3PLM 0.97 0.11 -0.43 0.20 0.16 0.07 NA NA
#> 12 G1I2 2 3PLM 0.90 0.14 1.21 0.13 0.11 0.04 NA NA
#> 13 G1I3 2 3PLM 1.55 0.27 1.30 0.09 0.19 0.03 NA NA
#> 14 G1I4 2 3PLM 1.58 0.22 0.30 0.12 0.30 0.04 NA NA
#> 15 G1I5 2 3PLM 1.36 0.14 -0.15 0.13 0.16 0.05 NA NA
#> 16 G1I6 2 3PLM 2.18 0.18 0.03 0.05 0.09 0.03 NA NA
#> 17 G1I7 2 3PLM 1.48 0.16 -0.04 0.12 0.20 0.05 NA NA
#> 18 G1I8 2 3PLM 2.57 0.47 1.18 0.07 0.32 0.02 NA NA
#> 19 G1I9 2 3PLM 2.43 0.27 -0.90 0.11 0.25 0.06 NA NA
#> 20 G1I10 2 3PLM 1.26 0.13 -1.73 0.23 0.24 0.10 NA NA
#> 21 G1I11 2 3PLM 1.55 0.15 -1.08 0.17 0.21 0.08 NA NA
#> 22 G1I12 2 3PLM 0.76 0.10 -0.78 0.32 0.20 0.08 NA NA
#> 23 G1I13 2 3PLM 1.06 0.14 -0.10 0.20 0.21 0.07 NA NA
#> 24 G1I14 2 3PLM 1.52 0.38 1.74 0.15 0.30 0.02 NA NA
#> 25 G1I15 2 3PLM 0.87 0.10 -1.41 0.30 0.22 0.09 NA NA
#> 26 G1I16 2 3PLM 1.05 0.11 -1.93 0.27 0.23 0.10 NA NA
#> 27 G1I17 2 3PLM 1.07 0.13 0.28 0.15 0.16 0.05 NA NA
#> 28 G1I18 2 3PLM 2.13 0.21 -0.06 0.08 0.24 0.04 NA NA
#> 29 G1I19 2 3PLM 1.33 0.13 -1.36 0.20 0.21 0.09 NA NA
#> 30 G1I20 2 3PLM 1.04 0.18 0.54 0.18 0.23 0.06 NA NA
#> 31 G1I21 2 3PLM 0.93 0.14 0.78 0.15 0.13 0.05 NA NA
#> 32 G1I22 2 3PLM 1.82 0.22 -0.59 0.15 0.37 0.06 NA NA
#> 33 G1I23 2 3PLM 1.32 0.15 -1.13 0.23 0.26 0.09 NA NA
#> 34 G1I24 2 3PLM 1.68 0.20 0.34 0.09 0.23 0.04 NA NA
#> 35 G1I25 2 3PLM 1.62 0.18 -0.09 0.12 0.26 0.05 NA NA
#> 36 G1I26 2 3PLM 1.94 0.26 0.67 0.08 0.26 0.03 NA NA
#> 37 G1I27 2 3PLM 1.63 0.19 -1.50 0.21 0.28 0.10 NA NA
#> 38 G1I28 2 3PLM 1.36 0.17 0.58 0.10 0.15 0.04 NA NA
#> 39 G1I29 2 3PLM 0.93 0.09 -0.35 0.17 0.13 0.06 NA NA
#> 40 G1I30 2 3PLM 1.06 0.29 2.24 0.25 0.17 0.03 NA NA
#> 41 G1I31 2 3PLM 2.47 0.49 1.62 0.09 0.18 0.01 NA NA
#> 42 G1I32 2 3PLM 1.12 0.12 -0.05 0.15 0.15 0.05 NA NA
#> 43 G1I33 2 3PLM 1.64 0.18 0.20 0.09 0.16 0.04 NA NA
#> 44 G1I34 2 3PLM 1.35 0.14 0.26 0.09 0.11 0.04 NA NA
#> 45 G1I35 2 3PLM 1.36 0.17 1.29 0.08 0.07 0.02 NA NA
#> 46 G1I36 2 3PLM 1.45 0.15 -1.20 0.19 0.23 0.09 NA NA
#> 47 G1I37 2 3PLM 1.08 0.15 -0.54 0.27 0.28 0.09 NA NA
#> 48 G1I38 5 GRM 1.07 0.06 -0.35 0.05 0.23 0.05 0.87 0.06
#> 49 C1I11 5 GRM 1.19 0.05 -2.18 0.10 -1.43 0.07 -0.72 0.05
#> 50 C1I12 5 GRM 0.92 0.04 -0.66 0.06 0.05 0.04 0.70 0.04
#> 51 G2I1 2 3PLM 1.79 0.20 -0.81 0.17 0.24 0.10 NA NA
#> 52 G2I2 2 3PLM 0.86 0.12 -0.40 0.30 0.21 0.09 NA NA
#> 53 G2I3 2 3PLM 1.11 0.14 0.12 0.20 0.18 0.08 NA NA
#> 54 G2I4 2 3PLM 1.53 0.30 1.46 0.09 0.18 0.04 NA NA
#> 55 G2I5 2 3PLM 0.73 0.11 -1.60 0.39 0.20 0.09 NA NA
#> 56 G2I6 2 3PLM 1.11 0.15 -1.54 0.29 0.22 0.09 NA NA
#> 57 G2I7 2 3PLM 1.35 0.14 0.29 0.12 0.13 0.05 NA NA
#> 58 G2I8 2 3PLM 2.26 0.20 -0.05 0.08 0.14 0.05 NA NA
#> 59 G2I9 2 3PLM 1.10 0.13 -1.50 0.27 0.21 0.09 NA NA
#> 60 G2I10 2 3PLM 1.68 0.29 0.90 0.11 0.29 0.05 NA NA
#> 61 G2I11 2 3PLM 0.98 0.13 0.88 0.14 0.11 0.05 NA NA
#> 62 G2I12 2 3PLM 1.71 0.19 -0.64 0.18 0.26 0.10 NA NA
#> 63 G2I13 2 3PLM 1.19 0.14 -1.25 0.24 0.21 0.09 NA NA
#> 64 G2I14 2 3PLM 1.46 0.15 0.25 0.11 0.13 0.05 NA NA
#> 65 G2I15 2 3PLM 1.60 0.21 0.08 0.17 0.27 0.08 NA NA
#> 66 G2I16 2 3PLM 1.80 0.25 0.76 0.09 0.22 0.05 NA NA
#> 67 G2I17 2 3PLM 2.14 0.22 -1.16 0.15 0.20 0.09 NA NA
#> 68 G2I18 2 3PLM 1.82 0.21 0.65 0.08 0.14 0.04 NA NA
#> 69 G2I19 2 3PLM 1.15 0.15 0.08 0.21 0.21 0.08 NA NA
#> 70 G2I20 2 3PLM 1.72 0.48 2.16 0.18 0.16 0.02 NA NA
#> 71 G2I21 2 3PLM 2.52 0.38 1.54 0.06 0.12 0.02 NA NA
#> 72 G2I22 2 3PLM 1.52 0.19 0.27 0.15 0.22 0.07 NA NA
#> 73 G2I23 2 3PLM 2.22 0.28 0.47 0.09 0.28 0.05 NA NA
#> 74 G2I24 2 3PLM 1.46 0.12 0.38 0.07 0.07 0.03 NA NA
#> 75 G2I25 2 3PLM 1.84 0.23 1.38 0.06 0.07 0.02 NA NA
#> 76 G2I26 2 3PLM 1.93 0.20 -0.83 0.16 0.25 0.10 NA NA
#> 77 G2I27 2 3PLM 1.01 0.12 -0.54 0.24 0.20 0.09 NA NA
#> 78 G2I28 5 GRM 1.16 0.07 -0.33 0.07 0.17 0.05 0.80 0.05
#> 79 C2I1 2 3PLM 1.10 0.08 -0.26 0.11 0.12 0.04 NA NA
#> 80 C2I2 2 3PLM 1.02 0.09 1.24 0.07 0.06 0.02 NA NA
#> 81 C2I3 2 3PLM 1.66 0.16 1.38 0.05 0.13 0.01 NA NA
#> 82 C2I4 2 3PLM 1.59 0.11 0.27 0.06 0.18 0.02 NA NA
#> 83 C2I5 2 3PLM 1.46 0.10 -0.03 0.07 0.12 0.03 NA NA
#> 84 C2I6 2 3PLM 2.08 0.11 -0.02 0.04 0.05 0.01 NA NA
#> 85 C2I7 2 3PLM 1.59 0.11 0.03 0.07 0.18 0.03 NA NA
#> 86 C2I8 2 3PLM 1.56 0.16 1.28 0.06 0.19 0.02 NA NA
#> 87 C2I9 2 3PLM 2.22 0.14 -0.95 0.07 0.14 0.03 NA NA
#> 88 C2I10 2 3PLM 1.61 0.12 -1.30 0.14 0.25 0.06 NA NA
#> 89 G3I1 2 3PLM 1.56 0.15 -1.04 0.12 0.16 0.05 NA NA
#> 90 G3I2 2 3PLM 0.79 0.10 -0.55 0.27 0.19 0.07 NA NA
#> 91 G3I3 2 3PLM 1.18 0.13 0.11 0.12 0.17 0.04 NA NA
#> 92 G3I4 2 3PLM 1.34 0.24 1.71 0.12 0.22 0.02 NA NA
#> 93 G3I5 2 3PLM 0.81 0.11 -0.97 0.35 0.28 0.08 NA NA
#> 94 G3I6 2 3PLM 1.20 0.15 -1.26 0.25 0.31 0.08 NA NA
#> 95 G3I7 2 3PLM 1.40 0.14 0.29 0.08 0.14 0.03 NA NA
#> 96 G3I8 2 3PLM 1.97 0.18 -0.04 0.06 0.15 0.02 NA NA
#> 97 G3I9 2 3PLM 1.16 0.12 -1.14 0.20 0.20 0.07 NA NA
#> 98 G3I10 2 3PLM 1.55 0.22 0.98 0.09 0.29 0.02 NA NA
#> 99 G3I11 2 3PLM 0.93 0.10 0.81 0.11 0.08 0.03 NA NA
#> 100 G3I12 2 3PLM 1.46 0.17 -0.72 0.15 0.26 0.05 NA NA
#> 101 G3I13 2 3PLM 1.14 0.13 -1.04 0.21 0.23 0.07 NA NA
#> 102 G3I14 2 3PLM 1.41 0.15 0.33 0.09 0.17 0.03 NA NA
#> 103 G3I15 2 3PLM 1.32 0.14 -0.02 0.11 0.19 0.03 NA NA
#> 104 G3I16 2 3PLM 1.62 0.18 0.76 0.08 0.20 0.02 NA NA
#> 105 G3I17 2 3PLM 1.66 0.16 -1.47 0.15 0.18 0.06 NA NA
#> 106 G3I18 2 3PLM 1.41 0.15 0.73 0.08 0.12 0.02 NA NA
#> 107 G3I19 2 3PLM 1.02 0.12 0.12 0.14 0.16 0.04 NA NA
#> 108 G3I20 2 3PLM 1.19 0.24 2.25 0.19 0.12 0.02 NA NA
#> 109 G3I21 2 3PLM 3.09 0.57 1.63 0.06 0.14 0.01 NA NA
#> 110 G3I22 2 3PLM 1.20 0.12 0.12 0.10 0.10 0.03 NA NA
#> 111 G3I23 2 3PLM 1.84 0.17 0.35 0.06 0.15 0.02 NA NA
#> 112 G3I24 2 3PLM 1.16 0.10 0.35 0.08 0.05 0.02 NA NA
#> 113 G3I25 2 3PLM 1.42 0.15 1.35 0.08 0.05 0.01 NA NA
#> 114 G3I26 2 3PLM 1.70 0.17 -0.94 0.12 0.21 0.05 NA NA
#> 115 G3I27 2 3PLM 0.95 0.11 -0.57 0.20 0.18 0.06 NA NA
#> 116 G3I28 5 GRM 0.97 0.05 -0.32 0.06 0.19 0.06 0.83 0.07
#> par.5 se.5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 NA NA
#> 5 NA NA
#> 6 NA NA
#> 7 NA NA
#> 8 NA NA
#> 9 NA NA
#> 10 NA NA
#> 11 NA NA
#> 12 NA NA
#> 13 NA NA
#> 14 NA NA
#> 15 NA NA
#> 16 NA NA
#> 17 NA NA
#> 18 NA NA
#> 19 NA NA
#> 20 NA NA
#> 21 NA NA
#> 22 NA NA
#> 23 NA NA
#> 24 NA NA
#> 25 NA NA
#> 26 NA NA
#> 27 NA NA
#> 28 NA NA
#> 29 NA NA
#> 30 NA NA
#> 31 NA NA
#> 32 NA NA
#> 33 NA NA
#> 34 NA NA
#> 35 NA NA
#> 36 NA NA
#> 37 NA NA
#> 38 NA NA
#> 39 NA NA
#> 40 NA NA
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 1.43 0.08
#> 49 -0.10 0.03
#> 50 1.26 0.06
#> 51 NA NA
#> 52 NA NA
#> 53 NA NA
#> 54 NA NA
#> 55 NA NA
#> 56 NA NA
#> 57 NA NA
#> 58 NA NA
#> 59 NA NA
#> 60 NA NA
#> 61 NA NA
#> 62 NA NA
#> 63 NA NA
#> 64 NA NA
#> 65 NA NA
#> 66 NA NA
#> 67 NA NA
#> 68 NA NA
#> 69 NA NA
#> 70 NA NA
#> 71 NA NA
#> 72 NA NA
#> 73 NA NA
#> 74 NA NA
#> 75 NA NA
#> 76 NA NA
#> 77 NA NA
#> 78 1.45 0.07
#> 79 NA NA
#> 80 NA NA
#> 81 NA NA
#> 82 NA NA
#> 83 NA NA
#> 84 NA NA
#> 85 NA NA
#> 86 NA NA
#> 87 NA NA
#> 88 NA NA
#> 89 NA NA
#> 90 NA NA
#> 91 NA NA
#> 92 NA NA
#> 93 NA NA
#> 94 NA NA
#> 95 NA NA
#> 96 NA NA
#> 97 NA NA
#> 98 NA NA
#> 99 NA NA
#> 100 NA NA
#> 101 NA NA
#> 102 NA NA
#> 103 NA NA
#> 104 NA NA
#> 105 NA NA
#> 106 NA NA
#> 107 NA NA
#> 108 NA NA
#> 109 NA NA
#> 110 NA NA
#> 111 NA NA
#> 112 NA NA
#> 113 NA NA
#> 114 NA NA
#> 115 NA NA
#> 116 1.55 0.09
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) 0.00 1.00 1.00
#> se(Group1) NA NA NA
#> estimate(Group2) 0.51 0.54 0.73
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.31 1.80 1.34
#> se(Group3) 0.03 0.06 0.02
#>
## ------------------------------------------------------------------------------
# 2. MG calibration with FIPC using simMG data
# - Details:
# (a) Fix the parameters of the common items between the groups
# (i.e., items C1I1–C1I12 between Groups 1 and 2, and
# items C2I1–C2I10 between Groups 2 and 3)
# (b) Freely estimate the means and variances of the ability
# distributions for all three groups
## ------------------------------------------------------------------------------
# 2-(1). Freely estimate the means and variances for all three groups
# Set all three groups as free groups in which the scales
# of the ability distributions are to be freely estimated
free.group <- 1:3 # or use 'free.group <- group.name'
# Specify the locations of items to be fixed in each group's metadata
# For Group 1: C1I1–C1I12 are located in rows 1–10 and 49–50
# For Group 2: C1I1–C1I12 are in rows 1–12, and
# C2I1–C2I10 are in rows 41–50
# For Group 3: C2I1–C2I10 are in rows 1–10
fix.loc <- list(
c(1:10, 49:50),
c(1:12, 41:50),
c(1:10)
)
# Estimate IRT parameters using MG-FIPC:
# When FIPC is implemented, item metadata for all groups
# must be provided via the 'x' argument.
# For fixed items, their item parameters must be specified
# in the metadata. For non-fixed items, any placeholder values
# can be used in the metadata.
# Also set fipc = TRUE and fipc.method = "MEM"
fit.3 <-
est_mg(
x = x, data = data, group.name = group.name, D = 1,
free.group = free.group, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)),
EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
fipc.method = "MEM", fix.loc = fix.loc
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -56756.7548, Max-Change: 3.554166
EM iteration: 2, Loglike: -160424.0878, Max-Change: 0.780368
EM iteration: 3, Loglike: -159755.3559, Max-Change: 0.276071
EM iteration: 4, Loglike: -159686.2158, Max-Change: 0.151073
EM iteration: 5, Loglike: -159657.5520, Max-Change: 0.102849
EM iteration: 6, Loglike: -159642.1127, Max-Change: 0.080257
EM iteration: 7, Loglike: -159633.1411, Max-Change: 0.066343
EM iteration: 8, Loglike: -159627.6844, Max-Change: 0.055853
EM iteration: 9, Loglike: -159624.2459, Max-Change: 0.047172
EM iteration: 10, Loglike: -159622.0120, Max-Change: 0.039781
EM iteration: 11, Loglike: -159620.5195, Max-Change: 0.033468
EM iteration: 12, Loglike: -159619.4950, Max-Change: 0.028101
EM iteration: 13, Loglike: -159618.7723, Max-Change: 0.023565
EM iteration: 14, Loglike: -159618.2481, Max-Change: 0.019752
EM iteration: 15, Loglike: -159617.8570, Max-Change: 0.016845
EM iteration: 16, Loglike: -159617.5566, Max-Change: 0.014864
EM iteration: 17, Loglike: -159617.3191, Max-Change: 0.01318
EM iteration: 18, Loglike: -159617.1261, Max-Change: 0.011751
EM iteration: 19, Loglike: -159616.9650, Max-Change: 0.010538
EM iteration: 20, Loglike: -159616.8273, Max-Change: 0.009507
EM iteration: 21, Loglike: -159616.7072, Max-Change: 0.008626
EM iteration: 22, Loglike: -159616.6005, Max-Change: 0.007869
EM iteration: 23, Loglike: -159616.5042, Max-Change: 0.007214
EM iteration: 24, Loglike: -159616.4163, Max-Change: 0.006643
EM iteration: 25, Loglike: -159616.3352, Max-Change: 0.006141
EM iteration: 26, Loglike: -159616.2596, Max-Change: 0.005695
EM iteration: 27, Loglike: -159616.1888, Max-Change: 0.005295
EM iteration: 28, Loglike: -159616.1221, Max-Change: 0.004934
EM iteration: 29, Loglike: -159616.0589, Max-Change: 0.004606
EM iteration: 30, Loglike: -159615.9989, Max-Change: 0.004306
EM iteration: 31, Loglike: -159615.9416, Max-Change: 0.00403
EM iteration: 32, Loglike: -159615.8868, Max-Change: 0.003774
EM iteration: 33, Loglike: -159615.8343, Max-Change: 0.003537
EM iteration: 34, Loglike: -159615.7838, Max-Change: 0.003317
EM iteration: 35, Loglike: -159615.7352, Max-Change: 0.003111
EM iteration: 36, Loglike: -159615.6884, Max-Change: 0.002919
EM iteration: 37, Loglike: -159615.6431, Max-Change: 0.00274
EM iteration: 38, Loglike: -159615.5994, Max-Change: 0.002572
EM iteration: 39, Loglike: -159615.5570, Max-Change: 0.002416
EM iteration: 40, Loglike: -159615.5159, Max-Change: 0.002269
EM iteration: 41, Loglike: -159615.4761, Max-Change: 0.002131
EM iteration: 42, Loglike: -159615.4373, Max-Change: 0.002003
EM iteration: 43, Loglike: -159615.3997, Max-Change: 0.001882
EM iteration: 44, Loglike: -159615.3630, Max-Change: 0.00177
EM iteration: 45, Loglike: -159615.3274, Max-Change: 0.001665
EM iteration: 46, Loglike: -159615.2926, Max-Change: 0.001566
EM iteration: 47, Loglike: -159615.2587, Max-Change: 0.001474
EM iteration: 48, Loglike: -159615.2256, Max-Change: 0.001388
EM iteration: 49, Loglike: -159615.1933, Max-Change: 0.001308
EM iteration: 50, Loglike: -159615.1617, Max-Change: 0.001232
EM iteration: 51, Loglike: -159615.1309, Max-Change: 0.001162
EM iteration: 52, Loglike: -159615.1007, Max-Change: 0.001097
EM iteration: 53, Loglike: -159615.0711, Max-Change: 0.001035
EM iteration: 54, Loglike: -159615.0422, Max-Change: 0.000978
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 8.83 seconds.
# Summary of the estimation
summary(fit.3)
#>
#> Call:
#> est_mg(x = x, data = data, group.name = group.name, D = 1, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
#> fipc.method = "MEM", fix.loc = fix.loc)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 294
#> Number of fixed items:
#> Overall: 22
#> By group: 12(Group1), 22(Group2), 10(Group3)
#> Number of E-step cycles completed: 54
#> Maximum parameter change: 0.0009779691
#>
#> Processing time (in seconds)
#> EM algorithm: 8.14
#> Standard error computation: 0.15
#> Total computation: 8.83
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are satisfied.
#> Second-order test: Solution is a possible local maximum.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates is obtainable.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 319230.1
#> By group: 120354.311(Group1), 113985.392(Group2), 84890.382(Group3)
#>
#> Akaike Information Criterion (AIC): 319818.1
#> Bayesian Information Criterion (BIC): 321787.7
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 C1I1 2 3PLM 0.76 NA 1.46 NA 0.26 NA NA NA
#> 2 C1I2 2 3PLM 1.92 NA -1.05 NA 0.18 NA NA NA
#> 3 C1I3 2 3PLM 0.93 NA 0.39 NA 0.10 NA NA NA
#> 4 C1I4 2 3PLM 1.05 NA -0.41 NA 0.20 NA NA NA
#> 5 C1I5 2 3PLM 0.87 NA -0.12 NA 0.16 NA NA NA
#> 6 C1I6 2 3PLM 1.70 NA 0.63 NA 0.07 NA NA NA
#> 7 C1I7 2 3PLM 0.91 NA 1.02 NA 0.12 NA NA NA
#> 8 C1I8 2 3PLM 0.84 NA 0.80 NA 0.11 NA NA NA
#> 9 C1I9 2 3PLM 0.85 NA 0.85 NA 0.26 NA NA NA
#> 10 C1I10 2 3PLM 1.53 NA 0.09 NA 0.14 NA NA NA
#> 11 G1I1 2 3PLM 0.96 0.10 -0.46 0.20 0.16 0.07 NA NA
#> 12 G1I2 2 3PLM 0.88 0.13 1.21 0.14 0.10 0.04 NA NA
#> 13 G1I3 2 3PLM 1.49 0.26 1.31 0.09 0.18 0.03 NA NA
#> 14 G1I4 2 3PLM 1.52 0.21 0.27 0.12 0.30 0.04 NA NA
#> 15 G1I5 2 3PLM 1.33 0.14 -0.18 0.13 0.16 0.05 NA NA
#> 16 G1I6 2 3PLM 2.15 0.18 0.01 0.05 0.08 0.03 NA NA
#> 17 G1I7 2 3PLM 1.45 0.16 -0.07 0.12 0.20 0.05 NA NA
#> 18 G1I8 2 3PLM 2.50 0.46 1.18 0.07 0.32 0.02 NA NA
#> 19 G1I9 2 3PLM 2.40 0.26 -0.93 0.11 0.24 0.06 NA NA
#> 20 G1I10 2 3PLM 1.26 0.13 -1.75 0.23 0.24 0.10 NA NA
#> 21 G1I11 2 3PLM 1.55 0.15 -1.11 0.16 0.21 0.08 NA NA
#> 22 G1I12 2 3PLM 0.75 0.09 -0.81 0.31 0.19 0.08 NA NA
#> 23 G1I13 2 3PLM 1.04 0.14 -0.13 0.21 0.20 0.07 NA NA
#> 24 G1I14 2 3PLM 1.46 0.37 1.77 0.15 0.30 0.03 NA NA
#> 25 G1I15 2 3PLM 0.86 0.09 -1.44 0.29 0.21 0.09 NA NA
#> 26 G1I16 2 3PLM 1.05 0.11 -1.95 0.27 0.23 0.10 NA NA
#> 27 G1I17 2 3PLM 1.04 0.13 0.25 0.15 0.15 0.05 NA NA
#> 28 G1I18 2 3PLM 2.08 0.20 -0.09 0.08 0.24 0.04 NA NA
#> 29 G1I19 2 3PLM 1.32 0.13 -1.38 0.19 0.20 0.08 NA NA
#> 30 G1I20 2 3PLM 1.01 0.17 0.51 0.19 0.22 0.06 NA NA
#> 31 G1I21 2 3PLM 0.92 0.13 0.77 0.15 0.13 0.05 NA NA
#> 32 G1I22 2 3PLM 1.77 0.21 -0.65 0.16 0.35 0.06 NA NA
#> 33 G1I23 2 3PLM 1.31 0.15 -1.17 0.23 0.25 0.09 NA NA
#> 34 G1I24 2 3PLM 1.64 0.19 0.32 0.10 0.23 0.04 NA NA
#> 35 G1I25 2 3PLM 1.58 0.18 -0.13 0.12 0.25 0.05 NA NA
#> 36 G1I26 2 3PLM 1.88 0.25 0.66 0.08 0.25 0.03 NA NA
#> 37 G1I27 2 3PLM 1.63 0.18 -1.54 0.20 0.27 0.10 NA NA
#> 38 G1I28 2 3PLM 1.33 0.16 0.57 0.10 0.15 0.04 NA NA
#> 39 G1I29 2 3PLM 0.92 0.09 -0.37 0.17 0.12 0.05 NA NA
#> 40 G1I30 2 3PLM 1.00 0.27 2.30 0.25 0.17 0.03 NA NA
#> 41 G1I31 2 3PLM 2.39 0.46 1.64 0.09 0.18 0.01 NA NA
#> 42 G1I32 2 3PLM 1.10 0.12 -0.08 0.15 0.15 0.05 NA NA
#> 43 G1I33 2 3PLM 1.60 0.17 0.18 0.09 0.16 0.04 NA NA
#> 44 G1I34 2 3PLM 1.33 0.13 0.24 0.09 0.11 0.04 NA NA
#> 45 G1I35 2 3PLM 1.33 0.17 1.30 0.08 0.07 0.02 NA NA
#> 46 G1I36 2 3PLM 1.44 0.14 -1.23 0.19 0.22 0.09 NA NA
#> 47 G1I37 2 3PLM 1.05 0.14 -0.60 0.27 0.27 0.09 NA NA
#> 48 G1I38 5 GRM 1.06 0.06 -0.37 0.05 0.22 0.05 0.87 0.06
#> 49 C1I11 5 GRM 1.23 NA -2.08 NA -1.35 NA -0.71 NA
#> 50 C1I12 5 GRM 0.88 NA -0.76 NA -0.01 NA 0.67 NA
#> 51 G2I1 2 3PLM 1.74 0.19 -0.87 0.17 0.23 0.10 NA NA
#> 52 G2I2 2 3PLM 0.83 0.11 -0.45 0.31 0.21 0.09 NA NA
#> 53 G2I3 2 3PLM 1.06 0.13 0.08 0.20 0.18 0.07 NA NA
#> 54 G2I4 2 3PLM 1.45 0.28 1.50 0.10 0.18 0.04 NA NA
#> 55 G2I5 2 3PLM 0.70 0.10 -1.68 0.40 0.20 0.09 NA NA
#> 56 G2I6 2 3PLM 1.08 0.14 -1.60 0.29 0.22 0.09 NA NA
#> 57 G2I7 2 3PLM 1.30 0.13 0.27 0.12 0.13 0.05 NA NA
#> 58 G2I8 2 3PLM 2.18 0.19 -0.09 0.08 0.14 0.05 NA NA
#> 59 G2I9 2 3PLM 1.07 0.13 -1.57 0.28 0.21 0.09 NA NA
#> 60 G2I10 2 3PLM 1.59 0.27 0.90 0.12 0.29 0.05 NA NA
#> 61 G2I11 2 3PLM 0.93 0.12 0.88 0.15 0.11 0.05 NA NA
#> 62 G2I12 2 3PLM 1.66 0.18 -0.70 0.18 0.25 0.10 NA NA
#> 63 G2I13 2 3PLM 1.16 0.13 -1.31 0.24 0.21 0.09 NA NA
#> 64 G2I14 2 3PLM 1.39 0.14 0.22 0.11 0.13 0.05 NA NA
#> 65 G2I15 2 3PLM 1.53 0.20 0.03 0.17 0.26 0.08 NA NA
#> 66 G2I16 2 3PLM 1.70 0.23 0.75 0.10 0.21 0.05 NA NA
#> 67 G2I17 2 3PLM 2.11 0.22 -1.20 0.14 0.20 0.09 NA NA
#> 68 G2I18 2 3PLM 1.72 0.20 0.64 0.08 0.14 0.04 NA NA
#> 69 G2I19 2 3PLM 1.10 0.14 0.05 0.22 0.21 0.08 NA NA
#> 70 G2I20 2 3PLM 1.62 0.45 2.24 0.19 0.16 0.02 NA NA
#> 71 G2I21 2 3PLM 2.39 0.36 1.59 0.06 0.12 0.02 NA NA
#> 72 G2I22 2 3PLM 1.43 0.17 0.22 0.15 0.20 0.07 NA NA
#> 73 G2I23 2 3PLM 2.09 0.26 0.44 0.10 0.28 0.05 NA NA
#> 74 G2I24 2 3PLM 1.40 0.12 0.37 0.08 0.07 0.03 NA NA
#> 75 G2I25 2 3PLM 1.74 0.22 1.42 0.06 0.07 0.02 NA NA
#> 76 G2I26 2 3PLM 1.89 0.20 -0.88 0.16 0.24 0.10 NA NA
#> 77 G2I27 2 3PLM 0.98 0.12 -0.59 0.25 0.20 0.09 NA NA
#> 78 G2I28 5 GRM 1.12 0.07 -0.37 0.07 0.15 0.05 0.80 0.05
#> 79 C2I1 2 3PLM 0.97 NA -0.46 NA 0.05 NA NA NA
#> 80 C2I2 2 3PLM 0.85 NA 1.18 NA 0.01 NA NA NA
#> 81 C2I3 2 3PLM 1.43 NA 1.41 NA 0.10 NA NA NA
#> 82 C2I4 2 3PLM 1.48 NA 0.18 NA 0.17 NA NA NA
#> 83 C2I5 2 3PLM 1.27 NA -0.23 NA 0.03 NA NA NA
#> 84 C2I6 2 3PLM 2.02 NA -0.09 NA 0.01 NA NA NA
#> 85 C2I7 2 3PLM 1.37 NA -0.13 NA 0.10 NA NA NA
#> 86 C2I8 2 3PLM 1.67 NA 1.25 NA 0.19 NA NA NA
#> 87 C2I9 2 3PLM 2.28 NA -1.01 NA 0.10 NA NA NA
#> 88 C2I10 2 3PLM 1.42 NA -1.65 NA 0.11 NA NA NA
#> 89 G3I1 2 3PLM 1.60 0.14 -1.04 0.12 0.14 0.05 NA NA
#> 90 G3I2 2 3PLM 0.79 0.09 -0.62 0.25 0.16 0.07 NA NA
#> 91 G3I3 2 3PLM 1.16 0.12 0.07 0.12 0.16 0.04 NA NA
#> 92 G3I4 2 3PLM 1.30 0.24 1.72 0.12 0.22 0.02 NA NA
#> 93 G3I5 2 3PLM 0.80 0.10 -1.09 0.33 0.24 0.09 NA NA
#> 94 G3I6 2 3PLM 1.18 0.13 -1.38 0.24 0.26 0.08 NA NA
#> 95 G3I7 2 3PLM 1.37 0.13 0.26 0.09 0.13 0.03 NA NA
#> 96 G3I8 2 3PLM 1.95 0.18 -0.07 0.06 0.14 0.02 NA NA
#> 97 G3I9 2 3PLM 1.18 0.11 -1.16 0.19 0.18 0.07 NA NA
#> 98 G3I10 2 3PLM 1.50 0.21 0.98 0.10 0.29 0.02 NA NA
#> 99 G3I11 2 3PLM 0.91 0.10 0.80 0.11 0.08 0.03 NA NA
#> 100 G3I12 2 3PLM 1.44 0.17 -0.78 0.15 0.23 0.06 NA NA
#> 101 G3I13 2 3PLM 1.15 0.13 -1.06 0.20 0.21 0.07 NA NA
#> 102 G3I14 2 3PLM 1.38 0.14 0.31 0.09 0.16 0.03 NA NA
#> 103 G3I15 2 3PLM 1.29 0.13 -0.06 0.11 0.18 0.04 NA NA
#> 104 G3I16 2 3PLM 1.58 0.18 0.75 0.08 0.20 0.02 NA NA
#> 105 G3I17 2 3PLM 1.72 0.15 -1.46 0.13 0.16 0.06 NA NA
#> 106 G3I18 2 3PLM 1.37 0.14 0.71 0.08 0.11 0.02 NA NA
#> 107 G3I19 2 3PLM 0.99 0.11 0.07 0.15 0.15 0.04 NA NA
#> 108 G3I20 2 3PLM 1.14 0.23 2.30 0.20 0.12 0.02 NA NA
#> 109 G3I21 2 3PLM 2.97 0.55 1.66 0.06 0.14 0.01 NA NA
#> 110 G3I22 2 3PLM 1.19 0.11 0.10 0.10 0.10 0.03 NA NA
#> 111 G3I23 2 3PLM 1.79 0.17 0.33 0.06 0.15 0.02 NA NA
#> 112 G3I24 2 3PLM 1.15 0.09 0.34 0.08 0.05 0.02 NA NA
#> 113 G3I25 2 3PLM 1.38 0.15 1.36 0.08 0.05 0.01 NA NA
#> 114 G3I26 2 3PLM 1.72 0.17 -0.96 0.12 0.20 0.05 NA NA
#> 115 G3I27 2 3PLM 0.95 0.10 -0.61 0.20 0.16 0.06 NA NA
#> 116 G3I28 5 GRM 1.00 0.05 -0.31 0.05 0.19 0.05 0.82 0.07
#> par.5 se.5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 NA NA
#> 5 NA NA
#> 6 NA NA
#> 7 NA NA
#> 8 NA NA
#> 9 NA NA
#> 10 NA NA
#> 11 NA NA
#> 12 NA NA
#> 13 NA NA
#> 14 NA NA
#> 15 NA NA
#> 16 NA NA
#> 17 NA NA
#> 18 NA NA
#> 19 NA NA
#> 20 NA NA
#> 21 NA NA
#> 22 NA NA
#> 23 NA NA
#> 24 NA NA
#> 25 NA NA
#> 26 NA NA
#> 27 NA NA
#> 28 NA NA
#> 29 NA NA
#> 30 NA NA
#> 31 NA NA
#> 32 NA NA
#> 33 NA NA
#> 34 NA NA
#> 35 NA NA
#> 36 NA NA
#> 37 NA NA
#> 38 NA NA
#> 39 NA NA
#> 40 NA NA
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 1.44 0.08
#> 49 -0.12 NA
#> 50 1.25 NA
#> 51 NA NA
#> 52 NA NA
#> 53 NA NA
#> 54 NA NA
#> 55 NA NA
#> 56 NA NA
#> 57 NA NA
#> 58 NA NA
#> 59 NA NA
#> 60 NA NA
#> 61 NA NA
#> 62 NA NA
#> 63 NA NA
#> 64 NA NA
#> 65 NA NA
#> 66 NA NA
#> 67 NA NA
#> 68 NA NA
#> 69 NA NA
#> 70 NA NA
#> 71 NA NA
#> 72 NA NA
#> 73 NA NA
#> 74 NA NA
#> 75 NA NA
#> 76 NA NA
#> 77 NA NA
#> 78 1.48 0.07
#> 79 NA NA
#> 80 NA NA
#> 81 NA NA
#> 82 NA NA
#> 83 NA NA
#> 84 NA NA
#> 85 NA NA
#> 86 NA NA
#> 87 NA NA
#> 88 NA NA
#> 89 NA NA
#> 90 NA NA
#> 91 NA NA
#> 92 NA NA
#> 93 NA NA
#> 94 NA NA
#> 95 NA NA
#> 96 NA NA
#> 97 NA NA
#> 98 NA NA
#> 99 NA NA
#> 100 NA NA
#> 101 NA NA
#> 102 NA NA
#> 103 NA NA
#> 104 NA NA
#> 105 NA NA
#> 106 NA NA
#> 107 NA NA
#> 108 NA NA
#> 109 NA NA
#> 110 NA NA
#> 111 NA NA
#> 112 NA NA
#> 113 NA NA
#> 114 NA NA
#> 115 NA NA
#> 116 1.52 0.09
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) -0.01 1.01 1.01
#> se(Group1) 0.02 0.03 0.02
#> estimate(Group2) 0.50 0.58 0.76
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.28 1.66 1.29
#> se(Group3) 0.03 0.05 0.02
#>
# Extract the item parameter estimates
getirt(fit.3, what = "par.est")
#> $overall
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.7600000 1.46000000 0.26000000 NA NA
#> 2 C1I2 2 3PLM 1.9200000 -1.05000000 0.18000000 NA NA
#> 3 C1I3 2 3PLM 0.9300000 0.39000000 0.10000000 NA NA
#> 4 C1I4 2 3PLM 1.0500000 -0.41000000 0.20000000 NA NA
#> 5 C1I5 2 3PLM 0.8700000 -0.12000000 0.16000000 NA NA
#> 6 C1I6 2 3PLM 1.7000000 0.63000000 0.07000000 NA NA
#> 7 C1I7 2 3PLM 0.9100000 1.02000000 0.12000000 NA NA
#> 8 C1I8 2 3PLM 0.8400000 0.80000000 0.11000000 NA NA
#> 9 C1I9 2 3PLM 0.8500000 0.85000000 0.26000000 NA NA
#> 10 C1I10 2 3PLM 1.5300000 0.09000000 0.14000000 NA NA
#> 11 G1I1 2 3PLM 0.9601094 -0.46323480 0.15743926 NA NA
#> 12 G1I2 2 3PLM 0.8792351 1.21120501 0.10365721 NA NA
#> 13 G1I3 2 3PLM 1.4922037 1.31254694 0.18433436 NA NA
#> 14 G1I4 2 3PLM 1.5246246 0.26709705 0.29751014 NA NA
#> 15 G1I5 2 3PLM 1.3343885 -0.18476888 0.15642097 NA NA
#> 16 G1I6 2 3PLM 2.1457296 0.01122821 0.08373745 NA NA
#> 17 G1I7 2 3PLM 1.4492421 -0.07232467 0.19831474 NA NA
#> 18 G1I8 2 3PLM 2.4981366 1.18142115 0.32459740 NA NA
#> 19 G1I9 2 3PLM 2.4036619 -0.93389393 0.24090792 NA NA
#> 20 G1I10 2 3PLM 1.2603565 -1.75076139 0.23712596 NA NA
#> 21 G1I11 2 3PLM 1.5482444 -1.11447546 0.20564573 NA NA
#> 22 G1I12 2 3PLM 0.7501881 -0.81274221 0.19483606 NA NA
#> 23 G1I13 2 3PLM 1.0391850 -0.13129452 0.20305864 NA NA
#> 24 G1I14 2 3PLM 1.4641086 1.76817734 0.29587746 NA NA
#> 25 G1I15 2 3PLM 0.8642507 -1.44005202 0.21246953 NA NA
#> 26 G1I16 2 3PLM 1.0481967 -1.94936219 0.22996558 NA NA
#> 27 G1I17 2 3PLM 1.0413440 0.24963719 0.15297903 NA NA
#> 28 G1I18 2 3PLM 2.0821164 -0.08782853 0.23783714 NA NA
#> 29 G1I19 2 3PLM 1.3246385 -1.38457105 0.20248019 NA NA
#> 30 G1I20 2 3PLM 1.0078270 0.50901778 0.22362359 NA NA
#> 31 G1I21 2 3PLM 0.9153677 0.76786397 0.13229024 NA NA
#> 32 G1I22 2 3PLM 1.7709516 -0.64567759 0.35461144 NA NA
#> 33 G1I23 2 3PLM 1.3100376 -1.16619310 0.25418714 NA NA
#> 34 G1I24 2 3PLM 1.6392138 0.31576653 0.22824910 NA NA
#> 35 G1I25 2 3PLM 1.5820253 -0.12733170 0.25023679 NA NA
#> 36 G1I26 2 3PLM 1.8799489 0.66003503 0.25368918 NA NA
#> 37 G1I27 2 3PLM 1.6294671 -1.53964203 0.27165399 NA NA
#> 38 G1I28 2 3PLM 1.3331814 0.56546916 0.14913136 NA NA
#> 39 G1I29 2 3PLM 0.9154613 -0.37004169 0.12429485 NA NA
#> 40 G1I30 2 3PLM 1.0026860 2.29722730 0.16842602 NA NA
#> 41 G1I31 2 3PLM 2.3881153 1.64223591 0.18163836 NA NA
#> 42 G1I32 2 3PLM 1.1031428 -0.07825039 0.14531435 NA NA
#> 43 G1I33 2 3PLM 1.5998724 0.17672610 0.15654349 NA NA
#> 44 G1I34 2 3PLM 1.3266408 0.24185668 0.10791955 NA NA
#> 45 G1I35 2 3PLM 1.3307122 1.29621629 0.06712955 NA NA
#> 46 G1I36 2 3PLM 1.4375780 -1.23256008 0.21920779 NA NA
#> 47 G1I37 2 3PLM 1.0523257 -0.59860569 0.26551312 NA NA
#> 48 G1I38 5 GRM 1.0557817 -0.36687770 0.21653854 0.8654794 1.435633
#> 49 C1I11 5 GRM 1.2300000 -2.08000000 -1.35000000 -0.7100000 -0.120000
#> 50 C1I12 5 GRM 0.8800000 -0.76000000 -0.01000000 0.6700000 1.250000
#> 51 G2I1 2 3PLM 1.7426027 -0.86693468 0.23241989 NA NA
#> 52 G2I2 2 3PLM 0.8271656 -0.44864390 0.21072500 NA NA
#> 53 G2I3 2 3PLM 1.0594812 0.08411544 0.17868700 NA NA
#> 54 G2I4 2 3PLM 1.4496890 1.49538158 0.17845021 NA NA
#> 55 G2I5 2 3PLM 0.7000088 -1.68320349 0.19753124 NA NA
#> 56 G2I6 2 3PLM 1.0845772 -1.60171524 0.21553624 NA NA
#> 57 G2I7 2 3PLM 1.2984963 0.26873160 0.12783879 NA NA
#> 58 G2I8 2 3PLM 2.1768681 -0.08931817 0.13528274 NA NA
#> 59 G2I9 2 3PLM 1.0731850 -1.56763064 0.20570964 NA NA
#> 60 G2I10 2 3PLM 1.5904952 0.90286013 0.28755659 NA NA
#> 61 G2I11 2 3PLM 0.9314018 0.88217244 0.11179900 NA NA
#> 62 G2I12 2 3PLM 1.6623481 -0.69600414 0.24746346 NA NA
#> 63 G2I13 2 3PLM 1.1643479 -1.30658561 0.20913476 NA NA
#> 64 G2I14 2 3PLM 1.3949743 0.22018889 0.12742097 NA NA
#> 65 G2I15 2 3PLM 1.5256012 0.03274459 0.25930675 NA NA
#> 66 G2I16 2 3PLM 1.6958062 0.75377859 0.21478247 NA NA
#> 67 G2I17 2 3PLM 2.1138538 -1.19916943 0.19757122 NA NA
#> 68 G2I18 2 3PLM 1.7193451 0.64117712 0.13803059 NA NA
#> 69 G2I19 2 3PLM 1.0971580 0.04569867 0.20768248 NA NA
#> 70 G2I20 2 3PLM 1.6230735 2.23612968 0.15952981 NA NA
#> 71 G2I21 2 3PLM 2.3884669 1.58525725 0.11741983 NA NA
#> 72 G2I22 2 3PLM 1.4332531 0.22129279 0.20450739 NA NA
#> 73 G2I23 2 3PLM 2.0941037 0.44296609 0.27618451 NA NA
#> 74 G2I24 2 3PLM 1.3973606 0.36942946 0.07288178 NA NA
#> 75 G2I25 2 3PLM 1.7363207 1.41508375 0.07191836 NA NA
#> 76 G2I26 2 3PLM 1.8858048 -0.88197041 0.23993266 NA NA
#> 77 G2I27 2 3PLM 0.9754090 -0.59038894 0.19672791 NA NA
#> 78 G2I28 5 GRM 1.1216203 -0.37176001 0.15040063 0.7990619 1.476485
#> 79 C2I1 2 3PLM 0.9700000 -0.46000000 0.05000000 NA NA
#> 80 C2I2 2 3PLM 0.8500000 1.18000000 0.01000000 NA NA
#> 81 C2I3 2 3PLM 1.4300000 1.41000000 0.10000000 NA NA
#> 82 C2I4 2 3PLM 1.4800000 0.18000000 0.17000000 NA NA
#> 83 C2I5 2 3PLM 1.2700000 -0.23000000 0.03000000 NA NA
#> 84 C2I6 2 3PLM 2.0200000 -0.09000000 0.01000000 NA NA
#> 85 C2I7 2 3PLM 1.3700000 -0.13000000 0.10000000 NA NA
#> 86 C2I8 2 3PLM 1.6700000 1.25000000 0.19000000 NA NA
#> 87 C2I9 2 3PLM 2.2800000 -1.01000000 0.10000000 NA NA
#> 88 C2I10 2 3PLM 1.4200000 -1.65000000 0.11000000 NA NA
#> 89 G3I1 2 3PLM 1.5973952 -1.04293518 0.14221272 NA NA
#> 90 G3I2 2 3PLM 0.7882034 -0.61710502 0.16466619 NA NA
#> 91 G3I3 2 3PLM 1.1574588 0.07488161 0.15704670 NA NA
#> 92 G3I4 2 3PLM 1.3010656 1.72470571 0.22305233 NA NA
#> 93 G3I5 2 3PLM 0.8030039 -1.08728779 0.23797751 NA NA
#> 94 G3I6 2 3PLM 1.1828479 -1.37600012 0.26017944 NA NA
#> 95 G3I7 2 3PLM 1.3732288 0.26144127 0.13453648 NA NA
#> 96 G3I8 2 3PLM 1.9483776 -0.06609774 0.14303723 NA NA
#> 97 G3I9 2 3PLM 1.1769474 -1.16424114 0.18147943 NA NA
#> 98 G3I10 2 3PLM 1.4966087 0.98263824 0.28748102 NA NA
#> 99 G3I11 2 3PLM 0.9143147 0.79757776 0.07731952 NA NA
#> 100 G3I12 2 3PLM 1.4413693 -0.77635289 0.23363873 NA NA
#> 101 G3I13 2 3PLM 1.1547205 -1.06358212 0.20951365 NA NA
#> 102 G3I14 2 3PLM 1.3766468 0.30600869 0.15853392 NA NA
#> 103 G3I15 2 3PLM 1.2913722 -0.05844768 0.17903882 NA NA
#> 104 G3I16 2 3PLM 1.5776924 0.75034401 0.19938501 NA NA
#> 105 G3I17 2 3PLM 1.7191587 -1.46022828 0.15855847 NA NA
#> 106 G3I18 2 3PLM 1.3690901 0.71412800 0.11276074 NA NA
#> 107 G3I19 2 3PLM 0.9937729 0.07222966 0.14756849 NA NA
#> 108 G3I20 2 3PLM 1.1444553 2.29572750 0.11629624 NA NA
#> 109 G3I21 2 3PLM 2.9714475 1.65685452 0.14005235 NA NA
#> 110 G3I22 2 3PLM 1.1948944 0.10009253 0.09517841 NA NA
#> 111 G3I23 2 3PLM 1.7915379 0.32938893 0.14617082 NA NA
#> 112 G3I24 2 3PLM 1.1522431 0.33724431 0.05080719 NA NA
#> 113 G3I25 2 3PLM 1.3842436 1.36390607 0.04998934 NA NA
#> 114 G3I26 2 3PLM 1.7163634 -0.96107355 0.19794829 NA NA
#> 115 G3I27 2 3PLM 0.9521484 -0.60866897 0.16408973 NA NA
#> 116 G3I28 5 GRM 0.9955303 -0.31405937 0.18617231 0.8178505 1.523770
#>
#> $group
#> $group$Group1
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.7600000 1.46000000 0.26000000 NA NA
#> 2 C1I2 2 3PLM 1.9200000 -1.05000000 0.18000000 NA NA
#> 3 C1I3 2 3PLM 0.9300000 0.39000000 0.10000000 NA NA
#> 4 C1I4 2 3PLM 1.0500000 -0.41000000 0.20000000 NA NA
#> 5 C1I5 2 3PLM 0.8700000 -0.12000000 0.16000000 NA NA
#> 6 C1I6 2 3PLM 1.7000000 0.63000000 0.07000000 NA NA
#> 7 C1I7 2 3PLM 0.9100000 1.02000000 0.12000000 NA NA
#> 8 C1I8 2 3PLM 0.8400000 0.80000000 0.11000000 NA NA
#> 9 C1I9 2 3PLM 0.8500000 0.85000000 0.26000000 NA NA
#> 10 C1I10 2 3PLM 1.5300000 0.09000000 0.14000000 NA NA
#> 11 G1I1 2 3PLM 0.9601094 -0.46323480 0.15743926 NA NA
#> 12 G1I2 2 3PLM 0.8792351 1.21120501 0.10365721 NA NA
#> 13 G1I3 2 3PLM 1.4922037 1.31254694 0.18433436 NA NA
#> 14 G1I4 2 3PLM 1.5246246 0.26709705 0.29751014 NA NA
#> 15 G1I5 2 3PLM 1.3343885 -0.18476888 0.15642097 NA NA
#> 16 G1I6 2 3PLM 2.1457296 0.01122821 0.08373745 NA NA
#> 17 G1I7 2 3PLM 1.4492421 -0.07232467 0.19831474 NA NA
#> 18 G1I8 2 3PLM 2.4981366 1.18142115 0.32459740 NA NA
#> 19 G1I9 2 3PLM 2.4036619 -0.93389393 0.24090792 NA NA
#> 20 G1I10 2 3PLM 1.2603565 -1.75076139 0.23712596 NA NA
#> 21 G1I11 2 3PLM 1.5482444 -1.11447546 0.20564573 NA NA
#> 22 G1I12 2 3PLM 0.7501881 -0.81274221 0.19483606 NA NA
#> 23 G1I13 2 3PLM 1.0391850 -0.13129452 0.20305864 NA NA
#> 24 G1I14 2 3PLM 1.4641086 1.76817734 0.29587746 NA NA
#> 25 G1I15 2 3PLM 0.8642507 -1.44005202 0.21246953 NA NA
#> 26 G1I16 2 3PLM 1.0481967 -1.94936219 0.22996558 NA NA
#> 27 G1I17 2 3PLM 1.0413440 0.24963719 0.15297903 NA NA
#> 28 G1I18 2 3PLM 2.0821164 -0.08782853 0.23783714 NA NA
#> 29 G1I19 2 3PLM 1.3246385 -1.38457105 0.20248019 NA NA
#> 30 G1I20 2 3PLM 1.0078270 0.50901778 0.22362359 NA NA
#> 31 G1I21 2 3PLM 0.9153677 0.76786397 0.13229024 NA NA
#> 32 G1I22 2 3PLM 1.7709516 -0.64567759 0.35461144 NA NA
#> 33 G1I23 2 3PLM 1.3100376 -1.16619310 0.25418714 NA NA
#> 34 G1I24 2 3PLM 1.6392138 0.31576653 0.22824910 NA NA
#> 35 G1I25 2 3PLM 1.5820253 -0.12733170 0.25023679 NA NA
#> 36 G1I26 2 3PLM 1.8799489 0.66003503 0.25368918 NA NA
#> 37 G1I27 2 3PLM 1.6294671 -1.53964203 0.27165399 NA NA
#> 38 G1I28 2 3PLM 1.3331814 0.56546916 0.14913136 NA NA
#> 39 G1I29 2 3PLM 0.9154613 -0.37004169 0.12429485 NA NA
#> 40 G1I30 2 3PLM 1.0026860 2.29722730 0.16842602 NA NA
#> 41 G1I31 2 3PLM 2.3881153 1.64223591 0.18163836 NA NA
#> 42 G1I32 2 3PLM 1.1031428 -0.07825039 0.14531435 NA NA
#> 43 G1I33 2 3PLM 1.5998724 0.17672610 0.15654349 NA NA
#> 44 G1I34 2 3PLM 1.3266408 0.24185668 0.10791955 NA NA
#> 45 G1I35 2 3PLM 1.3307122 1.29621629 0.06712955 NA NA
#> 46 G1I36 2 3PLM 1.4375780 -1.23256008 0.21920779 NA NA
#> 47 G1I37 2 3PLM 1.0523257 -0.59860569 0.26551312 NA NA
#> 48 G1I38 5 GRM 1.0557817 -0.36687770 0.21653854 0.8654794 1.435633
#> 49 C1I11 5 GRM 1.2300000 -2.08000000 -1.35000000 -0.7100000 -0.120000
#> 50 C1I12 5 GRM 0.8800000 -0.76000000 -0.01000000 0.6700000 1.250000
#>
#> $group$Group2
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM 0.7600000 1.46000000 0.26000000 NA NA
#> 2 C1I2 2 3PLM 1.9200000 -1.05000000 0.18000000 NA NA
#> 3 C1I3 2 3PLM 0.9300000 0.39000000 0.10000000 NA NA
#> 4 C1I4 2 3PLM 1.0500000 -0.41000000 0.20000000 NA NA
#> 5 C1I5 2 3PLM 0.8700000 -0.12000000 0.16000000 NA NA
#> 6 C1I6 2 3PLM 1.7000000 0.63000000 0.07000000 NA NA
#> 7 C1I7 2 3PLM 0.9100000 1.02000000 0.12000000 NA NA
#> 8 C1I8 2 3PLM 0.8400000 0.80000000 0.11000000 NA NA
#> 9 C1I9 2 3PLM 0.8500000 0.85000000 0.26000000 NA NA
#> 10 C1I10 2 3PLM 1.5300000 0.09000000 0.14000000 NA NA
#> 11 C1I11 5 GRM 1.2300000 -2.08000000 -1.35000000 -0.7100000 -0.120000
#> 12 C1I12 5 GRM 0.8800000 -0.76000000 -0.01000000 0.6700000 1.250000
#> 13 G2I1 2 3PLM 1.7426027 -0.86693468 0.23241989 NA NA
#> 14 G2I2 2 3PLM 0.8271656 -0.44864390 0.21072500 NA NA
#> 15 G2I3 2 3PLM 1.0594812 0.08411544 0.17868700 NA NA
#> 16 G2I4 2 3PLM 1.4496890 1.49538158 0.17845021 NA NA
#> 17 G2I5 2 3PLM 0.7000088 -1.68320349 0.19753124 NA NA
#> 18 G2I6 2 3PLM 1.0845772 -1.60171524 0.21553624 NA NA
#> 19 G2I7 2 3PLM 1.2984963 0.26873160 0.12783879 NA NA
#> 20 G2I8 2 3PLM 2.1768681 -0.08931817 0.13528274 NA NA
#> 21 G2I9 2 3PLM 1.0731850 -1.56763064 0.20570964 NA NA
#> 22 G2I10 2 3PLM 1.5904952 0.90286013 0.28755659 NA NA
#> 23 G2I11 2 3PLM 0.9314018 0.88217244 0.11179900 NA NA
#> 24 G2I12 2 3PLM 1.6623481 -0.69600414 0.24746346 NA NA
#> 25 G2I13 2 3PLM 1.1643479 -1.30658561 0.20913476 NA NA
#> 26 G2I14 2 3PLM 1.3949743 0.22018889 0.12742097 NA NA
#> 27 G2I15 2 3PLM 1.5256012 0.03274459 0.25930675 NA NA
#> 28 G2I16 2 3PLM 1.6958062 0.75377859 0.21478247 NA NA
#> 29 G2I17 2 3PLM 2.1138538 -1.19916943 0.19757122 NA NA
#> 30 G2I18 2 3PLM 1.7193451 0.64117712 0.13803059 NA NA
#> 31 G2I19 2 3PLM 1.0971580 0.04569867 0.20768248 NA NA
#> 32 G2I20 2 3PLM 1.6230735 2.23612968 0.15952981 NA NA
#> 33 G2I21 2 3PLM 2.3884669 1.58525725 0.11741983 NA NA
#> 34 G2I22 2 3PLM 1.4332531 0.22129279 0.20450739 NA NA
#> 35 G2I23 2 3PLM 2.0941037 0.44296609 0.27618451 NA NA
#> 36 G2I24 2 3PLM 1.3973606 0.36942946 0.07288178 NA NA
#> 37 G2I25 2 3PLM 1.7363207 1.41508375 0.07191836 NA NA
#> 38 G2I26 2 3PLM 1.8858048 -0.88197041 0.23993266 NA NA
#> 39 G2I27 2 3PLM 0.9754090 -0.59038894 0.19672791 NA NA
#> 40 G2I28 5 GRM 1.1216203 -0.37176001 0.15040063 0.7990619 1.476485
#> 41 C2I1 2 3PLM 0.9700000 -0.46000000 0.05000000 NA NA
#> 42 C2I2 2 3PLM 0.8500000 1.18000000 0.01000000 NA NA
#> 43 C2I3 2 3PLM 1.4300000 1.41000000 0.10000000 NA NA
#> 44 C2I4 2 3PLM 1.4800000 0.18000000 0.17000000 NA NA
#> 45 C2I5 2 3PLM 1.2700000 -0.23000000 0.03000000 NA NA
#> 46 C2I6 2 3PLM 2.0200000 -0.09000000 0.01000000 NA NA
#> 47 C2I7 2 3PLM 1.3700000 -0.13000000 0.10000000 NA NA
#> 48 C2I8 2 3PLM 1.6700000 1.25000000 0.19000000 NA NA
#> 49 C2I9 2 3PLM 2.2800000 -1.01000000 0.10000000 NA NA
#> 50 C2I10 2 3PLM 1.4200000 -1.65000000 0.11000000 NA NA
#>
#> $group$Group3
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C2I1 2 3PLM 0.9700000 -0.46000000 0.05000000 NA NA
#> 2 C2I2 2 3PLM 0.8500000 1.18000000 0.01000000 NA NA
#> 3 C2I3 2 3PLM 1.4300000 1.41000000 0.10000000 NA NA
#> 4 C2I4 2 3PLM 1.4800000 0.18000000 0.17000000 NA NA
#> 5 C2I5 2 3PLM 1.2700000 -0.23000000 0.03000000 NA NA
#> 6 C2I6 2 3PLM 2.0200000 -0.09000000 0.01000000 NA NA
#> 7 C2I7 2 3PLM 1.3700000 -0.13000000 0.10000000 NA NA
#> 8 C2I8 2 3PLM 1.6700000 1.25000000 0.19000000 NA NA
#> 9 C2I9 2 3PLM 2.2800000 -1.01000000 0.10000000 NA NA
#> 10 C2I10 2 3PLM 1.4200000 -1.65000000 0.11000000 NA NA
#> 11 G3I1 2 3PLM 1.5973952 -1.04293518 0.14221272 NA NA
#> 12 G3I2 2 3PLM 0.7882034 -0.61710502 0.16466619 NA NA
#> 13 G3I3 2 3PLM 1.1574588 0.07488161 0.15704670 NA NA
#> 14 G3I4 2 3PLM 1.3010656 1.72470571 0.22305233 NA NA
#> 15 G3I5 2 3PLM 0.8030039 -1.08728779 0.23797751 NA NA
#> 16 G3I6 2 3PLM 1.1828479 -1.37600012 0.26017944 NA NA
#> 17 G3I7 2 3PLM 1.3732288 0.26144127 0.13453648 NA NA
#> 18 G3I8 2 3PLM 1.9483776 -0.06609774 0.14303723 NA NA
#> 19 G3I9 2 3PLM 1.1769474 -1.16424114 0.18147943 NA NA
#> 20 G3I10 2 3PLM 1.4966087 0.98263824 0.28748102 NA NA
#> 21 G3I11 2 3PLM 0.9143147 0.79757776 0.07731952 NA NA
#> 22 G3I12 2 3PLM 1.4413693 -0.77635289 0.23363873 NA NA
#> 23 G3I13 2 3PLM 1.1547205 -1.06358212 0.20951365 NA NA
#> 24 G3I14 2 3PLM 1.3766468 0.30600869 0.15853392 NA NA
#> 25 G3I15 2 3PLM 1.2913722 -0.05844768 0.17903882 NA NA
#> 26 G3I16 2 3PLM 1.5776924 0.75034401 0.19938501 NA NA
#> 27 G3I17 2 3PLM 1.7191587 -1.46022828 0.15855847 NA NA
#> 28 G3I18 2 3PLM 1.3690901 0.71412800 0.11276074 NA NA
#> 29 G3I19 2 3PLM 0.9937729 0.07222966 0.14756849 NA NA
#> 30 G3I20 2 3PLM 1.1444553 2.29572750 0.11629624 NA NA
#> 31 G3I21 2 3PLM 2.9714475 1.65685452 0.14005235 NA NA
#> 32 G3I22 2 3PLM 1.1948944 0.10009253 0.09517841 NA NA
#> 33 G3I23 2 3PLM 1.7915379 0.32938893 0.14617082 NA NA
#> 34 G3I24 2 3PLM 1.1522431 0.33724431 0.05080719 NA NA
#> 35 G3I25 2 3PLM 1.3842436 1.36390607 0.04998934 NA NA
#> 36 G3I26 2 3PLM 1.7163634 -0.96107355 0.19794829 NA NA
#> 37 G3I27 2 3PLM 0.9521484 -0.60866897 0.16408973 NA NA
#> 38 G3I28 5 GRM 0.9955303 -0.31405937 0.18617231 0.8178505 1.52377
#>
#>
# Extract the standard error estimates
getirt(fit.3, what = "se.est")
#> $overall
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM NA NA NA NA NA
#> 2 C1I2 2 3PLM NA NA NA NA NA
#> 3 C1I3 2 3PLM NA NA NA NA NA
#> 4 C1I4 2 3PLM NA NA NA NA NA
#> 5 C1I5 2 3PLM NA NA NA NA NA
#> 6 C1I6 2 3PLM NA NA NA NA NA
#> 7 C1I7 2 3PLM NA NA NA NA NA
#> 8 C1I8 2 3PLM NA NA NA NA NA
#> 9 C1I9 2 3PLM NA NA NA NA NA
#> 10 C1I10 2 3PLM NA NA NA NA NA
#> 11 G1I1 2 3PLM 0.10426168 0.19914118 0.06583145 NA NA
#> 12 G1I2 2 3PLM 0.13011827 0.13758723 0.03866179 NA NA
#> 13 G1I3 2 3PLM 0.25521536 0.09288148 0.02598262 NA NA
#> 14 G1I4 2 3PLM 0.21216024 0.12139692 0.04369469 NA NA
#> 15 G1I5 2 3PLM 0.13737157 0.12762451 0.05144114 NA NA
#> 16 G1I6 2 3PLM 0.17837536 0.05370898 0.02614114 NA NA
#> 17 G1I7 2 3PLM 0.15675133 0.12128691 0.04842894 NA NA
#> 18 G1I8 2 3PLM 0.46148303 0.06925484 0.01882411 NA NA
#> 19 G1I9 2 3PLM 0.25992134 0.10854364 0.06176901 NA NA
#> 20 G1I10 2 3PLM 0.12525002 0.22773298 0.09804119 NA NA
#> 21 G1I11 2 3PLM 0.14906877 0.16092483 0.07743255 NA NA
#> 22 G1I12 2 3PLM 0.09144445 0.31119356 0.08351947 NA NA
#> 23 G1I13 2 3PLM 0.13678756 0.20744666 0.06854745 NA NA
#> 24 G1I14 2 3PLM 0.36846246 0.15351046 0.02514203 NA NA
#> 25 G1I15 2 3PLM 0.09478648 0.29483636 0.09102878 NA NA
#> 26 G1I16 2 3PLM 0.10986557 0.26721069 0.09771458 NA NA
#> 27 G1I17 2 3PLM 0.12646970 0.15451738 0.05176849 NA NA
#> 28 G1I18 2 3PLM 0.20058125 0.08013120 0.03656393 NA NA
#> 29 G1I19 2 3PLM 0.12663826 0.19277821 0.08479494 NA NA
#> 30 G1I20 2 3PLM 0.17409361 0.19113321 0.06033487 NA NA
#> 31 G1I21 2 3PLM 0.13256306 0.15087630 0.04704321 NA NA
#> 32 G1I22 2 3PLM 0.21340356 0.15629299 0.06435608 NA NA
#> 33 G1I23 2 3PLM 0.14898851 0.22567950 0.09214904 NA NA
#> 34 G1I24 2 3PLM 0.19188388 0.09525298 0.03753622 NA NA
#> 35 G1I25 2 3PLM 0.17877681 0.12332508 0.04964582 NA NA
#> 36 G1I26 2 3PLM 0.25183655 0.07738128 0.02912676 NA NA
#> 37 G1I27 2 3PLM 0.17771713 0.20258618 0.10060823 NA NA
#> 38 G1I28 2 3PLM 0.16142785 0.09763951 0.03660579 NA NA
#> 39 G1I29 2 3PLM 0.08893330 0.17133724 0.05492922 NA NA
#> 40 G1I30 2 3PLM 0.26897282 0.25352870 0.03089404 NA NA
#> 41 G1I31 2 3PLM 0.46169957 0.09359258 0.01431405 NA NA
#> 42 G1I32 2 3PLM 0.11905116 0.15068461 0.05352540 NA NA
#> 43 G1I33 2 3PLM 0.17012521 0.08891040 0.03755055 NA NA
#> 44 G1I34 2 3PLM 0.13288626 0.09359115 0.03655936 NA NA
#> 45 G1I35 2 3PLM 0.16791769 0.08361518 0.02044036 NA NA
#> 46 G1I36 2 3PLM 0.14309878 0.18590021 0.08516936 NA NA
#> 47 G1I37 2 3PLM 0.14194404 0.26869625 0.08697510 NA NA
#> 48 G1I38 5 GRM 0.05705443 0.05322210 0.04926777 0.06290244 0.08428075
#> 49 C1I11 5 GRM NA NA NA NA NA
#> 50 C1I12 5 GRM NA NA NA NA NA
#> 51 G2I1 2 3PLM 0.18701977 0.17226079 0.09591121 NA NA
#> 52 G2I2 2 3PLM 0.11055188 0.30549386 0.09111811 NA NA
#> 53 G2I3 2 3PLM 0.12900982 0.20135385 0.07488982 NA NA
#> 54 G2I4 2 3PLM 0.28006193 0.09631836 0.03881020 NA NA
#> 55 G2I5 2 3PLM 0.10228622 0.40358987 0.08893723 NA NA
#> 56 G2I6 2 3PLM 0.14204281 0.29399636 0.09476517 NA NA
#> 57 G2I7 2 3PLM 0.13098448 0.12235808 0.05447273 NA NA
#> 58 G2I8 2 3PLM 0.18554592 0.08066166 0.05149244 NA NA
#> 59 G2I9 2 3PLM 0.13004997 0.27643093 0.09157031 NA NA
#> 60 G2I10 2 3PLM 0.27183179 0.12027438 0.05121721 NA NA
#> 61 G2I11 2 3PLM 0.12329519 0.14644859 0.05005698 NA NA
#> 62 G2I12 2 3PLM 0.18329666 0.18051784 0.09670036 NA NA
#> 63 G2I13 2 3PLM 0.13036275 0.23937423 0.09227547 NA NA
#> 64 G2I14 2 3PLM 0.13691011 0.11354387 0.05286438 NA NA
#> 65 G2I15 2 3PLM 0.19565359 0.17450556 0.08012343 NA NA
#> 66 G2I16 2 3PLM 0.22938735 0.09966642 0.04736991 NA NA
#> 67 G2I17 2 3PLM 0.21703924 0.14435249 0.08787073 NA NA
#> 68 G2I18 2 3PLM 0.19775206 0.08387898 0.04368134 NA NA
#> 69 G2I19 2 3PLM 0.14342944 0.22082957 0.08261270 NA NA
#> 70 G2I20 2 3PLM 0.45488499 0.19197090 0.02387855 NA NA
#> 71 G2I21 2 3PLM 0.35929005 0.05999541 0.01724135 NA NA
#> 72 G2I22 2 3PLM 0.17462991 0.15301616 0.06937934 NA NA
#> 73 G2I23 2 3PLM 0.26460348 0.09594883 0.04984224 NA NA
#> 74 G2I24 2 3PLM 0.11632156 0.07551221 0.03397862 NA NA
#> 75 G2I25 2 3PLM 0.21505543 0.06239024 0.02239864 NA NA
#> 76 G2I26 2 3PLM 0.19522559 0.16121604 0.09680686 NA NA
#> 77 G2I27 2 3PLM 0.11542196 0.24707543 0.08656505 NA NA
#> 78 G2I28 5 GRM 0.07020432 0.06705796 0.04891269 0.04705132 0.07019674
#> 79 C2I1 2 3PLM NA NA NA NA NA
#> 80 C2I2 2 3PLM NA NA NA NA NA
#> 81 C2I3 2 3PLM NA NA NA NA NA
#> 82 C2I4 2 3PLM NA NA NA NA NA
#> 83 C2I5 2 3PLM NA NA NA NA NA
#> 84 C2I6 2 3PLM NA NA NA NA NA
#> 85 C2I7 2 3PLM NA NA NA NA NA
#> 86 C2I8 2 3PLM NA NA NA NA NA
#> 87 C2I9 2 3PLM NA NA NA NA NA
#> 88 C2I10 2 3PLM NA NA NA NA NA
#> 89 G3I1 2 3PLM 0.13986318 0.11556266 0.04828949 NA NA
#> 90 G3I2 2 3PLM 0.08945397 0.25055681 0.06577738 NA NA
#> 91 G3I3 2 3PLM 0.12166153 0.12145104 0.03777657 NA NA
#> 92 G3I4 2 3PLM 0.23742580 0.12346854 0.02115715 NA NA
#> 93 G3I5 2 3PLM 0.09747072 0.33207410 0.08571279 NA NA
#> 94 G3I6 2 3PLM 0.13415716 0.24170387 0.08325843 NA NA
#> 95 G3I7 2 3PLM 0.13182139 0.08662754 0.02782581 NA NA
#> 96 G3I8 2 3PLM 0.17855395 0.06374914 0.02406454 NA NA
#> 97 G3I9 2 3PLM 0.11323201 0.18515456 0.06633175 NA NA
#> 98 G3I10 2 3PLM 0.21267233 0.09577230 0.02369318 NA NA
#> 99 G3I11 2 3PLM 0.09929092 0.11096928 0.02888083 NA NA
#> 100 G3I12 2 3PLM 0.16578402 0.15209966 0.05508812 NA NA
#> 101 G3I13 2 3PLM 0.12510673 0.20472281 0.06955329 NA NA
#> 102 G3I14 2 3PLM 0.14193927 0.08926242 0.02823279 NA NA
#> 103 G3I15 2 3PLM 0.13431761 0.11420069 0.03726663 NA NA
#> 104 G3I16 2 3PLM 0.17708800 0.07754598 0.02161000 NA NA
#> 105 G3I17 2 3PLM 0.14820688 0.12802058 0.05977877 NA NA
#> 106 G3I18 2 3PLM 0.14295569 0.07697678 0.02235150 NA NA
#> 107 G3I19 2 3PLM 0.11089570 0.14924845 0.04377532 NA NA
#> 108 G3I20 2 3PLM 0.23479290 0.19832103 0.01759904 NA NA
#> 109 G3I21 2 3PLM 0.54769558 0.06208590 0.01022861 NA NA
#> 110 G3I22 2 3PLM 0.11351503 0.09624776 0.03123112 NA NA
#> 111 G3I23 2 3PLM 0.16621787 0.06369671 0.02083676 NA NA
#> 112 G3I24 2 3PLM 0.09162888 0.07576239 0.02065526 NA NA
#> 113 G3I25 2 3PLM 0.14521791 0.07831223 0.01301757 NA NA
#> 114 G3I26 2 3PLM 0.16527458 0.12057791 0.04950403 NA NA
#> 115 G3I27 2 3PLM 0.09992189 0.19902502 0.05904246 NA NA
#> 116 G3I28 5 GRM 0.04870285 0.05360023 0.05471689 0.06669018 0.08789166
#>
#> $group
#> $group$Group1
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM NA NA NA NA NA
#> 2 C1I2 2 3PLM NA NA NA NA NA
#> 3 C1I3 2 3PLM NA NA NA NA NA
#> 4 C1I4 2 3PLM NA NA NA NA NA
#> 5 C1I5 2 3PLM NA NA NA NA NA
#> 6 C1I6 2 3PLM NA NA NA NA NA
#> 7 C1I7 2 3PLM NA NA NA NA NA
#> 8 C1I8 2 3PLM NA NA NA NA NA
#> 9 C1I9 2 3PLM NA NA NA NA NA
#> 10 C1I10 2 3PLM NA NA NA NA NA
#> 11 G1I1 2 3PLM 0.10426168 0.19914118 0.06583145 NA NA
#> 12 G1I2 2 3PLM 0.13011827 0.13758723 0.03866179 NA NA
#> 13 G1I3 2 3PLM 0.25521536 0.09288148 0.02598262 NA NA
#> 14 G1I4 2 3PLM 0.21216024 0.12139692 0.04369469 NA NA
#> 15 G1I5 2 3PLM 0.13737157 0.12762451 0.05144114 NA NA
#> 16 G1I6 2 3PLM 0.17837536 0.05370898 0.02614114 NA NA
#> 17 G1I7 2 3PLM 0.15675133 0.12128691 0.04842894 NA NA
#> 18 G1I8 2 3PLM 0.46148303 0.06925484 0.01882411 NA NA
#> 19 G1I9 2 3PLM 0.25992134 0.10854364 0.06176901 NA NA
#> 20 G1I10 2 3PLM 0.12525002 0.22773298 0.09804119 NA NA
#> 21 G1I11 2 3PLM 0.14906877 0.16092483 0.07743255 NA NA
#> 22 G1I12 2 3PLM 0.09144445 0.31119356 0.08351947 NA NA
#> 23 G1I13 2 3PLM 0.13678756 0.20744666 0.06854745 NA NA
#> 24 G1I14 2 3PLM 0.36846246 0.15351046 0.02514203 NA NA
#> 25 G1I15 2 3PLM 0.09478648 0.29483636 0.09102878 NA NA
#> 26 G1I16 2 3PLM 0.10986557 0.26721069 0.09771458 NA NA
#> 27 G1I17 2 3PLM 0.12646970 0.15451738 0.05176849 NA NA
#> 28 G1I18 2 3PLM 0.20058125 0.08013120 0.03656393 NA NA
#> 29 G1I19 2 3PLM 0.12663826 0.19277821 0.08479494 NA NA
#> 30 G1I20 2 3PLM 0.17409361 0.19113321 0.06033487 NA NA
#> 31 G1I21 2 3PLM 0.13256306 0.15087630 0.04704321 NA NA
#> 32 G1I22 2 3PLM 0.21340356 0.15629299 0.06435608 NA NA
#> 33 G1I23 2 3PLM 0.14898851 0.22567950 0.09214904 NA NA
#> 34 G1I24 2 3PLM 0.19188388 0.09525298 0.03753622 NA NA
#> 35 G1I25 2 3PLM 0.17877681 0.12332508 0.04964582 NA NA
#> 36 G1I26 2 3PLM 0.25183655 0.07738128 0.02912676 NA NA
#> 37 G1I27 2 3PLM 0.17771713 0.20258618 0.10060823 NA NA
#> 38 G1I28 2 3PLM 0.16142785 0.09763951 0.03660579 NA NA
#> 39 G1I29 2 3PLM 0.08893330 0.17133724 0.05492922 NA NA
#> 40 G1I30 2 3PLM 0.26897282 0.25352870 0.03089404 NA NA
#> 41 G1I31 2 3PLM 0.46169957 0.09359258 0.01431405 NA NA
#> 42 G1I32 2 3PLM 0.11905116 0.15068461 0.05352540 NA NA
#> 43 G1I33 2 3PLM 0.17012521 0.08891040 0.03755055 NA NA
#> 44 G1I34 2 3PLM 0.13288626 0.09359115 0.03655936 NA NA
#> 45 G1I35 2 3PLM 0.16791769 0.08361518 0.02044036 NA NA
#> 46 G1I36 2 3PLM 0.14309878 0.18590021 0.08516936 NA NA
#> 47 G1I37 2 3PLM 0.14194404 0.26869625 0.08697510 NA NA
#> 48 G1I38 5 GRM 0.05705443 0.05322210 0.04926777 0.06290244 0.08428075
#> 49 C1I11 5 GRM NA NA NA NA NA
#> 50 C1I12 5 GRM NA NA NA NA NA
#>
#> $group$Group2
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C1I1 2 3PLM NA NA NA NA NA
#> 2 C1I2 2 3PLM NA NA NA NA NA
#> 3 C1I3 2 3PLM NA NA NA NA NA
#> 4 C1I4 2 3PLM NA NA NA NA NA
#> 5 C1I5 2 3PLM NA NA NA NA NA
#> 6 C1I6 2 3PLM NA NA NA NA NA
#> 7 C1I7 2 3PLM NA NA NA NA NA
#> 8 C1I8 2 3PLM NA NA NA NA NA
#> 9 C1I9 2 3PLM NA NA NA NA NA
#> 10 C1I10 2 3PLM NA NA NA NA NA
#> 11 C1I11 5 GRM NA NA NA NA NA
#> 12 C1I12 5 GRM NA NA NA NA NA
#> 13 G2I1 2 3PLM 0.18701977 0.17226079 0.09591121 NA NA
#> 14 G2I2 2 3PLM 0.11055188 0.30549386 0.09111811 NA NA
#> 15 G2I3 2 3PLM 0.12900982 0.20135385 0.07488982 NA NA
#> 16 G2I4 2 3PLM 0.28006193 0.09631836 0.03881020 NA NA
#> 17 G2I5 2 3PLM 0.10228622 0.40358987 0.08893723 NA NA
#> 18 G2I6 2 3PLM 0.14204281 0.29399636 0.09476517 NA NA
#> 19 G2I7 2 3PLM 0.13098448 0.12235808 0.05447273 NA NA
#> 20 G2I8 2 3PLM 0.18554592 0.08066166 0.05149244 NA NA
#> 21 G2I9 2 3PLM 0.13004997 0.27643093 0.09157031 NA NA
#> 22 G2I10 2 3PLM 0.27183179 0.12027438 0.05121721 NA NA
#> 23 G2I11 2 3PLM 0.12329519 0.14644859 0.05005698 NA NA
#> 24 G2I12 2 3PLM 0.18329666 0.18051784 0.09670036 NA NA
#> 25 G2I13 2 3PLM 0.13036275 0.23937423 0.09227547 NA NA
#> 26 G2I14 2 3PLM 0.13691011 0.11354387 0.05286438 NA NA
#> 27 G2I15 2 3PLM 0.19565359 0.17450556 0.08012343 NA NA
#> 28 G2I16 2 3PLM 0.22938735 0.09966642 0.04736991 NA NA
#> 29 G2I17 2 3PLM 0.21703924 0.14435249 0.08787073 NA NA
#> 30 G2I18 2 3PLM 0.19775206 0.08387898 0.04368134 NA NA
#> 31 G2I19 2 3PLM 0.14342944 0.22082957 0.08261270 NA NA
#> 32 G2I20 2 3PLM 0.45488499 0.19197090 0.02387855 NA NA
#> 33 G2I21 2 3PLM 0.35929005 0.05999541 0.01724135 NA NA
#> 34 G2I22 2 3PLM 0.17462991 0.15301616 0.06937934 NA NA
#> 35 G2I23 2 3PLM 0.26460348 0.09594883 0.04984224 NA NA
#> 36 G2I24 2 3PLM 0.11632156 0.07551221 0.03397862 NA NA
#> 37 G2I25 2 3PLM 0.21505543 0.06239024 0.02239864 NA NA
#> 38 G2I26 2 3PLM 0.19522559 0.16121604 0.09680686 NA NA
#> 39 G2I27 2 3PLM 0.11542196 0.24707543 0.08656505 NA NA
#> 40 G2I28 5 GRM 0.07020432 0.06705796 0.04891269 0.04705132 0.07019674
#> 41 C2I1 2 3PLM NA NA NA NA NA
#> 42 C2I2 2 3PLM NA NA NA NA NA
#> 43 C2I3 2 3PLM NA NA NA NA NA
#> 44 C2I4 2 3PLM NA NA NA NA NA
#> 45 C2I5 2 3PLM NA NA NA NA NA
#> 46 C2I6 2 3PLM NA NA NA NA NA
#> 47 C2I7 2 3PLM NA NA NA NA NA
#> 48 C2I8 2 3PLM NA NA NA NA NA
#> 49 C2I9 2 3PLM NA NA NA NA NA
#> 50 C2I10 2 3PLM NA NA NA NA NA
#>
#> $group$Group3
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 C2I1 2 3PLM NA NA NA NA NA
#> 2 C2I2 2 3PLM NA NA NA NA NA
#> 3 C2I3 2 3PLM NA NA NA NA NA
#> 4 C2I4 2 3PLM NA NA NA NA NA
#> 5 C2I5 2 3PLM NA NA NA NA NA
#> 6 C2I6 2 3PLM NA NA NA NA NA
#> 7 C2I7 2 3PLM NA NA NA NA NA
#> 8 C2I8 2 3PLM NA NA NA NA NA
#> 9 C2I9 2 3PLM NA NA NA NA NA
#> 10 C2I10 2 3PLM NA NA NA NA NA
#> 11 G3I1 2 3PLM 0.13986318 0.11556266 0.04828949 NA NA
#> 12 G3I2 2 3PLM 0.08945397 0.25055681 0.06577738 NA NA
#> 13 G3I3 2 3PLM 0.12166153 0.12145104 0.03777657 NA NA
#> 14 G3I4 2 3PLM 0.23742580 0.12346854 0.02115715 NA NA
#> 15 G3I5 2 3PLM 0.09747072 0.33207410 0.08571279 NA NA
#> 16 G3I6 2 3PLM 0.13415716 0.24170387 0.08325843 NA NA
#> 17 G3I7 2 3PLM 0.13182139 0.08662754 0.02782581 NA NA
#> 18 G3I8 2 3PLM 0.17855395 0.06374914 0.02406454 NA NA
#> 19 G3I9 2 3PLM 0.11323201 0.18515456 0.06633175 NA NA
#> 20 G3I10 2 3PLM 0.21267233 0.09577230 0.02369318 NA NA
#> 21 G3I11 2 3PLM 0.09929092 0.11096928 0.02888083 NA NA
#> 22 G3I12 2 3PLM 0.16578402 0.15209966 0.05508812 NA NA
#> 23 G3I13 2 3PLM 0.12510673 0.20472281 0.06955329 NA NA
#> 24 G3I14 2 3PLM 0.14193927 0.08926242 0.02823279 NA NA
#> 25 G3I15 2 3PLM 0.13431761 0.11420069 0.03726663 NA NA
#> 26 G3I16 2 3PLM 0.17708800 0.07754598 0.02161000 NA NA
#> 27 G3I17 2 3PLM 0.14820688 0.12802058 0.05977877 NA NA
#> 28 G3I18 2 3PLM 0.14295569 0.07697678 0.02235150 NA NA
#> 29 G3I19 2 3PLM 0.11089570 0.14924845 0.04377532 NA NA
#> 30 G3I20 2 3PLM 0.23479290 0.19832103 0.01759904 NA NA
#> 31 G3I21 2 3PLM 0.54769558 0.06208590 0.01022861 NA NA
#> 32 G3I22 2 3PLM 0.11351503 0.09624776 0.03123112 NA NA
#> 33 G3I23 2 3PLM 0.16621787 0.06369671 0.02083676 NA NA
#> 34 G3I24 2 3PLM 0.09162888 0.07576239 0.02065526 NA NA
#> 35 G3I25 2 3PLM 0.14521791 0.07831223 0.01301757 NA NA
#> 36 G3I26 2 3PLM 0.16527458 0.12057791 0.04950403 NA NA
#> 37 G3I27 2 3PLM 0.09992189 0.19902502 0.05904246 NA NA
#> 38 G3I28 5 GRM 0.04870285 0.05360023 0.05471689 0.06669018 0.08789166
#>
#>
# Extract the group parameter estimates (i.e., scale parameters)
getirt(fit.3, what = "group.par")
#> $Group1
#> mu sigma2 sigma
#> estimates -0.01450724 1.01249024 1.0062257
#> se 0.02249989 0.03202576 0.0159138
#>
#> $Group2
#> mu sigma2 sigma
#> estimates 0.50413571 0.58171603 0.76270311
#> se 0.01705456 0.01840008 0.01206241
#>
#> $Group3
#> mu sigma2 sigma
#> estimates -0.28118672 1.66447266 1.29014443
#> se 0.02884851 0.05264841 0.02040408
#>
# Extract the posterior latent ability distributions of the groups
getirt(fit.3, what = "weights")
#> $Group1
#> theta weight
#> 1 -6.00 7.662190e-12
#> 2 -5.75 2.451684e-11
#> 3 -5.50 7.119151e-11
#> 4 -5.25 1.891374e-10
#> 5 -5.00 4.676083e-10
#> 6 -4.75 1.108652e-09
#> 7 -4.50 2.644856e-09
#> 8 -4.25 6.812933e-09
#> 9 -4.00 2.081206e-08
#> 10 -3.75 8.401450e-08
#> 11 -3.50 4.930076e-07
#> 12 -3.25 4.326576e-06
#> 13 -3.00 5.074488e-05
#> 14 -2.75 5.872308e-04
#> 15 -2.50 4.332804e-03
#> 16 -2.25 1.444351e-02
#> 17 -2.00 2.242166e-02
#> 18 -1.75 2.444472e-02
#> 19 -1.50 2.775462e-02
#> 20 -1.25 3.781543e-02
#> 21 -1.00 5.911397e-02
#> 22 -0.75 7.686054e-02
#> 23 -0.50 8.228516e-02
#> 24 -0.25 1.049100e-01
#> 25 0.00 1.078960e-01
#> 26 0.25 8.138445e-02
#> 27 0.50 7.575408e-02
#> 28 0.75 8.485785e-02
#> 29 1.00 8.007142e-02
#> 30 1.25 4.680550e-02
#> 31 1.50 2.165959e-02
#> 32 1.75 1.619189e-02
#> 33 2.00 1.539816e-02
#> 34 2.25 8.170377e-03
#> 35 2.50 2.384944e-03
#> 36 2.75 7.954930e-04
#> 37 3.00 5.389228e-04
#> 38 3.25 6.906744e-04
#> 39 3.50 9.912521e-04
#> 40 3.75 9.167267e-04
#> 41 4.00 3.910055e-04
#> 42 4.25 7.029895e-05
#> 43 4.50 5.775249e-06
#> 44 4.75 2.563307e-07
#> 45 5.00 7.455139e-09
#> 46 5.25 1.703871e-10
#> 47 5.50 3.561747e-12
#> 48 5.75 7.640892e-14
#> 49 6.00 1.820327e-15
#>
#> $Group2
#> theta weight
#> 1 -6.00 3.894817e-89
#> 2 -5.75 3.951307e-84
#> 3 -5.50 7.764026e-79
#> 4 -5.25 2.603004e-73
#> 5 -5.00 1.291279e-67
#> 6 -4.75 8.143648e-62
#> 7 -4.50 5.597431e-56
#> 8 -4.25 3.620629e-50
#> 9 -4.00 1.945094e-44
#> 10 -3.75 7.996024e-39
#> 11 -3.50 2.475576e-33
#> 12 -3.25 6.096104e-28
#> 13 -3.00 1.277570e-22
#> 14 -2.75 2.100737e-17
#> 15 -2.50 1.722718e-12
#> 16 -2.25 2.851606e-08
#> 17 -2.00 3.328725e-05
#> 18 -1.75 1.652181e-03
#> 19 -1.50 7.124061e-03
#> 20 -1.25 1.323762e-02
#> 21 -1.00 2.233184e-02
#> 22 -0.75 2.551256e-02
#> 23 -0.50 4.082653e-02
#> 24 -0.25 1.029622e-01
#> 25 0.00 9.278880e-02
#> 26 0.25 8.719857e-02
#> 27 0.50 1.665702e-01
#> 28 0.75 1.473383e-01
#> 29 1.00 8.777312e-02
#> 30 1.25 7.526865e-02
#> 31 1.50 6.301574e-02
#> 32 1.75 3.752019e-02
#> 33 2.00 1.769110e-02
#> 34 2.25 6.091144e-03
#> 35 2.50 1.740485e-03
#> 36 2.75 7.205189e-04
#> 37 3.00 5.733371e-04
#> 38 3.25 6.627171e-04
#> 39 3.50 6.883348e-04
#> 40 3.75 4.588606e-04
#> 41 4.00 1.743136e-04
#> 42 4.25 3.899078e-05
#> 43 4.50 5.702020e-06
#> 44 4.75 6.165462e-07
#> 45 5.00 5.519581e-08
#> 46 5.25 4.482665e-09
#> 47 5.50 3.531305e-10
#> 48 5.75 2.821138e-11
#> 49 6.00 2.345691e-12
#>
#> $Group3
#> theta weight
#> 1 -6.00 6.924473e-08
#> 2 -5.75 2.943789e-07
#> 3 -5.50 1.166017e-06
#> 4 -5.25 4.289972e-06
#> 5 -5.00 1.460129e-05
#> 6 -4.75 4.573324e-05
#> 7 -4.50 1.309612e-04
#> 8 -4.25 3.402905e-04
#> 9 -4.00 7.962462e-04
#> 10 -3.75 1.668503e-03
#> 11 -3.50 3.132224e-03
#> 12 -3.25 5.329452e-03
#> 13 -3.00 8.445236e-03
#> 14 -2.75 1.295753e-02
#> 15 -2.50 1.981722e-02
#> 16 -2.25 2.965113e-02
#> 17 -2.00 3.982099e-02
#> 18 -1.75 4.375602e-02
#> 19 -1.50 4.160532e-02
#> 20 -1.25 4.561268e-02
#> 21 -1.00 6.646806e-02
#> 22 -0.75 8.026361e-02
#> 23 -0.50 6.427858e-02
#> 24 -0.25 6.407623e-02
#> 25 0.00 8.542032e-02
#> 26 0.25 8.548725e-02
#> 27 0.50 6.053382e-02
#> 28 0.75 4.722574e-02
#> 29 1.00 4.420511e-02
#> 30 1.25 3.945090e-02
#> 31 1.50 3.541132e-02
#> 32 1.75 3.265182e-02
#> 33 2.00 2.150663e-02
#> 34 2.25 9.341872e-03
#> 35 2.50 3.769655e-03
#> 36 2.75 1.886082e-03
#> 37 3.00 1.256293e-03
#> 38 3.25 1.030125e-03
#> 39 3.50 8.997076e-04
#> 40 3.75 7.280932e-04
#> 41 4.00 4.987633e-04
#> 42 4.25 2.792318e-04
#> 43 4.50 1.282712e-04
#> 44 4.75 4.948786e-05
#> 45 5.00 1.649488e-05
#> 46 5.25 4.873378e-06
#> 47 5.50 1.302434e-06
#> 48 5.75 3.195413e-07
#> 49 6.00 7.269746e-08
#>
# 2-(2). Alternatively, MG-FIPC can be implemented by specifying the
# IDs of the items to be fixed using the 'fix.id' argument.
# Provide a character vector of fixed item IDs to 'fix.id'
fix.id <- c(paste0("C1I", 1:12), paste0("C2I", 1:10))
fit.4 <-
est_mg(
x = x, data = data, group.name = group.name, D = 1,
free.group = free.group, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)),
EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
fipc.method = "MEM", fix.id = fix.id
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -56756.7548, Max-Change: 3.554166
EM iteration: 2, Loglike: -160424.0878, Max-Change: 0.780368
EM iteration: 3, Loglike: -159755.3559, Max-Change: 0.276071
EM iteration: 4, Loglike: -159686.2158, Max-Change: 0.151073
EM iteration: 5, Loglike: -159657.5520, Max-Change: 0.102849
EM iteration: 6, Loglike: -159642.1127, Max-Change: 0.080257
EM iteration: 7, Loglike: -159633.1411, Max-Change: 0.066343
EM iteration: 8, Loglike: -159627.6844, Max-Change: 0.055853
EM iteration: 9, Loglike: -159624.2459, Max-Change: 0.047172
EM iteration: 10, Loglike: -159622.0120, Max-Change: 0.039781
EM iteration: 11, Loglike: -159620.5195, Max-Change: 0.033468
EM iteration: 12, Loglike: -159619.4950, Max-Change: 0.028101
EM iteration: 13, Loglike: -159618.7723, Max-Change: 0.023565
EM iteration: 14, Loglike: -159618.2481, Max-Change: 0.019752
EM iteration: 15, Loglike: -159617.8570, Max-Change: 0.016845
EM iteration: 16, Loglike: -159617.5566, Max-Change: 0.014864
EM iteration: 17, Loglike: -159617.3191, Max-Change: 0.01318
EM iteration: 18, Loglike: -159617.1261, Max-Change: 0.011751
EM iteration: 19, Loglike: -159616.9650, Max-Change: 0.010538
EM iteration: 20, Loglike: -159616.8273, Max-Change: 0.009507
EM iteration: 21, Loglike: -159616.7072, Max-Change: 0.008626
EM iteration: 22, Loglike: -159616.6005, Max-Change: 0.007869
EM iteration: 23, Loglike: -159616.5042, Max-Change: 0.007214
EM iteration: 24, Loglike: -159616.4163, Max-Change: 0.006643
EM iteration: 25, Loglike: -159616.3352, Max-Change: 0.006141
EM iteration: 26, Loglike: -159616.2596, Max-Change: 0.005695
EM iteration: 27, Loglike: -159616.1888, Max-Change: 0.005295
EM iteration: 28, Loglike: -159616.1221, Max-Change: 0.004934
EM iteration: 29, Loglike: -159616.0589, Max-Change: 0.004606
EM iteration: 30, Loglike: -159615.9989, Max-Change: 0.004306
EM iteration: 31, Loglike: -159615.9416, Max-Change: 0.00403
EM iteration: 32, Loglike: -159615.8868, Max-Change: 0.003774
EM iteration: 33, Loglike: -159615.8343, Max-Change: 0.003537
EM iteration: 34, Loglike: -159615.7838, Max-Change: 0.003317
EM iteration: 35, Loglike: -159615.7352, Max-Change: 0.003111
EM iteration: 36, Loglike: -159615.6884, Max-Change: 0.002919
EM iteration: 37, Loglike: -159615.6431, Max-Change: 0.00274
EM iteration: 38, Loglike: -159615.5994, Max-Change: 0.002572
EM iteration: 39, Loglike: -159615.5570, Max-Change: 0.002416
EM iteration: 40, Loglike: -159615.5159, Max-Change: 0.002269
EM iteration: 41, Loglike: -159615.4761, Max-Change: 0.002131
EM iteration: 42, Loglike: -159615.4373, Max-Change: 0.002003
EM iteration: 43, Loglike: -159615.3997, Max-Change: 0.001882
EM iteration: 44, Loglike: -159615.3630, Max-Change: 0.00177
EM iteration: 45, Loglike: -159615.3274, Max-Change: 0.001665
EM iteration: 46, Loglike: -159615.2926, Max-Change: 0.001566
EM iteration: 47, Loglike: -159615.2587, Max-Change: 0.001474
EM iteration: 48, Loglike: -159615.2256, Max-Change: 0.001388
EM iteration: 49, Loglike: -159615.1933, Max-Change: 0.001308
EM iteration: 50, Loglike: -159615.1617, Max-Change: 0.001232
EM iteration: 51, Loglike: -159615.1309, Max-Change: 0.001162
EM iteration: 52, Loglike: -159615.1007, Max-Change: 0.001097
EM iteration: 53, Loglike: -159615.0711, Max-Change: 0.001035
EM iteration: 54, Loglike: -159615.0422, Max-Change: 0.000978
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 8.77 seconds.
# Summary of the estimation
summary(fit.4)
#>
#> Call:
#> est_mg(x = x, data = data, group.name = group.name, D = 1, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
#> fipc.method = "MEM", fix.id = fix.id)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 294
#> Number of fixed items:
#> Overall: 22
#> By group: 12(Group1), 22(Group2), 10(Group3)
#> Number of E-step cycles completed: 54
#> Maximum parameter change: 0.0009779691
#>
#> Processing time (in seconds)
#> EM algorithm: 8.1
#> Standard error computation: 0.16
#> Total computation: 8.77
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are satisfied.
#> Second-order test: Solution is a possible local maximum.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates is obtainable.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 319230.1
#> By group: 120354.311(Group1), 113985.392(Group2), 84890.382(Group3)
#>
#> Akaike Information Criterion (AIC): 319818.1
#> Bayesian Information Criterion (BIC): 321787.7
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 C1I1 2 3PLM 0.76 NA 1.46 NA 0.26 NA NA NA
#> 2 C1I2 2 3PLM 1.92 NA -1.05 NA 0.18 NA NA NA
#> 3 C1I3 2 3PLM 0.93 NA 0.39 NA 0.10 NA NA NA
#> 4 C1I4 2 3PLM 1.05 NA -0.41 NA 0.20 NA NA NA
#> 5 C1I5 2 3PLM 0.87 NA -0.12 NA 0.16 NA NA NA
#> 6 C1I6 2 3PLM 1.70 NA 0.63 NA 0.07 NA NA NA
#> 7 C1I7 2 3PLM 0.91 NA 1.02 NA 0.12 NA NA NA
#> 8 C1I8 2 3PLM 0.84 NA 0.80 NA 0.11 NA NA NA
#> 9 C1I9 2 3PLM 0.85 NA 0.85 NA 0.26 NA NA NA
#> 10 C1I10 2 3PLM 1.53 NA 0.09 NA 0.14 NA NA NA
#> 11 G1I1 2 3PLM 0.96 0.10 -0.46 0.20 0.16 0.07 NA NA
#> 12 G1I2 2 3PLM 0.88 0.13 1.21 0.14 0.10 0.04 NA NA
#> 13 G1I3 2 3PLM 1.49 0.26 1.31 0.09 0.18 0.03 NA NA
#> 14 G1I4 2 3PLM 1.52 0.21 0.27 0.12 0.30 0.04 NA NA
#> 15 G1I5 2 3PLM 1.33 0.14 -0.18 0.13 0.16 0.05 NA NA
#> 16 G1I6 2 3PLM 2.15 0.18 0.01 0.05 0.08 0.03 NA NA
#> 17 G1I7 2 3PLM 1.45 0.16 -0.07 0.12 0.20 0.05 NA NA
#> 18 G1I8 2 3PLM 2.50 0.46 1.18 0.07 0.32 0.02 NA NA
#> 19 G1I9 2 3PLM 2.40 0.26 -0.93 0.11 0.24 0.06 NA NA
#> 20 G1I10 2 3PLM 1.26 0.13 -1.75 0.23 0.24 0.10 NA NA
#> 21 G1I11 2 3PLM 1.55 0.15 -1.11 0.16 0.21 0.08 NA NA
#> 22 G1I12 2 3PLM 0.75 0.09 -0.81 0.31 0.19 0.08 NA NA
#> 23 G1I13 2 3PLM 1.04 0.14 -0.13 0.21 0.20 0.07 NA NA
#> 24 G1I14 2 3PLM 1.46 0.37 1.77 0.15 0.30 0.03 NA NA
#> 25 G1I15 2 3PLM 0.86 0.09 -1.44 0.29 0.21 0.09 NA NA
#> 26 G1I16 2 3PLM 1.05 0.11 -1.95 0.27 0.23 0.10 NA NA
#> 27 G1I17 2 3PLM 1.04 0.13 0.25 0.15 0.15 0.05 NA NA
#> 28 G1I18 2 3PLM 2.08 0.20 -0.09 0.08 0.24 0.04 NA NA
#> 29 G1I19 2 3PLM 1.32 0.13 -1.38 0.19 0.20 0.08 NA NA
#> 30 G1I20 2 3PLM 1.01 0.17 0.51 0.19 0.22 0.06 NA NA
#> 31 G1I21 2 3PLM 0.92 0.13 0.77 0.15 0.13 0.05 NA NA
#> 32 G1I22 2 3PLM 1.77 0.21 -0.65 0.16 0.35 0.06 NA NA
#> 33 G1I23 2 3PLM 1.31 0.15 -1.17 0.23 0.25 0.09 NA NA
#> 34 G1I24 2 3PLM 1.64 0.19 0.32 0.10 0.23 0.04 NA NA
#> 35 G1I25 2 3PLM 1.58 0.18 -0.13 0.12 0.25 0.05 NA NA
#> 36 G1I26 2 3PLM 1.88 0.25 0.66 0.08 0.25 0.03 NA NA
#> 37 G1I27 2 3PLM 1.63 0.18 -1.54 0.20 0.27 0.10 NA NA
#> 38 G1I28 2 3PLM 1.33 0.16 0.57 0.10 0.15 0.04 NA NA
#> 39 G1I29 2 3PLM 0.92 0.09 -0.37 0.17 0.12 0.05 NA NA
#> 40 G1I30 2 3PLM 1.00 0.27 2.30 0.25 0.17 0.03 NA NA
#> 41 G1I31 2 3PLM 2.39 0.46 1.64 0.09 0.18 0.01 NA NA
#> 42 G1I32 2 3PLM 1.10 0.12 -0.08 0.15 0.15 0.05 NA NA
#> 43 G1I33 2 3PLM 1.60 0.17 0.18 0.09 0.16 0.04 NA NA
#> 44 G1I34 2 3PLM 1.33 0.13 0.24 0.09 0.11 0.04 NA NA
#> 45 G1I35 2 3PLM 1.33 0.17 1.30 0.08 0.07 0.02 NA NA
#> 46 G1I36 2 3PLM 1.44 0.14 -1.23 0.19 0.22 0.09 NA NA
#> 47 G1I37 2 3PLM 1.05 0.14 -0.60 0.27 0.27 0.09 NA NA
#> 48 G1I38 5 GRM 1.06 0.06 -0.37 0.05 0.22 0.05 0.87 0.06
#> 49 C1I11 5 GRM 1.23 NA -2.08 NA -1.35 NA -0.71 NA
#> 50 C1I12 5 GRM 0.88 NA -0.76 NA -0.01 NA 0.67 NA
#> 51 G2I1 2 3PLM 1.74 0.19 -0.87 0.17 0.23 0.10 NA NA
#> 52 G2I2 2 3PLM 0.83 0.11 -0.45 0.31 0.21 0.09 NA NA
#> 53 G2I3 2 3PLM 1.06 0.13 0.08 0.20 0.18 0.07 NA NA
#> 54 G2I4 2 3PLM 1.45 0.28 1.50 0.10 0.18 0.04 NA NA
#> 55 G2I5 2 3PLM 0.70 0.10 -1.68 0.40 0.20 0.09 NA NA
#> 56 G2I6 2 3PLM 1.08 0.14 -1.60 0.29 0.22 0.09 NA NA
#> 57 G2I7 2 3PLM 1.30 0.13 0.27 0.12 0.13 0.05 NA NA
#> 58 G2I8 2 3PLM 2.18 0.19 -0.09 0.08 0.14 0.05 NA NA
#> 59 G2I9 2 3PLM 1.07 0.13 -1.57 0.28 0.21 0.09 NA NA
#> 60 G2I10 2 3PLM 1.59 0.27 0.90 0.12 0.29 0.05 NA NA
#> 61 G2I11 2 3PLM 0.93 0.12 0.88 0.15 0.11 0.05 NA NA
#> 62 G2I12 2 3PLM 1.66 0.18 -0.70 0.18 0.25 0.10 NA NA
#> 63 G2I13 2 3PLM 1.16 0.13 -1.31 0.24 0.21 0.09 NA NA
#> 64 G2I14 2 3PLM 1.39 0.14 0.22 0.11 0.13 0.05 NA NA
#> 65 G2I15 2 3PLM 1.53 0.20 0.03 0.17 0.26 0.08 NA NA
#> 66 G2I16 2 3PLM 1.70 0.23 0.75 0.10 0.21 0.05 NA NA
#> 67 G2I17 2 3PLM 2.11 0.22 -1.20 0.14 0.20 0.09 NA NA
#> 68 G2I18 2 3PLM 1.72 0.20 0.64 0.08 0.14 0.04 NA NA
#> 69 G2I19 2 3PLM 1.10 0.14 0.05 0.22 0.21 0.08 NA NA
#> 70 G2I20 2 3PLM 1.62 0.45 2.24 0.19 0.16 0.02 NA NA
#> 71 G2I21 2 3PLM 2.39 0.36 1.59 0.06 0.12 0.02 NA NA
#> 72 G2I22 2 3PLM 1.43 0.17 0.22 0.15 0.20 0.07 NA NA
#> 73 G2I23 2 3PLM 2.09 0.26 0.44 0.10 0.28 0.05 NA NA
#> 74 G2I24 2 3PLM 1.40 0.12 0.37 0.08 0.07 0.03 NA NA
#> 75 G2I25 2 3PLM 1.74 0.22 1.42 0.06 0.07 0.02 NA NA
#> 76 G2I26 2 3PLM 1.89 0.20 -0.88 0.16 0.24 0.10 NA NA
#> 77 G2I27 2 3PLM 0.98 0.12 -0.59 0.25 0.20 0.09 NA NA
#> 78 G2I28 5 GRM 1.12 0.07 -0.37 0.07 0.15 0.05 0.80 0.05
#> 79 C2I1 2 3PLM 0.97 NA -0.46 NA 0.05 NA NA NA
#> 80 C2I2 2 3PLM 0.85 NA 1.18 NA 0.01 NA NA NA
#> 81 C2I3 2 3PLM 1.43 NA 1.41 NA 0.10 NA NA NA
#> 82 C2I4 2 3PLM 1.48 NA 0.18 NA 0.17 NA NA NA
#> 83 C2I5 2 3PLM 1.27 NA -0.23 NA 0.03 NA NA NA
#> 84 C2I6 2 3PLM 2.02 NA -0.09 NA 0.01 NA NA NA
#> 85 C2I7 2 3PLM 1.37 NA -0.13 NA 0.10 NA NA NA
#> 86 C2I8 2 3PLM 1.67 NA 1.25 NA 0.19 NA NA NA
#> 87 C2I9 2 3PLM 2.28 NA -1.01 NA 0.10 NA NA NA
#> 88 C2I10 2 3PLM 1.42 NA -1.65 NA 0.11 NA NA NA
#> 89 G3I1 2 3PLM 1.60 0.14 -1.04 0.12 0.14 0.05 NA NA
#> 90 G3I2 2 3PLM 0.79 0.09 -0.62 0.25 0.16 0.07 NA NA
#> 91 G3I3 2 3PLM 1.16 0.12 0.07 0.12 0.16 0.04 NA NA
#> 92 G3I4 2 3PLM 1.30 0.24 1.72 0.12 0.22 0.02 NA NA
#> 93 G3I5 2 3PLM 0.80 0.10 -1.09 0.33 0.24 0.09 NA NA
#> 94 G3I6 2 3PLM 1.18 0.13 -1.38 0.24 0.26 0.08 NA NA
#> 95 G3I7 2 3PLM 1.37 0.13 0.26 0.09 0.13 0.03 NA NA
#> 96 G3I8 2 3PLM 1.95 0.18 -0.07 0.06 0.14 0.02 NA NA
#> 97 G3I9 2 3PLM 1.18 0.11 -1.16 0.19 0.18 0.07 NA NA
#> 98 G3I10 2 3PLM 1.50 0.21 0.98 0.10 0.29 0.02 NA NA
#> 99 G3I11 2 3PLM 0.91 0.10 0.80 0.11 0.08 0.03 NA NA
#> 100 G3I12 2 3PLM 1.44 0.17 -0.78 0.15 0.23 0.06 NA NA
#> 101 G3I13 2 3PLM 1.15 0.13 -1.06 0.20 0.21 0.07 NA NA
#> 102 G3I14 2 3PLM 1.38 0.14 0.31 0.09 0.16 0.03 NA NA
#> 103 G3I15 2 3PLM 1.29 0.13 -0.06 0.11 0.18 0.04 NA NA
#> 104 G3I16 2 3PLM 1.58 0.18 0.75 0.08 0.20 0.02 NA NA
#> 105 G3I17 2 3PLM 1.72 0.15 -1.46 0.13 0.16 0.06 NA NA
#> 106 G3I18 2 3PLM 1.37 0.14 0.71 0.08 0.11 0.02 NA NA
#> 107 G3I19 2 3PLM 0.99 0.11 0.07 0.15 0.15 0.04 NA NA
#> 108 G3I20 2 3PLM 1.14 0.23 2.30 0.20 0.12 0.02 NA NA
#> 109 G3I21 2 3PLM 2.97 0.55 1.66 0.06 0.14 0.01 NA NA
#> 110 G3I22 2 3PLM 1.19 0.11 0.10 0.10 0.10 0.03 NA NA
#> 111 G3I23 2 3PLM 1.79 0.17 0.33 0.06 0.15 0.02 NA NA
#> 112 G3I24 2 3PLM 1.15 0.09 0.34 0.08 0.05 0.02 NA NA
#> 113 G3I25 2 3PLM 1.38 0.15 1.36 0.08 0.05 0.01 NA NA
#> 114 G3I26 2 3PLM 1.72 0.17 -0.96 0.12 0.20 0.05 NA NA
#> 115 G3I27 2 3PLM 0.95 0.10 -0.61 0.20 0.16 0.06 NA NA
#> 116 G3I28 5 GRM 1.00 0.05 -0.31 0.05 0.19 0.05 0.82 0.07
#> par.5 se.5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 NA NA
#> 5 NA NA
#> 6 NA NA
#> 7 NA NA
#> 8 NA NA
#> 9 NA NA
#> 10 NA NA
#> 11 NA NA
#> 12 NA NA
#> 13 NA NA
#> 14 NA NA
#> 15 NA NA
#> 16 NA NA
#> 17 NA NA
#> 18 NA NA
#> 19 NA NA
#> 20 NA NA
#> 21 NA NA
#> 22 NA NA
#> 23 NA NA
#> 24 NA NA
#> 25 NA NA
#> 26 NA NA
#> 27 NA NA
#> 28 NA NA
#> 29 NA NA
#> 30 NA NA
#> 31 NA NA
#> 32 NA NA
#> 33 NA NA
#> 34 NA NA
#> 35 NA NA
#> 36 NA NA
#> 37 NA NA
#> 38 NA NA
#> 39 NA NA
#> 40 NA NA
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 1.44 0.08
#> 49 -0.12 NA
#> 50 1.25 NA
#> 51 NA NA
#> 52 NA NA
#> 53 NA NA
#> 54 NA NA
#> 55 NA NA
#> 56 NA NA
#> 57 NA NA
#> 58 NA NA
#> 59 NA NA
#> 60 NA NA
#> 61 NA NA
#> 62 NA NA
#> 63 NA NA
#> 64 NA NA
#> 65 NA NA
#> 66 NA NA
#> 67 NA NA
#> 68 NA NA
#> 69 NA NA
#> 70 NA NA
#> 71 NA NA
#> 72 NA NA
#> 73 NA NA
#> 74 NA NA
#> 75 NA NA
#> 76 NA NA
#> 77 NA NA
#> 78 1.48 0.07
#> 79 NA NA
#> 80 NA NA
#> 81 NA NA
#> 82 NA NA
#> 83 NA NA
#> 84 NA NA
#> 85 NA NA
#> 86 NA NA
#> 87 NA NA
#> 88 NA NA
#> 89 NA NA
#> 90 NA NA
#> 91 NA NA
#> 92 NA NA
#> 93 NA NA
#> 94 NA NA
#> 95 NA NA
#> 96 NA NA
#> 97 NA NA
#> 98 NA NA
#> 99 NA NA
#> 100 NA NA
#> 101 NA NA
#> 102 NA NA
#> 103 NA NA
#> 104 NA NA
#> 105 NA NA
#> 106 NA NA
#> 107 NA NA
#> 108 NA NA
#> 109 NA NA
#> 110 NA NA
#> 111 NA NA
#> 112 NA NA
#> 113 NA NA
#> 114 NA NA
#> 115 NA NA
#> 116 1.52 0.09
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) -0.01 1.01 1.01
#> se(Group1) 0.02 0.03 0.02
#> estimate(Group2) 0.50 0.58 0.76
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.28 1.66 1.29
#> se(Group3) 0.03 0.05 0.02
#>
## ------------------------------------------------------------------------------
# 3. MG calibration with FIPC using simMG data
# (Estimate group parameters only)
# - Details:
# (a) Fix all item parameters across all three groups
# (b) Freely estimate the means and variances of the ability
# distributions for all three groups
## ------------------------------------------------------------------------------
# 3-(1). Freely estimate the means and variances for all three groups
# Set all three groups as free groups in which the scales
# of the ability distributions will be freely estimated
free.group <- 1:3 # or use 'free.group <- group.name'
# Specify the locations of all fixed items in each group's metadata
fix.loc <- list(1:50, 1:50, 1:38)
# Estimate group parameters only using MG-FIPC
fit.5 <-
est_mg(
x = x, data = data, group.name = group.name, D = 1,
free.group = free.group, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)),
EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
fipc.method = "MEM", fix.loc = fix.loc
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -159735.7617, Max-Change: 0.476403
EM iteration: 2, Loglike: -159719.0182, Max-Change: 0.138031
EM iteration: 3, Loglike: -159716.3699, Max-Change: 0.04617
EM iteration: 4, Loglike: -159715.2802, Max-Change: 0.018371
EM iteration: 5, Loglike: -159714.6363, Max-Change: 0.009115
EM iteration: 6, Loglike: -159714.1843, Max-Change: 0.005329
EM iteration: 7, Loglike: -159713.8343, Max-Change: 0.003463
EM iteration: 8, Loglike: -159713.5471, Max-Change: 0.002427
EM iteration: 9, Loglike: -159713.3033, Max-Change: 0.00181
EM iteration: 10, Loglike: -159713.0914, Max-Change: 0.001421
EM iteration: 11, Loglike: -159712.9045, Max-Change: 0.001165
EM iteration: 12, Loglike: -159712.7377, Max-Change: 0.000987
#> Estimation is finished in 0.66 seconds.
# Summary of the estimation
summary(fit.5)
#>
#> Call:
#> est_mg(x = x, data = data, group.name = group.name, D = 1, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
#> fipc.method = "MEM", fix.loc = fix.loc)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 6
#> Number of fixed items:
#> Overall: 116
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of E-step cycles completed: 12
#> Maximum parameter change: 0.0009867474
#>
#> Processing time (in seconds)
#> EM algorithm: 0.43
#> Standard error computation:
#> Total computation: 0.66
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are satisfied.
#> Second-order test: Solution is a possible local maximum.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates was not estimated.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 319425.5
#> By group: 120445.354(Group1), 114033.356(Group2), 84946.765(Group3)
#>
#> Akaike Information Criterion (AIC): 319437.5
#> Bayesian Information Criterion (BIC): 319477.7
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 C1I1 2 3PLM 0.76 NA 1.46 NA 0.26 NA NA NA
#> 2 C1I2 2 3PLM 1.92 NA -1.05 NA 0.18 NA NA NA
#> 3 C1I3 2 3PLM 0.93 NA 0.39 NA 0.10 NA NA NA
#> 4 C1I4 2 3PLM 1.05 NA -0.41 NA 0.20 NA NA NA
#> 5 C1I5 2 3PLM 0.87 NA -0.12 NA 0.16 NA NA NA
#> 6 C1I6 2 3PLM 1.70 NA 0.63 NA 0.07 NA NA NA
#> 7 C1I7 2 3PLM 0.91 NA 1.02 NA 0.12 NA NA NA
#> 8 C1I8 2 3PLM 0.84 NA 0.80 NA 0.11 NA NA NA
#> 9 C1I9 2 3PLM 0.85 NA 0.85 NA 0.26 NA NA NA
#> 10 C1I10 2 3PLM 1.53 NA 0.09 NA 0.14 NA NA NA
#> 11 G1I1 2 3PLM 1.00 NA -0.46 NA 0.13 NA NA NA
#> 12 G1I2 2 3PLM 0.88 NA 1.18 NA 0.09 NA NA NA
#> 13 G1I3 2 3PLM 1.46 NA 1.41 NA 0.18 NA NA NA
#> 14 G1I4 2 3PLM 1.51 NA 0.18 NA 0.25 NA NA NA
#> 15 G1I5 2 3PLM 1.30 NA -0.23 NA 0.11 NA NA NA
#> 16 G1I6 2 3PLM 2.05 NA -0.09 NA 0.05 NA NA NA
#> 17 G1I7 2 3PLM 1.40 NA -0.13 NA 0.18 NA NA NA
#> 18 G1I8 2 3PLM 1.70 NA 1.25 NA 0.27 NA NA NA
#> 19 G1I9 2 3PLM 2.31 NA -1.01 NA 0.18 NA NA NA
#> 20 G1I10 2 3PLM 1.45 NA -1.65 NA 0.19 NA NA NA
#> 21 G1I11 2 3PLM 1.63 NA -1.19 NA 0.12 NA NA NA
#> 22 G1I12 2 3PLM 0.83 NA -0.68 NA 0.20 NA NA NA
#> 23 G1I13 2 3PLM 0.98 NA -0.26 NA 0.13 NA NA NA
#> 24 G1I14 2 3PLM 1.14 NA 1.68 NA 0.25 NA NA NA
#> 25 G1I15 2 3PLM 0.79 NA -1.39 NA 0.26 NA NA NA
#> 26 G1I16 2 3PLM 1.09 NA -1.85 NA 0.17 NA NA NA
#> 27 G1I17 2 3PLM 1.17 NA 0.07 NA 0.13 NA NA NA
#> 28 G1I18 2 3PLM 2.15 NA -0.09 NA 0.21 NA NA NA
#> 29 G1I19 2 3PLM 1.28 NA -1.38 NA 0.20 NA NA NA
#> 30 G1I20 2 3PLM 1.35 NA 0.82 NA 0.32 NA NA NA
#> 31 G1I21 2 3PLM 0.82 NA 0.71 NA 0.08 NA NA NA
#> 32 G1I22 2 3PLM 1.52 NA -0.89 NA 0.26 NA NA NA
#> 33 G1I23 2 3PLM 1.27 NA -1.31 NA 0.19 NA NA NA
#> 34 G1I24 2 3PLM 1.31 NA 0.19 NA 0.16 NA NA NA
#> 35 G1I25 2 3PLM 1.47 NA -0.14 NA 0.23 NA NA NA
#> 36 G1I26 2 3PLM 1.47 NA 0.64 NA 0.23 NA NA NA
#> 37 G1I27 2 3PLM 1.76 NA -1.53 NA 0.16 NA NA NA
#> 38 G1I28 2 3PLM 1.44 NA 0.54 NA 0.14 NA NA NA
#> 39 G1I29 2 3PLM 0.98 NA -0.37 NA 0.13 NA NA NA
#> 40 G1I30 2 3PLM 0.99 NA 2.37 NA 0.16 NA NA NA
#> 41 G1I31 2 3PLM 2.27 NA 1.62 NA 0.18 NA NA NA
#> 42 G1I32 2 3PLM 1.23 NA -0.07 NA 0.13 NA NA NA
#> 43 G1I33 2 3PLM 1.64 NA 0.17 NA 0.18 NA NA NA
#> 44 G1I34 2 3PLM 1.21 NA 0.24 NA 0.08 NA NA NA
#> 45 G1I35 2 3PLM 1.32 NA 1.34 NA 0.08 NA NA NA
#> 46 G1I36 2 3PLM 1.74 NA -1.00 NA 0.25 NA NA NA
#> 47 G1I37 2 3PLM 0.97 NA -0.73 NA 0.22 NA NA NA
#> 48 G1I38 5 GRM 1.14 NA -0.37 NA 0.22 NA 0.85 NA
#> 49 C1I11 5 GRM 1.23 NA -2.08 NA -1.35 NA -0.71 NA
#> 50 C1I12 5 GRM 0.88 NA -0.76 NA -0.01 NA 0.67 NA
#> 51 G2I1 2 3PLM 1.60 NA -1.19 NA 0.04 NA NA NA
#> 52 G2I2 2 3PLM 0.80 NA -0.68 NA 0.12 NA NA NA
#> 53 G2I3 2 3PLM 0.95 NA -0.26 NA 0.05 NA NA NA
#> 54 G2I4 2 3PLM 1.11 NA 1.68 NA 0.17 NA NA NA
#> 55 G2I5 2 3PLM 0.76 NA -1.39 NA 0.18 NA NA NA
#> 56 G2I6 2 3PLM 1.06 NA -1.85 NA 0.09 NA NA NA
#> 57 G2I7 2 3PLM 1.14 NA 0.07 NA 0.05 NA NA NA
#> 58 G2I8 2 3PLM 2.12 NA -0.09 NA 0.13 NA NA NA
#> 59 G2I9 2 3PLM 1.25 NA -1.38 NA 0.12 NA NA NA
#> 60 G2I10 2 3PLM 1.32 NA 0.82 NA 0.24 NA NA NA
#> 61 G2I11 2 3PLM 0.79 NA 0.71 NA 0.01 NA NA NA
#> 62 G2I12 2 3PLM 1.49 NA -0.89 NA 0.18 NA NA NA
#> 63 G2I13 2 3PLM 1.24 NA -1.31 NA 0.11 NA NA NA
#> 64 G2I14 2 3PLM 1.28 NA 0.19 NA 0.08 NA NA NA
#> 65 G2I15 2 3PLM 1.44 NA -0.14 NA 0.15 NA NA NA
#> 66 G2I16 2 3PLM 1.44 NA 0.64 NA 0.15 NA NA NA
#> 67 G2I17 2 3PLM 1.73 NA -1.53 NA 0.08 NA NA NA
#> 68 G2I18 2 3PLM 1.41 NA 0.54 NA 0.06 NA NA NA
#> 69 G2I19 2 3PLM 0.95 NA -0.37 NA 0.05 NA NA NA
#> 70 G2I20 2 3PLM 0.96 NA 2.37 NA 0.08 NA NA NA
#> 71 G2I21 2 3PLM 2.24 NA 1.62 NA 0.10 NA NA NA
#> 72 G2I22 2 3PLM 1.20 NA -0.07 NA 0.05 NA NA NA
#> 73 G2I23 2 3PLM 1.61 NA 0.17 NA 0.10 NA NA NA
#> 74 G2I24 2 3PLM 1.18 NA 0.24 NA 0.01 NA NA NA
#> 75 G2I25 2 3PLM 1.29 NA 1.34 NA 0.01 NA NA NA
#> 76 G2I26 2 3PLM 1.71 NA -1.00 NA 0.17 NA NA NA
#> 77 G2I27 2 3PLM 0.94 NA -0.73 NA 0.14 NA NA NA
#> 78 G2I28 5 GRM 1.11 NA -0.37 NA 0.14 NA 0.78 NA
#> 79 C2I1 2 3PLM 0.97 NA -0.46 NA 0.05 NA NA NA
#> 80 C2I2 2 3PLM 0.85 NA 1.18 NA 0.01 NA NA NA
#> 81 C2I3 2 3PLM 1.43 NA 1.41 NA 0.10 NA NA NA
#> 82 C2I4 2 3PLM 1.48 NA 0.18 NA 0.17 NA NA NA
#> 83 C2I5 2 3PLM 1.27 NA -0.23 NA 0.03 NA NA NA
#> 84 C2I6 2 3PLM 2.02 NA -0.09 NA 0.01 NA NA NA
#> 85 C2I7 2 3PLM 1.37 NA -0.13 NA 0.10 NA NA NA
#> 86 C2I8 2 3PLM 1.67 NA 1.25 NA 0.19 NA NA NA
#> 87 C2I9 2 3PLM 2.28 NA -1.01 NA 0.10 NA NA NA
#> 88 C2I10 2 3PLM 1.42 NA -1.65 NA 0.11 NA NA NA
#> 89 G3I1 2 3PLM 1.55 NA -1.12 NA 0.07 NA NA NA
#> 90 G3I2 2 3PLM 0.75 NA -0.61 NA 0.15 NA NA NA
#> 91 G3I3 2 3PLM 0.90 NA -0.19 NA 0.08 NA NA NA
#> 92 G3I4 2 3PLM 1.06 NA 1.75 NA 0.20 NA NA NA
#> 93 G3I5 2 3PLM 0.71 NA -1.32 NA 0.21 NA NA NA
#> 94 G3I6 2 3PLM 1.01 NA -1.78 NA 0.12 NA NA NA
#> 95 G3I7 2 3PLM 1.09 NA 0.14 NA 0.08 NA NA NA
#> 96 G3I8 2 3PLM 2.07 NA -0.02 NA 0.16 NA NA NA
#> 97 G3I9 2 3PLM 1.20 NA -1.31 NA 0.15 NA NA NA
#> 98 G3I10 2 3PLM 1.27 NA 0.89 NA 0.27 NA NA NA
#> 99 G3I11 2 3PLM 0.74 NA 0.78 NA 0.04 NA NA NA
#> 100 G3I12 2 3PLM 1.44 NA -0.82 NA 0.21 NA NA NA
#> 101 G3I13 2 3PLM 1.19 NA -1.24 NA 0.14 NA NA NA
#> 102 G3I14 2 3PLM 1.23 NA 0.26 NA 0.11 NA NA NA
#> 103 G3I15 2 3PLM 1.39 NA -0.07 NA 0.18 NA NA NA
#> 104 G3I16 2 3PLM 1.39 NA 0.71 NA 0.18 NA NA NA
#> 105 G3I17 2 3PLM 1.68 NA -1.46 NA 0.11 NA NA NA
#> 106 G3I18 2 3PLM 1.36 NA 0.61 NA 0.09 NA NA NA
#> 107 G3I19 2 3PLM 0.90 NA -0.30 NA 0.08 NA NA NA
#> 108 G3I20 2 3PLM 0.91 NA 2.44 NA 0.11 NA NA NA
#> 109 G3I21 2 3PLM 2.19 NA 1.69 NA 0.13 NA NA NA
#> 110 G3I22 2 3PLM 1.15 NA 0.00 NA 0.08 NA NA NA
#> 111 G3I23 2 3PLM 1.56 NA 0.24 NA 0.13 NA NA NA
#> 112 G3I24 2 3PLM 1.13 NA 0.31 NA 0.04 NA NA NA
#> 113 G3I25 2 3PLM 1.24 NA 1.41 NA 0.04 NA NA NA
#> 114 G3I26 2 3PLM 1.66 NA -0.93 NA 0.20 NA NA NA
#> 115 G3I27 2 3PLM 0.89 NA -0.66 NA 0.17 NA NA NA
#> 116 G3I28 5 GRM 1.06 NA -0.30 NA 0.17 NA 0.78 NA
#> par.5 se.5
#> 1 NA NA
#> 2 NA NA
#> 3 NA NA
#> 4 NA NA
#> 5 NA NA
#> 6 NA NA
#> 7 NA NA
#> 8 NA NA
#> 9 NA NA
#> 10 NA NA
#> 11 NA NA
#> 12 NA NA
#> 13 NA NA
#> 14 NA NA
#> 15 NA NA
#> 16 NA NA
#> 17 NA NA
#> 18 NA NA
#> 19 NA NA
#> 20 NA NA
#> 21 NA NA
#> 22 NA NA
#> 23 NA NA
#> 24 NA NA
#> 25 NA NA
#> 26 NA NA
#> 27 NA NA
#> 28 NA NA
#> 29 NA NA
#> 30 NA NA
#> 31 NA NA
#> 32 NA NA
#> 33 NA NA
#> 34 NA NA
#> 35 NA NA
#> 36 NA NA
#> 37 NA NA
#> 38 NA NA
#> 39 NA NA
#> 40 NA NA
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 1.38 NA
#> 49 -0.12 NA
#> 50 1.25 NA
#> 51 NA NA
#> 52 NA NA
#> 53 NA NA
#> 54 NA NA
#> 55 NA NA
#> 56 NA NA
#> 57 NA NA
#> 58 NA NA
#> 59 NA NA
#> 60 NA NA
#> 61 NA NA
#> 62 NA NA
#> 63 NA NA
#> 64 NA NA
#> 65 NA NA
#> 66 NA NA
#> 67 NA NA
#> 68 NA NA
#> 69 NA NA
#> 70 NA NA
#> 71 NA NA
#> 72 NA NA
#> 73 NA NA
#> 74 NA NA
#> 75 NA NA
#> 76 NA NA
#> 77 NA NA
#> 78 1.44 NA
#> 79 NA NA
#> 80 NA NA
#> 81 NA NA
#> 82 NA NA
#> 83 NA NA
#> 84 NA NA
#> 85 NA NA
#> 86 NA NA
#> 87 NA NA
#> 88 NA NA
#> 89 NA NA
#> 90 NA NA
#> 91 NA NA
#> 92 NA NA
#> 93 NA NA
#> 94 NA NA
#> 95 NA NA
#> 96 NA NA
#> 97 NA NA
#> 98 NA NA
#> 99 NA NA
#> 100 NA NA
#> 101 NA NA
#> 102 NA NA
#> 103 NA NA
#> 104 NA NA
#> 105 NA NA
#> 106 NA NA
#> 107 NA NA
#> 108 NA NA
#> 109 NA NA
#> 110 NA NA
#> 111 NA NA
#> 112 NA NA
#> 113 NA NA
#> 114 NA NA
#> 115 NA NA
#> 116 1.39 NA
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) 0.01 0.96 0.98
#> se(Group1) 0.02 0.03 0.02
#> estimate(Group2) 0.52 0.60 0.78
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.28 1.63 1.28
#> se(Group3) 0.03 0.05 0.02
#>
# Extract the group parameter estimates (i.e., scale parameters)
getirt(fit.5, what = "group.par")
#> $Group1
#> mu sigma2 sigma
#> estimates 0.005021632 0.96136149 0.98049044
#> se 0.021924433 0.03040852 0.01550679
#>
#> $Group2
#> mu sigma2 sigma
#> estimates 0.51580977 0.60138258 0.77548861
#> se 0.01734045 0.01902214 0.01226462
#>
#> $Group3
#> mu sigma2 sigma
#> estimates -0.27507220 1.63376235 1.27818714
#> se 0.02858113 0.05167702 0.02021497
#>
## ------------------------------------------------------------------------------
# 4. MG calibration with FIPC using simMG data
# (Fix only the unique items of Group 1)
# - Details:
# (a) Fix item parameters of the unique items in Group 1 only
# (b) Constrain the common items across groups to have
# the same item parameters (i.e., C1I1–C1I12 between
# Groups 1 and 2, and C2I1–C2I10 between Groups 2 and 3)
# (c) Freely estimate the means and variances of the ability
# distributions for all three groups
## ------------------------------------------------------------------------------
# 4-(1). Freely estimate the means and variances for all three groups
# Set all three groups as free groups in which the scales
# of the ability distributions will be freely estimated
free.group <- group.name # or use 'free.group <- 1:3'
# Specify the item IDs of the unique items in Group 1 to be fixed using
# the `fix.id` argument.
fix.id <- paste0("G1I", 1:38)
# Alternatively, use the 'fix.loc' argument as
# 'fix.loc = list(11:48, NULL, NULL)'
# Estimate IRT parameters using MG-FIPC
fit.6 <-
est_mg(
x = x, data = data, group.name = group.name, D = 1,
free.group = free.group, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)),
EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
fipc.method = "MEM", fix.loc = NULL, fix.id = fix.id
)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -43183.7384, Max-Change: 432.57651
EM iteration: 2, Loglike: -171691.1579, Max-Change: 4501.79291
EM iteration: 3, Loglike: -167102.6836, Max-Change: 21514.29256
EM iteration: 4, Loglike: -161125.0804, Max-Change: 0.614658
EM iteration: 5, Loglike: -160697.8752, Max-Change: 15745.96473
EM iteration: 6, Loglike: -160607.1903, Max-Change: 0.223705
EM iteration: 7, Loglike: -160564.3088, Max-Change: 44701.60439
EM iteration: 8, Loglike: -160537.2418, Max-Change: 0.114086
EM iteration: 9, Loglike: -160522.5507, Max-Change: 0.085219
EM iteration: 10, Loglike: -160512.8183, Max-Change: 0.065365
EM iteration: 11, Loglike: -160505.9064, Max-Change: 0.051414
EM iteration: 12, Loglike: -160500.7067, Max-Change: 0.041546
EM iteration: 13, Loglike: -160496.6073, Max-Change: 0.037669
EM iteration: 14, Loglike: -160493.2514, Max-Change: 0.034155
EM iteration: 15, Loglike: -160490.4210, Max-Change: 0.031016
EM iteration: 16, Loglike: -160487.9770, Max-Change: 0.028238
EM iteration: 17, Loglike: -160485.8270, Max-Change: 0.025795
EM iteration: 18, Loglike: -160483.9076, Max-Change: 0.024255
EM iteration: 19, Loglike: -160482.1744, Max-Change: 0.023508
EM iteration: 20, Loglike: -160480.5948, Max-Change: 0.022739
EM iteration: 21, Loglike: -160479.1451, Max-Change: 0.021973
EM iteration: 22, Loglike: -160477.8067, Max-Change: 0.021227
EM iteration: 23, Loglike: -160476.5657, Max-Change: 0.02051
EM iteration: 24, Loglike: -160475.4104, Max-Change: 0.019825
EM iteration: 25, Loglike: -160474.3324, Max-Change: 0.019174
EM iteration: 26, Loglike: -160473.3235, Max-Change: 0.018558
EM iteration: 27, Loglike: -160472.3778, Max-Change: 0.017975
EM iteration: 28, Loglike: -160471.4899, Max-Change: 0.017422
EM iteration: 29, Loglike: -160470.6550, Max-Change: 0.016898
EM iteration: 30, Loglike: -160469.8690, Max-Change: 0.016399
EM iteration: 31, Loglike: -160469.1285, Max-Change: 0.015925
EM iteration: 32, Loglike: -160468.4300, Max-Change: 0.015472
EM iteration: 33, Loglike: -160467.7707, Max-Change: 0.015038
EM iteration: 34, Loglike: -160467.1479, Max-Change: 0.014622
EM iteration: 35, Loglike: -160466.5592, Max-Change: 0.014223
EM iteration: 36, Loglike: -160466.0024, Max-Change: 0.013838
EM iteration: 37, Loglike: -160465.4753, Max-Change: 0.013467
EM iteration: 38, Loglike: -160464.9761, Max-Change: 0.013108
EM iteration: 39, Loglike: -160464.5030, Max-Change: 0.012761
EM iteration: 40, Loglike: -160464.0543, Max-Change: 0.012424
EM iteration: 41, Loglike: -160463.6286, Max-Change: 0.012098
EM iteration: 42, Loglike: -160463.2244, Max-Change: 0.011782
EM iteration: 43, Loglike: -160462.8404, Max-Change: 0.011475
EM iteration: 44, Loglike: -160462.4753, Max-Change: 0.011176
EM iteration: 45, Loglike: -160462.1280, Max-Change: 0.010886
EM iteration: 46, Loglike: -160461.7973, Max-Change: 0.010604
EM iteration: 47, Loglike: -160461.4822, Max-Change: 0.01033
EM iteration: 48, Loglike: -160461.1818, Max-Change: 0.010063
EM iteration: 49, Loglike: -160460.8951, Max-Change: 0.009804
EM iteration: 50, Loglike: -160460.6215, Max-Change: 0.009551
EM iteration: 51, Loglike: -160460.3601, Max-Change: 0.009306
EM iteration: 52, Loglike: -160460.1103, Max-Change: 0.009067
EM iteration: 53, Loglike: -160459.8716, Max-Change: 0.008836
EM iteration: 54, Loglike: -160459.6434, Max-Change: 0.00861
EM iteration: 55, Loglike: -160459.4254, Max-Change: 0.008391
EM iteration: 56, Loglike: -160459.2169, Max-Change: 0.008178
EM iteration: 57, Loglike: -160459.0178, Max-Change: 0.00797
EM iteration: 58, Loglike: -160458.8274, Max-Change: 0.007769
EM iteration: 59, Loglike: -160458.6455, Max-Change: 0.007573
EM iteration: 60, Loglike: -160458.4716, Max-Change: 0.007383
EM iteration: 61, Loglike: -160458.3053, Max-Change: 0.007199
EM iteration: 62, Loglike: -160458.1463, Max-Change: 0.007019
EM iteration: 63, Loglike: -160457.9940, Max-Change: 0.006845
EM iteration: 64, Loglike: -160457.8483, Max-Change: 0.006676
EM iteration: 65, Loglike: -160457.7087, Max-Change: 0.006512
EM iteration: 66, Loglike: -160457.5748, Max-Change: 0.006352
EM iteration: 67, Loglike: -160457.4465, Max-Change: 0.006198
EM iteration: 68, Loglike: -160457.3234, Max-Change: 0.006047
EM iteration: 69, Loglike: -160457.2053, Max-Change: 0.005901
EM iteration: 70, Loglike: -160457.0919, Max-Change: 0.00576
EM iteration: 71, Loglike: -160456.9830, Max-Change: 0.005623
EM iteration: 72, Loglike: -160456.8784, Max-Change: 0.005489
EM iteration: 73, Loglike: -160456.7779, Max-Change: 0.00536
EM iteration: 74, Loglike: -160456.6812, Max-Change: 0.005234
EM iteration: 75, Loglike: -160456.5883, Max-Change: 0.005112
EM iteration: 76, Loglike: -160456.4989, Max-Change: 0.004994
EM iteration: 77, Loglike: -160456.4129, Max-Change: 0.004879
EM iteration: 78, Loglike: -160456.3300, Max-Change: 0.004767
EM iteration: 79, Loglike: -160456.2503, Max-Change: 0.004658
EM iteration: 80, Loglike: -160456.1735, Max-Change: 0.004553
EM iteration: 81, Loglike: -160456.0995, Max-Change: 0.00445
EM iteration: 82, Loglike: -160456.0281, Max-Change: 0.004351
EM iteration: 83, Loglike: -160455.9593, Max-Change: 0.004254
EM iteration: 84, Loglike: -160455.8929, Max-Change: 0.00416
EM iteration: 85, Loglike: -160455.8289, Max-Change: 0.004069
EM iteration: 86, Loglike: -160455.7671, Max-Change: 0.00398
EM iteration: 87, Loglike: -160455.7074, Max-Change: 0.003893
EM iteration: 88, Loglike: -160455.6498, Max-Change: 0.003809
EM iteration: 89, Loglike: -160455.5941, Max-Change: 0.003727
EM iteration: 90, Loglike: -160455.5403, Max-Change: 0.003648
EM iteration: 91, Loglike: -160455.4883, Max-Change: 0.00357
EM iteration: 92, Loglike: -160455.4381, Max-Change: 0.003495
EM iteration: 93, Loglike: -160455.3894, Max-Change: 0.003421
EM iteration: 94, Loglike: -160455.3423, Max-Change: 0.00335
EM iteration: 95, Loglike: -160455.2968, Max-Change: 0.00328
EM iteration: 96, Loglike: -160455.2527, Max-Change: 0.003212
EM iteration: 97, Loglike: -160455.2100, Max-Change: 0.003146
EM iteration: 98, Loglike: -160455.1686, Max-Change: 0.003082
EM iteration: 99, Loglike: -160455.1286, Max-Change: 0.003019
EM iteration: 100, Loglike: -160455.0897, Max-Change: 0.002958
EM iteration: 101, Loglike: -160455.0520, Max-Change: 0.002898
EM iteration: 102, Loglike: -160455.0155, Max-Change: 0.00284
EM iteration: 103, Loglike: -160454.9800, Max-Change: 0.002783
EM iteration: 104, Loglike: -160454.9456, Max-Change: 0.002728
EM iteration: 105, Loglike: -160454.9121, Max-Change: 0.002674
EM iteration: 106, Loglike: -160454.8797, Max-Change: 0.002622
EM iteration: 107, Loglike: -160454.8482, Max-Change: 0.00257
EM iteration: 108, Loglike: -160454.8176, Max-Change: 0.00252
EM iteration: 109, Loglike: -160454.7878, Max-Change: 0.002471
EM iteration: 110, Loglike: -160454.7588, Max-Change: 0.002424
EM iteration: 111, Loglike: -160454.7307, Max-Change: 0.002377
EM iteration: 112, Loglike: -160454.7033, Max-Change: 0.002332
EM iteration: 113, Loglike: -160454.6767, Max-Change: 0.002287
EM iteration: 114, Loglike: -160454.6507, Max-Change: 0.002244
EM iteration: 115, Loglike: -160454.6255, Max-Change: 0.002201
EM iteration: 116, Loglike: -160454.6009, Max-Change: 0.00216
EM iteration: 117, Loglike: -160454.5769, Max-Change: 0.002119
EM iteration: 118, Loglike: -160454.5536, Max-Change: 0.00208
EM iteration: 119, Loglike: -160454.5308, Max-Change: 0.002041
EM iteration: 120, Loglike: -160454.5086, Max-Change: 0.002003
EM iteration: 121, Loglike: -160454.4869, Max-Change: 0.001967
EM iteration: 122, Loglike: -160454.4658, Max-Change: 0.001931
EM iteration: 123, Loglike: -160454.4452, Max-Change: 0.001895
EM iteration: 124, Loglike: -160454.4251, Max-Change: 0.001861
EM iteration: 125, Loglike: -160454.4054, Max-Change: 0.001827
EM iteration: 126, Loglike: -160454.3862, Max-Change: 0.001794
EM iteration: 127, Loglike: -160454.3674, Max-Change: 0.001762
EM iteration: 128, Loglike: -160454.3491, Max-Change: 0.00173
EM iteration: 129, Loglike: -160454.3312, Max-Change: 0.001699
EM iteration: 130, Loglike: -160454.3137, Max-Change: 0.001669
EM iteration: 131, Loglike: -160454.2966, Max-Change: 0.00164
EM iteration: 132, Loglike: -160454.2798, Max-Change: 0.001611
EM iteration: 133, Loglike: -160454.2634, Max-Change: 0.001582
EM iteration: 134, Loglike: -160454.2473, Max-Change: 0.001555
EM iteration: 135, Loglike: -160454.2316, Max-Change: 0.001528
EM iteration: 136, Loglike: -160454.2162, Max-Change: 0.001501
EM iteration: 137, Loglike: -160454.2011, Max-Change: 0.001475
EM iteration: 138, Loglike: -160454.1863, Max-Change: 0.00145
EM iteration: 139, Loglike: -160454.1718, Max-Change: 0.001425
EM iteration: 140, Loglike: -160454.1577, Max-Change: 0.00140
EM iteration: 141, Loglike: -160454.1437, Max-Change: 0.001377
EM iteration: 142, Loglike: -160454.1301, Max-Change: 0.001353
EM iteration: 143, Loglike: -160454.1166, Max-Change: 0.00133
EM iteration: 144, Loglike: -160454.1035, Max-Change: 0.001308
EM iteration: 145, Loglike: -160454.0906, Max-Change: 0.001286
EM iteration: 146, Loglike: -160454.0779, Max-Change: 0.001265
EM iteration: 147, Loglike: -160454.0655, Max-Change: 0.001243
EM iteration: 148, Loglike: -160454.0533, Max-Change: 0.001223
EM iteration: 149, Loglike: -160454.0413, Max-Change: 0.001203
EM iteration: 150, Loglike: -160454.0295, Max-Change: 0.001183
EM iteration: 151, Loglike: -160454.0179, Max-Change: 0.001164
EM iteration: 152, Loglike: -160454.0065, Max-Change: 0.001145
EM iteration: 153, Loglike: -160453.9953, Max-Change: 0.001126
EM iteration: 154, Loglike: -160453.9842, Max-Change: 0.001108
EM iteration: 155, Loglike: -160453.9734, Max-Change: 0.00109
EM iteration: 156, Loglike: -160453.9627, Max-Change: 0.001072
EM iteration: 157, Loglike: -160453.9522, Max-Change: 0.001055
EM iteration: 158, Loglike: -160453.9419, Max-Change: 0.001038
EM iteration: 159, Loglike: -160453.9317, Max-Change: 0.001022
EM iteration: 160, Loglike: -160453.9217, Max-Change: 0.001006
EM iteration: 161, Loglike: -160453.9118, Max-Change: 0.00099
#> Warning: Convergence criteria are not satisfied.
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 59.16 seconds.
# Summary of the estimation
summary(fit.6)
#>
#> Call:
#> est_mg(x = x, data = data, group.name = group.name, D = 1, free.group = free.group,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), EmpHist = TRUE, Etol = 0.001, MaxE = 500, fipc = TRUE,
#> fipc.method = "MEM", fix.loc = NULL, fix.id = fix.id)
#>
#> Summary of the Data
#> Number of Items:
#> Overall: 116 unique items
#> By group: 50(Group1), 50(Group2), 38(Group3)
#> Number of Cases:
#> Overall: 6000
#> By group: 2000(Group1), 2000(Group2), 2000(Group3)
#>
#> Summary of Estimation Process
#> Maximum number of EM cycles: 500
#> Convergence criterion of E-step: 0.001
#> Number of rectangular quadrature points: 49
#> Minimum & Maximum quadrature points: -6, 6
#> Number of free parameters: 248
#> Number of fixed items:
#> Overall: 38
#> By group: 38(Group1), 0(Group2), 0(Group3)
#> Number of E-step cycles completed: 161
#> Maximum parameter change: 0.0009898914
#>
#> Processing time (in seconds)
#> EM algorithm: 58.53
#> Standard error computation: 0.12
#> Total computation: 59.16
#>
#> Convergence and Stability of Solution
#> First-order test: Convergence criteria are not satisfied.
#> Second-order test: Information matrix of item parameter estimates is positive definite.
#> Computation of variance-covariance matrix:
#> Variance-covariance matrix of item parameter estimates is obtainable.
#>
#> Summary of Estimation Results
#> -2loglikelihood:
#> Overall: 320907.8
#> By group: 120433.219(Group1), 114532.034(Group2), 85942.567(Group3)
#>
#> Akaike Information Criterion (AIC): 321403.8
#> Bayesian Information Criterion (BIC): 323065.3
#> Item Parameters (Overall):
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4
#> 1 C1I1 2 3PLM 0.88 0.17 1.37 0.17 0.27 0.05 NA
#> 2 C1I2 2 3PLM 2.17 0.14 -0.97 0.09 0.17 0.06 NA
#> 3 C1I3 2 3PLM 1.05 0.12 0.63 0.13 0.18 0.05 NA
#> 4 C1I4 2 3PLM 1.05 0.12 -0.24 0.22 0.25 0.07 NA
#> 5 C1I5 2 3PLM 0.87 0.09 -0.16 0.21 0.17 0.07 NA
#> 6 C1I6 2 3PLM 1.87 0.13 0.61 0.04 0.08 0.02 NA
#> 7 C1I7 2 3PLM 1.07 0.13 1.12 0.09 0.14 0.03 NA
#> 8 C1I8 2 3PLM 0.93 0.12 0.90 0.14 0.16 0.05 NA
#> 9 C1I9 2 3PLM 0.89 0.12 0.63 0.19 0.20 0.06 NA
#> 10 C1I10 2 3PLM 1.46 0.11 0.13 0.09 0.14 0.04 NA
#> 11 G1I1 2 3PLM 1.00 NA -0.46 NA 0.13 NA NA
#> 12 G1I2 2 3PLM 0.88 NA 1.18 NA 0.09 NA NA
#> 13 G1I3 2 3PLM 1.46 NA 1.41 NA 0.18 NA NA
#> 14 G1I4 2 3PLM 1.51 NA 0.18 NA 0.25 NA NA
#> 15 G1I5 2 3PLM 1.30 NA -0.23 NA 0.11 NA NA
#> 16 G1I6 2 3PLM 2.05 NA -0.09 NA 0.05 NA NA
#> 17 G1I7 2 3PLM 1.40 NA -0.13 NA 0.18 NA NA
#> 18 G1I8 2 3PLM 1.70 NA 1.25 NA 0.27 NA NA
#> 19 G1I9 2 3PLM 2.31 NA -1.01 NA 0.18 NA NA
#> 20 G1I10 2 3PLM 1.45 NA -1.65 NA 0.19 NA NA
#> 21 G1I11 2 3PLM 1.63 NA -1.19 NA 0.12 NA NA
#> 22 G1I12 2 3PLM 0.83 NA -0.68 NA 0.20 NA NA
#> 23 G1I13 2 3PLM 0.98 NA -0.26 NA 0.13 NA NA
#> 24 G1I14 2 3PLM 1.14 NA 1.68 NA 0.25 NA NA
#> 25 G1I15 2 3PLM 0.79 NA -1.39 NA 0.26 NA NA
#> 26 G1I16 2 3PLM 1.09 NA -1.85 NA 0.17 NA NA
#> 27 G1I17 2 3PLM 1.17 NA 0.07 NA 0.13 NA NA
#> 28 G1I18 2 3PLM 2.15 NA -0.09 NA 0.21 NA NA
#> 29 G1I19 2 3PLM 1.28 NA -1.38 NA 0.20 NA NA
#> 30 G1I20 2 3PLM 1.35 NA 0.82 NA 0.32 NA NA
#> 31 G1I21 2 3PLM 0.82 NA 0.71 NA 0.08 NA NA
#> 32 G1I22 2 3PLM 1.52 NA -0.89 NA 0.26 NA NA
#> 33 G1I23 2 3PLM 1.27 NA -1.31 NA 0.19 NA NA
#> 34 G1I24 2 3PLM 1.31 NA 0.19 NA 0.16 NA NA
#> 35 G1I25 2 3PLM 1.47 NA -0.14 NA 0.23 NA NA
#> 36 G1I26 2 3PLM 1.47 NA 0.64 NA 0.23 NA NA
#> 37 G1I27 2 3PLM 1.76 NA -1.53 NA 0.16 NA NA
#> 38 G1I28 2 3PLM 1.44 NA 0.54 NA 0.14 NA NA
#> 39 G1I29 2 3PLM 0.98 NA -0.37 NA 0.13 NA NA
#> 40 G1I30 2 3PLM 0.99 NA 2.37 NA 0.16 NA NA
#> 41 G1I31 2 3PLM 2.27 NA 1.62 NA 0.18 NA NA
#> 42 G1I32 2 3PLM 1.23 NA -0.07 NA 0.13 NA NA
#> 43 G1I33 2 3PLM 1.64 NA 0.17 NA 0.18 NA NA
#> 44 G1I34 2 3PLM 1.21 NA 0.24 NA 0.08 NA NA
#> 45 G1I35 2 3PLM 1.32 NA 1.34 NA 0.08 NA NA
#> 46 G1I36 2 3PLM 1.74 NA -1.00 NA 0.25 NA NA
#> 47 G1I37 2 3PLM 0.97 NA -0.73 NA 0.22 NA NA
#> 48 G1I38 5 GRM 1.14 NA -0.37 NA 0.22 NA 0.85
#> 49 C1I11 5 GRM 1.21 0.05 -2.13 0.09 -1.39 0.06 -0.70
#> 50 C1I12 5 GRM 0.92 0.04 -0.66 0.05 0.05 0.04 0.70
#> 51 G2I1 2 3PLM 1.76 0.19 -0.85 0.17 0.22 0.09 NA
#> 52 G2I2 2 3PLM 0.00 0.09 21591.11 99999.00 0.21 0.09 NA
#> 53 G2I3 2 3PLM 1.08 0.14 0.12 0.20 0.18 0.08 NA
#> 54 G2I4 2 3PLM 1.53 0.30 1.47 0.09 0.18 0.04 NA
#> 55 G2I5 2 3PLM 0.00 0.09 16153.77 99999.00 0.21 0.09 NA
#> 56 G2I6 2 3PLM 1.07 0.15 -1.61 0.31 0.22 0.10 NA
#> 57 G2I7 2 3PLM 1.33 0.14 0.29 0.12 0.13 0.05 NA
#> 58 G2I8 2 3PLM 2.24 0.20 -0.06 0.08 0.14 0.05 NA
#> 59 G2I9 2 3PLM 1.08 0.13 -1.54 0.28 0.21 0.09 NA
#> 60 G2I10 2 3PLM 1.77 0.30 0.95 0.10 0.31 0.05 NA
#> 61 G2I11 2 3PLM 0.96 0.13 0.89 0.15 0.12 0.05 NA
#> 62 G2I12 2 3PLM 0.00 0.11 21352.80 99999.00 0.21 0.09 NA
#> 63 G2I13 2 3PLM 1.18 0.13 -1.27 0.24 0.21 0.09 NA
#> 64 G2I14 2 3PLM 1.41 0.14 0.23 0.11 0.12 0.05 NA
#> 65 G2I15 2 3PLM 1.58 0.21 0.09 0.17 0.28 0.08 NA
#> 66 G2I16 2 3PLM 1.79 0.25 0.78 0.09 0.22 0.05 NA
#> 67 G2I17 2 3PLM 2.07 0.22 -1.20 0.15 0.20 0.09 NA
#> 68 G2I18 2 3PLM 1.76 0.21 0.66 0.08 0.14 0.04 NA
#> 69 G2I19 2 3PLM 1.11 0.14 0.05 0.22 0.20 0.08 NA
#> 70 G2I20 2 3PLM 1.75 0.48 2.17 0.18 0.16 0.02 NA
#> 71 G2I21 2 3PLM 2.52 0.38 1.56 0.06 0.12 0.02 NA
#> 72 G2I22 2 3PLM 1.52 0.20 0.29 0.15 0.23 0.07 NA
#> 73 G2I23 2 3PLM 2.20 0.29 0.49 0.09 0.29 0.05 NA
#> 74 G2I24 2 3PLM 1.42 0.12 0.38 0.07 0.07 0.03 NA
#> 75 G2I25 2 3PLM 1.80 0.23 1.40 0.06 0.07 0.02 NA
#> 76 G2I26 2 3PLM 1.91 0.20 -0.84 0.17 0.25 0.10 NA
#> 77 G2I27 2 3PLM 1.00 0.12 -0.53 0.26 0.21 0.09 NA
#> 78 G2I28 5 GRM 1.14 0.07 -0.35 0.07 0.17 0.05 0.81
#> 79 C2I1 2 3PLM 1.08 0.08 -0.25 0.11 0.13 0.03 NA
#> 80 C2I2 2 3PLM 0.99 0.09 1.27 0.07 0.06 0.02 NA
#> 81 C2I3 2 3PLM 1.61 0.16 1.41 0.05 0.13 0.01 NA
#> 82 C2I4 2 3PLM 1.55 0.11 0.28 0.06 0.19 0.02 NA
#> 83 C2I5 2 3PLM 1.42 0.10 -0.03 0.07 0.12 0.03 NA
#> 84 C2I6 2 3PLM 2.06 0.11 -0.02 0.04 0.05 0.01 NA
#> 85 C2I7 2 3PLM 1.56 0.11 0.04 0.07 0.18 0.02 NA
#> 86 C2I8 2 3PLM 1.51 0.15 1.30 0.06 0.19 0.02 NA
#> 87 C2I9 2 3PLM 2.10 0.13 -1.03 0.07 0.13 0.03 NA
#> 88 C2I10 2 3PLM 0.00 0.04 45122.03 99999.00 0.21 0.09 NA
#> 89 G3I1 2 3PLM 1.50 0.14 -1.07 0.13 0.17 0.05 NA
#> 90 G3I2 2 3PLM 0.00 0.05 299.41 99999.00 0.24 0.10 NA
#> 91 G3I3 2 3PLM 1.10 0.12 0.07 0.12 0.16 0.03 NA
#> 92 G3I4 2 3PLM 1.32 0.24 1.75 0.12 0.23 0.02 NA
#> 93 G3I5 2 3PLM 0.00 0.05 4605.96 99999.00 0.21 0.09 NA
#> 94 G3I6 2 3PLM 1.17 0.15 -1.27 0.25 0.33 0.07 NA
#> 95 G3I7 2 3PLM 1.36 0.13 0.29 0.09 0.14 0.03 NA
#> 96 G3I8 2 3PLM 1.85 0.17 -0.07 0.07 0.14 0.02 NA
#> 97 G3I9 2 3PLM 1.12 0.12 -1.18 0.20 0.22 0.06 NA
#> 98 G3I10 2 3PLM 1.54 0.22 1.02 0.09 0.29 0.02 NA
#> 99 G3I11 2 3PLM 0.89 0.10 0.84 0.11 0.09 0.03 NA
#> 100 G3I12 2 3PLM 1.42 0.17 -0.73 0.15 0.27 0.05 NA
#> 101 G3I13 2 3PLM 1.13 0.13 -1.01 0.21 0.26 0.06 NA
#> 102 G3I14 2 3PLM 1.34 0.14 0.34 0.09 0.17 0.03 NA
#> 103 G3I15 2 3PLM 1.30 0.14 0.01 0.11 0.20 0.03 NA
#> 104 G3I16 2 3PLM 1.59 0.18 0.79 0.08 0.21 0.02 NA
#> 105 G3I17 2 3PLM 1.55 0.15 -1.59 0.15 0.17 0.06 NA
#> 106 G3I18 2 3PLM 1.36 0.14 0.74 0.08 0.12 0.02 NA
#> 107 G3I19 2 3PLM 0.98 0.11 0.13 0.15 0.17 0.04 NA
#> 108 G3I20 2 3PLM 1.15 0.23 2.32 0.20 0.12 0.02 NA
#> 109 G3I21 2 3PLM 3.02 0.56 1.68 0.06 0.14 0.01 NA
#> 110 G3I22 2 3PLM 1.13 0.11 0.09 0.10 0.09 0.03 NA
#> 111 G3I23 2 3PLM 1.77 0.17 0.35 0.07 0.15 0.02 NA
#> 112 G3I24 2 3PLM 1.12 0.09 0.35 0.08 0.06 0.02 NA
#> 113 G3I25 2 3PLM 1.36 0.15 1.40 0.08 0.05 0.01 NA
#> 114 G3I26 2 3PLM 1.61 0.16 -1.01 0.13 0.21 0.05 NA
#> 115 G3I27 2 3PLM 0.91 0.10 -0.62 0.21 0.18 0.06 NA
#> 116 G3I28 5 GRM 0.93 0.05 -0.36 0.06 0.18 0.06 0.86
#> se.4 par.5 se.5
#> 1 NA NA NA
#> 2 NA NA NA
#> 3 NA NA NA
#> 4 NA NA NA
#> 5 NA NA NA
#> 6 NA NA NA
#> 7 NA NA NA
#> 8 NA NA NA
#> 9 NA NA NA
#> 10 NA NA NA
#> 11 NA NA NA
#> 12 NA NA NA
#> 13 NA NA NA
#> 14 NA NA NA
#> 15 NA NA NA
#> 16 NA NA NA
#> 17 NA NA NA
#> 18 NA NA NA
#> 19 NA NA NA
#> 20 NA NA NA
#> 21 NA NA NA
#> 22 NA NA NA
#> 23 NA NA NA
#> 24 NA NA NA
#> 25 NA NA NA
#> 26 NA NA NA
#> 27 NA NA NA
#> 28 NA NA NA
#> 29 NA NA NA
#> 30 NA NA NA
#> 31 NA NA NA
#> 32 NA NA NA
#> 33 NA NA NA
#> 34 NA NA NA
#> 35 NA NA NA
#> 36 NA NA NA
#> 37 NA NA NA
#> 38 NA NA NA
#> 39 NA NA NA
#> 40 NA NA NA
#> 41 NA NA NA
#> 42 NA NA NA
#> 43 NA NA NA
#> 44 NA NA NA
#> 45 NA NA NA
#> 46 NA NA NA
#> 47 NA NA NA
#> 48 NA 1.38 NA
#> 49 0.04 -0.09 0.03
#> 50 0.04 1.27 0.06
#> 51 NA NA NA
#> 52 NA NA NA
#> 53 NA NA NA
#> 54 NA NA NA
#> 55 NA NA NA
#> 56 NA NA NA
#> 57 NA NA NA
#> 58 NA NA NA
#> 59 NA NA NA
#> 60 NA NA NA
#> 61 NA NA NA
#> 62 NA NA NA
#> 63 NA NA NA
#> 64 NA NA NA
#> 65 NA NA NA
#> 66 NA NA NA
#> 67 NA NA NA
#> 68 NA NA NA
#> 69 NA NA NA
#> 70 NA NA NA
#> 71 NA NA NA
#> 72 NA NA NA
#> 73 NA NA NA
#> 74 NA NA NA
#> 75 NA NA NA
#> 76 NA NA NA
#> 77 NA NA NA
#> 78 0.05 1.47 0.07
#> 79 NA NA NA
#> 80 NA NA NA
#> 81 NA NA NA
#> 82 NA NA NA
#> 83 NA NA NA
#> 84 NA NA NA
#> 85 NA NA NA
#> 86 NA NA NA
#> 87 NA NA NA
#> 88 NA NA NA
#> 89 NA NA NA
#> 90 NA NA NA
#> 91 NA NA NA
#> 92 NA NA NA
#> 93 NA NA NA
#> 94 NA NA NA
#> 95 NA NA NA
#> 96 NA NA NA
#> 97 NA NA NA
#> 98 NA NA NA
#> 99 NA NA NA
#> 100 NA NA NA
#> 101 NA NA NA
#> 102 NA NA NA
#> 103 NA NA NA
#> 104 NA NA NA
#> 105 NA NA NA
#> 106 NA NA NA
#> 107 NA NA NA
#> 108 NA NA NA
#> 109 NA NA NA
#> 110 NA NA NA
#> 111 NA NA NA
#> 112 NA NA NA
#> 113 NA NA NA
#> 114 NA NA NA
#> 115 NA NA NA
#> 116 0.07 1.61 0.10
#> Group Parameters:
#> mu sigma2 sigma
#> estimate(Group1) 0.01 0.96 0.98
#> se(Group1) 0.02 0.03 0.02
#> estimate(Group2) 0.51 0.56 0.75
#> se(Group2) 0.02 0.02 0.01
#> estimate(Group3) -0.36 2.11 1.45
#> se(Group3) 0.03 0.07 0.02
#>
# Extract the group parameter estimates (i.e., scale parameters)
getirt(fit.6, what = "group.par")
#> $Group1
#> mu sigma2 sigma
#> estimates 0.008398825 0.95861133 0.9790870
#> se 0.021893051 0.03032153 0.0154846
#>
#> $Group2
#> mu sigma2 sigma
#> estimates 0.51380432 0.55799843 0.74699293
#> se 0.01670327 0.01764987 0.01181395
#>
#> $Group3
#> mu sigma2 sigma
#> estimates -0.36201704 2.10782685 1.45183568
#> se 0.03246403 0.06667201 0.02296128
#>
# }