This function performs fixed ability parameter calibration (FAPC), often called Stocking's (1988) Method A, which estimates item parameters by maximum likelihood given ability estimates (Baker & Kim, 2004; Ban et al., 2001; Stocking, 1988). When prior distributions are specified for item parameters (by default, for the guessing parameters of 3PLM items), the estimates are the modes of the posterior distribution (Bayes modal estimates). It can also be considered a special case of joint maximum likelihood estimation in which only one cycle of item parameter estimation is conducted, conditioned on the given ability estimates (Birnbaum, 1968). FAPC is a potentially useful method for calibrating pretest (or newly developed) items in computerized adaptive testing (CAT), as it enables placing their parameter estimates on the same scale as operational items. In addition, it can be used to recalibrate operational items in the item bank to evaluate potential parameter drift (Chen & Wang, 2016; Stocking, 1988).
Usage
est_item(
x = NULL,
data,
score,
D = 1,
model = NULL,
cats = NULL,
item.id = 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,
use.startval = FALSE,
control = list(eval.max = 500, iter.max = 200, x.tol = 1e-04),
verbose = TRUE
)Arguments
- x
A data frame containing item metadata. This metadata is required to retrieve essential information for each item (e.g., number of score categories, IRT model type, etc.) necessary for calibration. You can create an empty item metadata frame using the function
shape_df().When
use.startval = TRUE, the item parameters specified in the metadata will be used as starting values for parameter estimation; otherwise they are ignored. Ifx = NULL, the models and numbers of score categories are taken from themodelandcatsarguments. Seeest_irt()orsimdat()for more details about the item metadata. Default isNULL.- data
A matrix of examinees' item responses, with rows for examinees and columns for items in the same order as the items in
x. Responses to an item with K score categories must be integers from 0 to K - 1. Missing responses are coded asNAor, in functions that have amissingargument, as the value given inmissing.- score
A numeric vector of examinees' ability estimates (theta values), which are treated as known. It must have one finite value per row of
data, in the same order as the rows.- D
A scaling constant used in IRT models to make the logistic function closely approximate the normal ogive function. A value of 1.702 is commonly used for this purpose. Default is 1.
- model
A character vector specifying the IRT model to fit each item. Available values are:
"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"is a general label for dichotomous items; items labeled"DRM"are fitted with the 3PLM, and a warning is issued. If a single model name is provided, it is recycled for all items. This argument is only used whenx = NULL. Default isNULL.- cats
Numeric vector specifying the number of score categories per item. For dichotomous items, this should be 2. If a single value is supplied, it will be recycled across all items. When
cats = NULLand all models specified in themodelargument are dichotomous ("1PLM","2PLM","3PLM", or"DRM"), the function defaults to 2 categories per item. This argument is used only whenx = NULL. Default isNULL.- item.id
Character vector of item identifiers. If
NULL, the IDs inxare used, or IDs are generated automatically whenx = NULL. A provideditem.idreplaces any IDs inxand must have one value per item. Default isNULL.- 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. The prior ingprioris then not used. 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 the prior distribution ingpriorto the guessing parameters of 3PLM items when they are estimated; the prior is not used whenfix.g = TRUE. Default isTRUE.- aprior, bprior, gprior
A list specifying the prior distribution for all item discrimination (slope), difficulty (or threshold), and guessing parameters. The slope prior is placed on
Dtimes the slope, that is, the density inaprioris evaluated atD * a; withD = 1(the default), this is the slope itself. The priors also enter the information matrix from which the standard errors are computed. 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, in addition to
NA, which is always treated as missing. Missing responses are omitted from the likelihood, which assumes that they are missing at random. Default isNA.- use.startval
Logical. If
TRUE, the item parameters provided in the item metadata (i.e., thexargument) are used as starting values for the items whose parameters are estimated;xmust then be supplied. Otherwise, internally generated starting values are used. Default isFALSE.- control
A named list of control options for
stats::nlminb(), which maximizes the objective of each item (see Details). The default islist(eval.max = 500, iter.max = 200, x.tol = 1e-4), whereeval.maxis the maximum number of objective function evaluations,iter.maxis the maximum number of optimizer iterations, andx.tolis the X-convergence tolerance ofstats::nlminb().
A partial list may be supplied; options that are not supplied keep their default values. Other options of
stats::nlminb(), such asrel.tolortrace, can also be supplied.- verbose
Logical. If
FALSE, all progress messages are suppressed. Default isTRUE.
Value
This function returns an object of class est_item. The returned
object contains the following components:
- estimates
A data frame containing both the item parameter estimates and their corresponding standard errors.
- par.est
A data frame of item parameter estimates, structured according to the item metadata format.
- se.est
A data frame of standard errors for the item parameter estimates, computed from the inverse of the observed information matrix (the Hessian of the negative log-likelihood, plus the negative second derivatives of the log prior densities when priors are used). The abilities in
scoreare treated as known, so their estimation error is not reflected in the standard errors.- pos.par
A data frame of the positions of the estimated item parameters in
covariance. The rows of the excluded items areNA, and a slope shared by 1PLM items appears only in the row of the first 1PLM item.- covariance
A variance-covariance matrix of the item parameter estimates. Items are estimated separately, so the covariances between the parameters of different items are 0, except among the 1PLM items that share a common slope.
- loglikelihood
The log-likelihood of the observed responses given the abilities in
score, summed over the items, at the final estimates. The log prior densities of the item parameters are not included. Printed results report -2 times this value as "-2loglikelihood".- group.par
A named numeric vector with the mean (
mu) and the standard deviation (sigma) of the abilities inscore.- data
A data frame of the response data used in the estimation, with missing responses as
NAand without the excluded items (seedeleted.item).- score
A vector of examinees' ability estimates used as fixed values during item parameter estimation.
- scale.D
The scaling factor used in the IRT model.
- convergence
A message indicating whether item parameter estimation successfully converged.
- nitem
The number of items in
dataas supplied, including the excluded items.- deleted.item
A numeric vector of the positions of the items without any response, which are excluded from the estimation (empty if there are none). Their rows in
par.estandse.estareNA.- npar.est
The number of estimated item parameters.
- n.response
A numeric vector of the numbers of non-missing responses to the items, with 0 for the excluded items.
- TotalTime
Total computation time in seconds.
- call
The matched call.
Note that you can easily extract components from the output using the
getirt() function.
Details
The parameters of each item are estimated separately by maximizing
the log-likelihood of its responses given the abilities in score (plus
the log prior densities when priors are used), except that the 1PLM items
share one slope, estimated jointly with their difficulties, when
fix.a.1pl = FALSE. Missing responses are omitted. Items without any
response are excluded from the estimation with a warning.
In most cases, the function est_item() returns successfully
converged item parameter estimates using its default internal starting
values. However, if convergence issues arise during calibration, one
possible solution is to use alternative starting values. If item parameter
values are already specified in the item metadata (i.e., the x argument),
they can be used as starting values for item parameter calibration by
setting use.startval = TRUE.
A maximum likelihood estimate does not exist for an item with a score
category that has no responses, which includes an item whose responses are
all the same. The estimates of such an item can be extreme or remain near
their starting values, and their standard errors are unreliable (a standard
error of 99999 means that it could not be obtained). After the items
without any response are excluded, one warning lists the IDs of the
remaining items of this kind. A parameter with a prior distribution, such
as the guessing parameter of a 3PLM item with use.gprior = TRUE, can
still be stable.
When prior distributions are used, the item parameters are Bayes modal
estimates, and loglikelihood is the log-likelihood at these estimates
without the log prior densities.
The print method of this class has an argument digits that is not used.
It prints the log-likelihood with the number of significant digits given
by getOption("digits") (7 by default).
References
Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques. CRC Press.
Ban, J. C., Hanson, B. A., Wang, T., Yi, Q., & Harris, D. J. (2001). A comparative study of on-line pretest item calibration/scaling methods in computerized adaptive testing. Journal of Educational Measurement, 38(3), 191-212. doi:10.1111/j.1745-3984.2001.tb01123.x .
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397-479). Reading, MA: Addison-Wesley.
Chen, P., & Wang, C. (2016). A new online calibration method for multidimensional computerized adaptive testing. Psychometrika, 81(3), 674-701.
Stocking, M. L. (1988). Scale drift in on-line calibration (Research Rep. 88-28). Princeton, NJ: ETS.
Author
Hwanggyu Lim hglim83@gmail.com
Examples
## Import the "-prm.txt" output file from flexMIRT
flex_sam <- system.file("extdata", "flexmirt_sample-prm.txt", package = "irtQ")
# Extract the item metadata
x <- bring.flexmirt(file = flex_sam, "par")$Group1$full_df
# Modify the item metadata so that some items follow 1PLM, 2PLM, and GPCM
x[c(1:3, 5), 3] <- "1PLM"
x[c(1:3, 5), 4] <- 1
x[c(1:3, 5), 6] <- 0
x[c(4, 8:12), 3] <- "2PLM"
x[c(4, 8:12), 6] <- 0
x[54:55, 3] <- "GPCM"
# Generate examinees' abilities from N(0, 1)
set.seed(23)
score <- rnorm(500, mean = 0, sd = 1)
# Simulate response data based on the item metadata and ability values
data <- simdat(x = x, theta = score, D = 1)
# \donttest{
# 1) Estimate item parameters: constrain the slope parameters of 1PLM items
# to be equal
(mod1 <- est_item(x, data, score,
D = 1, fix.a.1pl = FALSE, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)), use.startval = FALSE
))
#> Starting...
#> Parsing input...
#> Estimating item parameters...
#> Estimation is finished.
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = FALSE,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), use.startval = FALSE)
#>
#> Fixed ability parameter calibration (Stocking's Method A).
#> All item parameters were successfully converged.
#>
#> Log-likelihood: -15883.69
#>
summary(mod1)
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = FALSE,
#> use.gprior = TRUE, gprior = list(dist = "beta", params = c(5,
#> 16)), use.startval = FALSE)
#>
#> Summary of the Data
#> Number of Items in Response Data: 55
#> Number of Excluded Items: 0
#> Number of free parameters: 162
#> Number of Responses for Each Item:
#> id n
#> 1 CMC1 500
#> 2 CMC2 500
#> 3 CMC3 500
#> 4 CMC4 500
#> 5 CMC5 500
#> 6 CMC6 500
#> 7 CMC7 500
#> 8 CMC8 500
#> 9 CMC9 500
#> 10 CMC10 500
#> 11 CMC11 500
#> 12 CMC12 500
#> 13 CMC13 500
#> 14 CMC14 500
#> 15 CMC15 500
#> 16 CMC16 500
#> 17 CMC17 500
#> 18 CMC18 500
#> 19 CMC19 500
#> 20 CMC20 500
#> 21 CMC21 500
#> 22 CMC22 500
#> 23 CMC23 500
#> 24 CMC24 500
#> 25 CMC25 500
#> 26 CMC26 500
#> 27 CMC27 500
#> 28 CMC28 500
#> 29 CMC29 500
#> 30 CMC30 500
#> 31 CMC31 500
#> 32 CMC32 500
#> 33 CMC33 500
#> 34 CMC34 500
#> 35 CMC35 500
#> 36 CMC36 500
#> 37 CMC37 500
#> 38 CMC38 500
#> 39 CFR1 500
#> 40 CFR2 500
#> 41 AMC1 500
#> 42 AMC2 500
#> 43 AMC3 500
#> 44 AMC4 500
#> 45 AMC5 500
#> 46 AMC6 500
#> 47 AMC7 500
#> 48 AMC8 500
#> 49 AMC9 500
#> 50 AMC10 500
#> 51 AMC11 500
#> 52 AMC12 500
#> 53 AFR1 500
#> 54 AFR2 500
#> 55 AFR3 500
#>
#> Processing time (in seconds)
#> Total computation: 0.46
#>
#> Convergence of Solution
#> All item parameters were successfully converged.
#>
#> Summary of Estimation Results
#> -2loglikelihood: 31767.38
#> Item Parameters:
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 CMC1 2 1PLM 1.02 0.06 1.60 0.13 NA NA NA NA
#> 2 CMC2 2 1PLM 1.02 NA -1.06 0.12 NA NA NA NA
#> 3 CMC3 2 1PLM 1.02 NA 0.40 0.10 NA NA NA NA
#> 4 CMC4 2 2PLM 0.96 0.12 -0.43 0.11 NA NA NA NA
#> 5 CMC5 2 1PLM 1.02 NA -0.25 0.10 NA NA NA NA
#> 6 CMC6 2 3PLM 1.88 0.27 0.67 0.09 0.10 0.03 NA NA
#> 7 CMC7 2 3PLM 0.89 0.17 1.04 0.23 0.14 0.05 NA NA
#> 8 CMC8 2 2PLM 0.92 0.12 0.87 0.13 NA NA NA NA
#> 9 CMC9 2 2PLM 1.00 0.12 0.89 0.13 NA NA NA NA
#> 10 CMC10 2 2PLM 1.61 0.15 0.09 0.07 NA NA NA NA
#> 11 CMC11 2 2PLM 1.07 0.12 -0.37 0.10 NA NA NA NA
#> 12 CMC12 2 2PLM 0.94 0.12 1.10 0.15 NA NA NA NA
#> 13 CMC13 2 3PLM 1.36 0.34 1.32 0.17 0.17 0.04 NA NA
#> 14 CMC14 2 3PLM 1.39 0.32 0.17 0.24 0.25 0.08 NA NA
#> 15 CMC15 2 3PLM 1.54 0.27 0.02 0.17 0.21 0.07 NA NA
#> 16 CMC16 2 3PLM 2.10 0.25 0.04 0.08 0.10 0.04 NA NA
#> 17 CMC17 2 3PLM 1.02 0.16 -0.40 0.22 0.17 0.07 NA NA
#> 18 CMC18 2 3PLM 1.29 0.38 1.43 0.20 0.23 0.05 NA NA
#> 19 CMC19 2 3PLM 2.26 0.32 -1.10 0.14 0.18 0.07 NA NA
#> 20 CMC20 2 3PLM 1.47 0.22 -1.72 0.23 0.19 0.08 NA NA
#> 21 CMC21 2 3PLM 1.39 0.21 -1.23 0.23 0.21 0.09 NA NA
#> 22 CMC22 2 3PLM 0.93 0.16 -0.53 0.28 0.20 0.08 NA NA
#> 23 CMC23 2 3PLM 1.12 0.23 -0.09 0.28 0.23 0.09 NA NA
#> 24 CMC24 2 3PLM 1.23 0.34 1.44 0.21 0.22 0.05 NA NA
#> 25 CMC25 2 3PLM 0.83 0.16 -1.47 0.41 0.22 0.10 NA NA
#> 26 CMC26 2 3PLM 1.07 0.19 -2.14 0.35 0.20 0.09 NA NA
#> 27 CMC27 2 3PLM 1.18 0.18 0.10 0.17 0.15 0.06 NA NA
#> 28 CMC28 2 3PLM 2.20 0.32 -0.16 0.11 0.19 0.05 NA NA
#> 29 CMC29 2 3PLM 2.53 0.55 -0.79 0.19 0.40 0.09 NA NA
#> 30 CMC30 2 3PLM 1.90 0.45 0.70 0.15 0.34 0.05 NA NA
#> 31 CMC31 2 3PLM 0.71 0.16 1.02 0.33 0.16 0.07 NA NA
#> 32 CMC32 2 3PLM 1.76 0.31 -0.76 0.21 0.27 0.09 NA NA
#> 33 CMC33 2 3PLM 1.07 0.17 -1.43 0.28 0.20 0.09 NA NA
#> 34 CMC34 2 3PLM 1.05 0.17 0.22 0.20 0.16 0.06 NA NA
#> 35 CMC35 2 3PLM 1.37 0.19 -0.44 0.17 0.16 0.07 NA NA
#> 36 CMC36 2 3PLM 0.89 0.17 0.98 0.23 0.14 0.05 NA NA
#> 37 CMC37 2 3PLM 2.13 0.26 -0.24 0.09 0.13 0.05 NA NA
#> 38 CMC38 2 3PLM 0.88 0.17 -0.28 0.32 0.21 0.09 NA NA
#> 39 CFR1 5 GRM 2.00 0.14 -1.88 0.12 -1.25 0.08 -0.70 0.06
#> 40 CFR2 5 GRM 1.39 0.11 -0.80 0.09 -0.13 0.07 0.60 0.08
#> 41 AMC1 2 3PLM 1.83 0.39 0.74 0.14 0.28 0.05 NA NA
#> 42 AMC2 2 3PLM 1.71 0.25 -1.58 0.20 0.19 0.08 NA NA
#> 43 AMC3 2 3PLM 1.31 0.25 0.69 0.16 0.16 0.05 NA NA
#> 44 AMC4 2 3PLM 0.95 0.17 -0.15 0.26 0.19 0.08 NA NA
#> 45 AMC5 2 3PLM 1.70 0.65 2.11 0.26 0.19 0.03 NA NA
#> 46 AMC6 2 3PLM 2.84 0.64 1.44 0.10 0.15 0.02 NA NA
#> 47 AMC7 2 3PLM 1.72 0.41 0.39 0.18 0.26 0.07 NA NA
#> 48 AMC8 2 3PLM 1.66 0.29 0.40 0.14 0.20 0.05 NA NA
#> 49 AMC9 2 3PLM 1.56 0.26 0.49 0.13 0.15 0.05 NA NA
#> 50 AMC10 2 3PLM 2.49 0.51 1.31 0.10 0.13 0.02 NA NA
#> 51 AMC11 2 3PLM 1.74 0.23 -1.01 0.16 0.17 0.07 NA NA
#> 52 AMC12 2 3PLM 0.97 0.21 -0.78 0.40 0.26 0.11 NA NA
#> 53 AFR1 5 GRM 1.14 0.10 -0.30 0.09 0.30 0.09 0.92 0.11
#> 54 AFR2 5 GPCM 1.33 0.11 -1.99 0.21 -1.31 0.15 -0.72 0.12
#> 55 AFR3 5 GPCM 0.89 0.07 -0.80 0.15 0.15 0.15 0.46 0.16
#> 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 -0.23 0.06
#> 40 1.09 0.10
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 NA NA
#> 49 NA NA
#> 50 NA NA
#> 51 NA NA
#> 52 NA NA
#> 53 1.35 0.13
#> 54 -0.21 0.10
#> 55 1.35 0.19
#>
#> Group Parameters:
#> mu sigma
#> 0.03 1.02
#>
# Extract the item parameter estimates
getirt(mod1, what = "par.est")
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 CMC1 2 1PLM 1.0185279 1.60133220 NA NA NA
#> 2 CMC2 2 1PLM 1.0185279 -1.06375410 NA NA NA
#> 3 CMC3 2 1PLM 1.0185279 0.39651768 NA NA NA
#> 4 CMC4 2 2PLM 0.9627020 -0.42559338 NA NA NA
#> 5 CMC5 2 1PLM 1.0185279 -0.25036387 NA NA NA
#> 6 CMC6 2 3PLM 1.8846619 0.67350821 0.1041510 NA NA
#> 7 CMC7 2 3PLM 0.8866580 1.03619252 0.1374716 NA NA
#> 8 CMC8 2 2PLM 0.9232153 0.86515210 NA NA NA
#> 9 CMC9 2 2PLM 1.0043493 0.89227667 NA NA NA
#> 10 CMC10 2 2PLM 1.6128253 0.09253022 NA NA NA
#> 11 CMC11 2 2PLM 1.0684709 -0.37379104 NA NA NA
#> 12 CMC12 2 2PLM 0.9377669 1.09646572 NA NA NA
#> 13 CMC13 2 3PLM 1.3645089 1.31503341 0.1703375 NA NA
#> 14 CMC14 2 3PLM 1.3898925 0.17217473 0.2472123 NA NA
#> 15 CMC15 2 3PLM 1.5408435 0.01937278 0.2070791 NA NA
#> 16 CMC16 2 3PLM 2.1026954 0.04186170 0.1039632 NA NA
#> 17 CMC17 2 3PLM 1.0234932 -0.39553054 0.1653727 NA NA
#> 18 CMC18 2 3PLM 1.2856593 1.43007415 0.2250732 NA NA
#> 19 CMC19 2 3PLM 2.2594756 -1.10181795 0.1778769 NA NA
#> 20 CMC20 2 3PLM 1.4700031 -1.72399703 0.1889865 NA NA
#> 21 CMC21 2 3PLM 1.3912594 -1.23367452 0.2093723 NA NA
#> 22 CMC22 2 3PLM 0.9317523 -0.52661586 0.1982627 NA NA
#> 23 CMC23 2 3PLM 1.1204103 -0.09122518 0.2259506 NA NA
#> 24 CMC24 2 3PLM 1.2290146 1.43876383 0.2204891 NA NA
#> 25 CMC25 2 3PLM 0.8330125 -1.46925302 0.2244715 NA NA
#> 26 CMC26 2 3PLM 1.0676986 -2.13985943 0.1999090 NA NA
#> 27 CMC27 2 3PLM 1.1843144 0.09628328 0.1469717 NA NA
#> 28 CMC28 2 3PLM 2.2044237 -0.16348433 0.1944618 NA NA
#> 29 CMC29 2 3PLM 2.5307240 -0.78717016 0.3956548 NA NA
#> 30 CMC30 2 3PLM 1.9041795 0.70161781 0.3404332 NA NA
#> 31 CMC31 2 3PLM 0.7062845 1.02018205 0.1641299 NA NA
#> 32 CMC32 2 3PLM 1.7564751 -0.76184344 0.2681714 NA NA
#> 33 CMC33 2 3PLM 1.0744198 -1.42868292 0.1991516 NA NA
#> 34 CMC34 2 3PLM 1.0509163 0.22205598 0.1609429 NA NA
#> 35 CMC35 2 3PLM 1.3654004 -0.43712558 0.1629476 NA NA
#> 36 CMC36 2 3PLM 0.8871087 0.97700579 0.1423811 NA NA
#> 37 CMC37 2 3PLM 2.1311743 -0.24278137 0.1309809 NA NA
#> 38 CMC38 2 3PLM 0.8813430 -0.28321005 0.2131754 NA NA
#> 39 CFR1 5 GRM 2.0000867 -1.88248141 -1.2545794 -0.7031275 -0.2324418
#> 40 CFR2 5 GRM 1.3885998 -0.79658308 -0.1288726 0.6012371 1.0859619
#> 41 AMC1 2 3PLM 1.8272686 0.74245570 0.2788644 NA NA
#> 42 AMC2 2 3PLM 1.7110855 -1.58183908 0.1947024 NA NA
#> 43 AMC3 2 3PLM 1.3145385 0.68535647 0.1615132 NA NA
#> 44 AMC4 2 3PLM 0.9496703 -0.15473831 0.1915267 NA NA
#> 45 AMC5 2 3PLM 1.7029567 2.10717153 0.1910672 NA NA
#> 46 AMC6 2 3PLM 2.8374610 1.44493420 0.1542768 NA NA
#> 47 AMC7 2 3PLM 1.7188353 0.38574744 0.2586265 NA NA
#> 48 AMC8 2 3PLM 1.6576325 0.39605794 0.2033722 NA NA
#> 49 AMC9 2 3PLM 1.5568580 0.49337767 0.1543679 NA NA
#> 50 AMC10 2 3PLM 2.4905705 1.31162574 0.1294143 NA NA
#> 51 AMC11 2 3PLM 1.7412715 -1.01102653 0.1696460 NA NA
#> 52 AMC12 2 3PLM 0.9688530 -0.77937288 0.2552984 NA NA
#> 53 AFR1 5 GRM 1.1355459 -0.30016570 0.3028394 0.9182795 1.3525597
#> 54 AFR2 5 GPCM 1.3267609 -1.99444989 -1.3127161 -0.7196856 -0.2068705
#> 55 AFR3 5 GPCM 0.8941751 -0.79542779 0.1540945 0.4638485 1.3511384
# 2) Estimate item parameters: fix the slope parameters of 1PLM items to 1
(mod2 <- est_item(x, data, score,
D = 1, fix.a.1pl = TRUE, a.val.1pl = 1, use.gprior = TRUE,
gprior = list(dist = "beta", params = c(5, 16)), use.startval = FALSE
))
#> Starting...
#> Parsing input...
#> Estimating item parameters...
#> Estimation is finished.
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = TRUE,
#> a.val.1pl = 1, use.gprior = TRUE, gprior = list(dist = "beta",
#> params = c(5, 16)), use.startval = FALSE)
#>
#> Fixed ability parameter calibration (Stocking's Method A).
#> All item parameters were successfully converged.
#>
#> Log-likelihood: -15883.73
#>
summary(mod2)
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = TRUE,
#> a.val.1pl = 1, use.gprior = TRUE, gprior = list(dist = "beta",
#> params = c(5, 16)), use.startval = FALSE)
#>
#> Summary of the Data
#> Number of Items in Response Data: 55
#> Number of Excluded Items: 0
#> Number of free parameters: 161
#> Number of Responses for Each Item:
#> id n
#> 1 CMC1 500
#> 2 CMC2 500
#> 3 CMC3 500
#> 4 CMC4 500
#> 5 CMC5 500
#> 6 CMC6 500
#> 7 CMC7 500
#> 8 CMC8 500
#> 9 CMC9 500
#> 10 CMC10 500
#> 11 CMC11 500
#> 12 CMC12 500
#> 13 CMC13 500
#> 14 CMC14 500
#> 15 CMC15 500
#> 16 CMC16 500
#> 17 CMC17 500
#> 18 CMC18 500
#> 19 CMC19 500
#> 20 CMC20 500
#> 21 CMC21 500
#> 22 CMC22 500
#> 23 CMC23 500
#> 24 CMC24 500
#> 25 CMC25 500
#> 26 CMC26 500
#> 27 CMC27 500
#> 28 CMC28 500
#> 29 CMC29 500
#> 30 CMC30 500
#> 31 CMC31 500
#> 32 CMC32 500
#> 33 CMC33 500
#> 34 CMC34 500
#> 35 CMC35 500
#> 36 CMC36 500
#> 37 CMC37 500
#> 38 CMC38 500
#> 39 CFR1 500
#> 40 CFR2 500
#> 41 AMC1 500
#> 42 AMC2 500
#> 43 AMC3 500
#> 44 AMC4 500
#> 45 AMC5 500
#> 46 AMC6 500
#> 47 AMC7 500
#> 48 AMC8 500
#> 49 AMC9 500
#> 50 AMC10 500
#> 51 AMC11 500
#> 52 AMC12 500
#> 53 AFR1 500
#> 54 AFR2 500
#> 55 AFR3 500
#>
#> Processing time (in seconds)
#> Total computation: 0.45
#>
#> Convergence of Solution
#> All item parameters were successfully converged.
#>
#> Summary of Estimation Results
#> -2loglikelihood: 31767.47
#> Item Parameters:
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 CMC1 2 1PLM 1.00 NA 1.62 0.12 NA NA NA NA
#> 2 CMC2 2 1PLM 1.00 NA -1.08 0.11 NA NA NA NA
#> 3 CMC3 2 1PLM 1.00 NA 0.40 0.10 NA NA NA NA
#> 4 CMC4 2 2PLM 0.96 0.12 -0.43 0.11 NA NA NA NA
#> 5 CMC5 2 1PLM 1.00 NA -0.25 0.10 NA NA NA NA
#> 6 CMC6 2 3PLM 1.88 0.27 0.67 0.09 0.10 0.03 NA NA
#> 7 CMC7 2 3PLM 0.89 0.17 1.04 0.23 0.14 0.05 NA NA
#> 8 CMC8 2 2PLM 0.92 0.12 0.87 0.13 NA NA NA NA
#> 9 CMC9 2 2PLM 1.00 0.12 0.89 0.13 NA NA NA NA
#> 10 CMC10 2 2PLM 1.61 0.15 0.09 0.07 NA NA NA NA
#> 11 CMC11 2 2PLM 1.07 0.12 -0.37 0.10 NA NA NA NA
#> 12 CMC12 2 2PLM 0.94 0.12 1.10 0.15 NA NA NA NA
#> 13 CMC13 2 3PLM 1.36 0.34 1.32 0.17 0.17 0.04 NA NA
#> 14 CMC14 2 3PLM 1.39 0.32 0.17 0.24 0.25 0.08 NA NA
#> 15 CMC15 2 3PLM 1.54 0.27 0.02 0.17 0.21 0.07 NA NA
#> 16 CMC16 2 3PLM 2.10 0.25 0.04 0.08 0.10 0.04 NA NA
#> 17 CMC17 2 3PLM 1.02 0.16 -0.40 0.22 0.17 0.07 NA NA
#> 18 CMC18 2 3PLM 1.29 0.38 1.43 0.20 0.23 0.05 NA NA
#> 19 CMC19 2 3PLM 2.26 0.32 -1.10 0.14 0.18 0.07 NA NA
#> 20 CMC20 2 3PLM 1.47 0.22 -1.72 0.23 0.19 0.08 NA NA
#> 21 CMC21 2 3PLM 1.39 0.21 -1.23 0.23 0.21 0.09 NA NA
#> 22 CMC22 2 3PLM 0.93 0.16 -0.53 0.28 0.20 0.08 NA NA
#> 23 CMC23 2 3PLM 1.12 0.23 -0.09 0.28 0.23 0.09 NA NA
#> 24 CMC24 2 3PLM 1.23 0.34 1.44 0.21 0.22 0.05 NA NA
#> 25 CMC25 2 3PLM 0.83 0.16 -1.47 0.41 0.22 0.10 NA NA
#> 26 CMC26 2 3PLM 1.07 0.19 -2.14 0.35 0.20 0.09 NA NA
#> 27 CMC27 2 3PLM 1.18 0.18 0.10 0.17 0.15 0.06 NA NA
#> 28 CMC28 2 3PLM 2.20 0.32 -0.16 0.11 0.19 0.05 NA NA
#> 29 CMC29 2 3PLM 2.53 0.55 -0.79 0.19 0.40 0.09 NA NA
#> 30 CMC30 2 3PLM 1.90 0.45 0.70 0.15 0.34 0.05 NA NA
#> 31 CMC31 2 3PLM 0.71 0.16 1.02 0.33 0.16 0.07 NA NA
#> 32 CMC32 2 3PLM 1.76 0.31 -0.76 0.21 0.27 0.09 NA NA
#> 33 CMC33 2 3PLM 1.07 0.17 -1.43 0.28 0.20 0.09 NA NA
#> 34 CMC34 2 3PLM 1.05 0.17 0.22 0.20 0.16 0.06 NA NA
#> 35 CMC35 2 3PLM 1.37 0.19 -0.44 0.17 0.16 0.07 NA NA
#> 36 CMC36 2 3PLM 0.89 0.17 0.98 0.23 0.14 0.05 NA NA
#> 37 CMC37 2 3PLM 2.13 0.26 -0.24 0.09 0.13 0.05 NA NA
#> 38 CMC38 2 3PLM 0.88 0.17 -0.28 0.32 0.21 0.09 NA NA
#> 39 CFR1 5 GRM 2.00 0.14 -1.88 0.12 -1.25 0.08 -0.70 0.06
#> 40 CFR2 5 GRM 1.39 0.11 -0.80 0.09 -0.13 0.07 0.60 0.08
#> 41 AMC1 2 3PLM 1.83 0.39 0.74 0.14 0.28 0.05 NA NA
#> 42 AMC2 2 3PLM 1.71 0.25 -1.58 0.20 0.19 0.08 NA NA
#> 43 AMC3 2 3PLM 1.31 0.25 0.69 0.16 0.16 0.05 NA NA
#> 44 AMC4 2 3PLM 0.95 0.17 -0.15 0.26 0.19 0.08 NA NA
#> 45 AMC5 2 3PLM 1.70 0.65 2.11 0.26 0.19 0.03 NA NA
#> 46 AMC6 2 3PLM 2.84 0.64 1.44 0.10 0.15 0.02 NA NA
#> 47 AMC7 2 3PLM 1.72 0.41 0.39 0.18 0.26 0.07 NA NA
#> 48 AMC8 2 3PLM 1.66 0.29 0.40 0.14 0.20 0.05 NA NA
#> 49 AMC9 2 3PLM 1.56 0.26 0.49 0.13 0.15 0.05 NA NA
#> 50 AMC10 2 3PLM 2.49 0.51 1.31 0.10 0.13 0.02 NA NA
#> 51 AMC11 2 3PLM 1.74 0.23 -1.01 0.16 0.17 0.07 NA NA
#> 52 AMC12 2 3PLM 0.97 0.21 -0.78 0.40 0.26 0.11 NA NA
#> 53 AFR1 5 GRM 1.14 0.10 -0.30 0.09 0.30 0.09 0.92 0.11
#> 54 AFR2 5 GPCM 1.33 0.11 -1.99 0.21 -1.31 0.15 -0.72 0.12
#> 55 AFR3 5 GPCM 0.89 0.07 -0.80 0.15 0.15 0.15 0.46 0.16
#> 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 -0.23 0.06
#> 40 1.09 0.10
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 NA NA
#> 49 NA NA
#> 50 NA NA
#> 51 NA NA
#> 52 NA NA
#> 53 1.35 0.13
#> 54 -0.21 0.10
#> 55 1.35 0.19
#>
#> Group Parameters:
#> mu sigma
#> 0.03 1.02
#>
# Extract the standard error estimates
getirt(mod2, what = "se.est")
#> id cats model par.1 par.2 par.3 par.4 par.5
#> 1 CMC1 2 1PLM NA 0.11819685 NA NA NA
#> 2 CMC2 2 1PLM NA 0.10825953 NA NA NA
#> 3 CMC3 2 1PLM NA 0.09953834 NA NA NA
#> 4 CMC4 2 2PLM 0.11608725 0.11102431 NA NA NA
#> 5 CMC5 2 1PLM NA 0.09928963 NA NA NA
#> 6 CMC6 2 3PLM 0.26669060 0.09232536 0.03138242 NA NA
#> 7 CMC7 2 3PLM 0.17171857 0.22999854 0.05092018 NA NA
#> 8 CMC8 2 2PLM 0.11779263 0.13411409 NA NA NA
#> 9 CMC9 2 2PLM 0.12280227 0.12623451 NA NA NA
#> 10 CMC10 2 2PLM 0.15351879 0.06743190 NA NA NA
#> 11 CMC11 2 2PLM 0.12147067 0.09986851 NA NA NA
#> 12 CMC12 2 2PLM 0.12170130 0.14960502 NA NA NA
#> 13 CMC13 2 3PLM 0.33830056 0.16875186 0.04452707 NA NA
#> 14 CMC14 2 3PLM 0.32184562 0.23754432 0.08294538 NA NA
#> 15 CMC15 2 3PLM 0.27056505 0.17343671 0.06714419 NA NA
#> 16 CMC16 2 3PLM 0.24879579 0.08406154 0.03704144 NA NA
#> 17 CMC17 2 3PLM 0.15550550 0.22209049 0.07041155 NA NA
#> 18 CMC18 2 3PLM 0.38393374 0.20356474 0.05087416 NA NA
#> 19 CMC19 2 3PLM 0.32044597 0.14051114 0.07448965 NA NA
#> 20 CMC20 2 3PLM 0.21920822 0.22689431 0.08281388 NA NA
#> 21 CMC21 2 3PLM 0.21215536 0.22895293 0.08608492 NA NA
#> 22 CMC22 2 3PLM 0.15932023 0.28436101 0.08224986 NA NA
#> 23 CMC23 2 3PLM 0.22727469 0.27935617 0.08847770 NA NA
#> 24 CMC24 2 3PLM 0.33771111 0.21032077 0.04739131 NA NA
#> 25 CMC25 2 3PLM 0.16035815 0.41455949 0.09844718 NA NA
#> 26 CMC26 2 3PLM 0.18549120 0.35014363 0.08835993 NA NA
#> 27 CMC27 2 3PLM 0.17838470 0.17043885 0.05738007 NA NA
#> 28 CMC28 2 3PLM 0.31674844 0.10953967 0.05270285 NA NA
#> 29 CMC29 2 3PLM 0.54619578 0.19184713 0.08610236 NA NA
#> 30 CMC30 2 3PLM 0.44751927 0.15026890 0.04908313 NA NA
#> 31 CMC31 2 3PLM 0.16316408 0.32764850 0.06684690 NA NA
#> 32 CMC32 2 3PLM 0.31082457 0.21160840 0.08879304 NA NA
#> 33 CMC33 2 3PLM 0.17077250 0.28271978 0.08601695 NA NA
#> 34 CMC34 2 3PLM 0.17161904 0.19700301 0.06017396 NA NA
#> 35 CMC35 2 3PLM 0.19069948 0.16865435 0.06511108 NA NA
#> 36 CMC36 2 3PLM 0.17401848 0.23224001 0.05368437 NA NA
#> 37 CMC37 2 3PLM 0.26144273 0.09498708 0.04587033 NA NA
#> 38 CMC38 2 3PLM 0.17350226 0.32455119 0.08786132 NA NA
#> 39 CFR1 5 GRM 0.14447773 0.11978029 0.08307182 0.06307867 0.05703100
#> 40 CFR2 5 GRM 0.10798168 0.09234859 0.07429798 0.08110680 0.09995812
#> 41 AMC1 2 3PLM 0.39127793 0.14263810 0.04793931 NA NA
#> 42 AMC2 2 3PLM 0.25426145 0.20042801 0.08320344 NA NA
#> 43 AMC3 2 3PLM 0.25146602 0.16446443 0.05423568 NA NA
#> 44 AMC4 2 3PLM 0.17005564 0.26323511 0.07656965 NA NA
#> 45 AMC5 2 3PLM 0.64633195 0.26189935 0.02992857 NA NA
#> 46 AMC6 2 3PLM 0.63744855 0.09747301 0.02219971 NA NA
#> 47 AMC7 2 3PLM 0.41094702 0.17861264 0.06713238 NA NA
#> 48 AMC8 2 3PLM 0.29286642 0.13785201 0.05193618 NA NA
#> 49 AMC9 2 3PLM 0.26091218 0.13241328 0.04845912 NA NA
#> 50 AMC10 2 3PLM 0.50988663 0.09509815 0.02401244 NA NA
#> 51 AMC11 2 3PLM 0.22999194 0.15624576 0.07189865 NA NA
#> 52 AMC12 2 3PLM 0.20770051 0.39869458 0.10907235 NA NA
#> 53 AFR1 5 GRM 0.10188574 0.09221751 0.08931676 0.10902552 0.13282858
#> 54 AFR2 5 GPCM 0.10884827 0.21458427 0.15227381 0.11752786 0.10041751
#> 55 AFR3 5 GPCM 0.07361344 0.15373354 0.15429938 0.16257565 0.18586806
# 3) Estimate item parameters: fix the guessing parameters of 3PLM items to 0.2
(mod3 <- est_item(x, data, score,
D = 1, fix.a.1pl = TRUE, fix.g = TRUE, a.val.1pl = 1, g.val = .2,
use.startval = FALSE
))
#> Starting...
#> Parsing input...
#> Estimating item parameters...
#> Estimation is finished.
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = TRUE,
#> fix.g = TRUE, a.val.1pl = 1, g.val = 0.2, use.startval = FALSE)
#>
#> Fixed ability parameter calibration (Stocking's Method A).
#> All item parameters were successfully converged.
#>
#> Log-likelihood: -15916.26
#>
summary(mod3)
#>
#> Call:
#> est_item(x = x, data = data, score = score, D = 1, fix.a.1pl = TRUE,
#> fix.g = TRUE, a.val.1pl = 1, g.val = 0.2, use.startval = FALSE)
#>
#> Summary of the Data
#> Number of Items in Response Data: 55
#> Number of Excluded Items: 0
#> Number of free parameters: 121
#> Number of Responses for Each Item:
#> id n
#> 1 CMC1 500
#> 2 CMC2 500
#> 3 CMC3 500
#> 4 CMC4 500
#> 5 CMC5 500
#> 6 CMC6 500
#> 7 CMC7 500
#> 8 CMC8 500
#> 9 CMC9 500
#> 10 CMC10 500
#> 11 CMC11 500
#> 12 CMC12 500
#> 13 CMC13 500
#> 14 CMC14 500
#> 15 CMC15 500
#> 16 CMC16 500
#> 17 CMC17 500
#> 18 CMC18 500
#> 19 CMC19 500
#> 20 CMC20 500
#> 21 CMC21 500
#> 22 CMC22 500
#> 23 CMC23 500
#> 24 CMC24 500
#> 25 CMC25 500
#> 26 CMC26 500
#> 27 CMC27 500
#> 28 CMC28 500
#> 29 CMC29 500
#> 30 CMC30 500
#> 31 CMC31 500
#> 32 CMC32 500
#> 33 CMC33 500
#> 34 CMC34 500
#> 35 CMC35 500
#> 36 CMC36 500
#> 37 CMC37 500
#> 38 CMC38 500
#> 39 CFR1 500
#> 40 CFR2 500
#> 41 AMC1 500
#> 42 AMC2 500
#> 43 AMC3 500
#> 44 AMC4 500
#> 45 AMC5 500
#> 46 AMC6 500
#> 47 AMC7 500
#> 48 AMC8 500
#> 49 AMC9 500
#> 50 AMC10 500
#> 51 AMC11 500
#> 52 AMC12 500
#> 53 AFR1 500
#> 54 AFR2 500
#> 55 AFR3 500
#>
#> Processing time (in seconds)
#> Total computation: 0.28
#>
#> Convergence of Solution
#> All item parameters were successfully converged.
#>
#> Summary of Estimation Results
#> -2loglikelihood: 31832.52
#> Item Parameters:
#> id cats model par.1 se.1 par.2 se.2 par.3 se.3 par.4 se.4
#> 1 CMC1 2 1PLM 1.00 NA 1.62 0.12 NA NA NA NA
#> 2 CMC2 2 1PLM 1.00 NA -1.08 0.11 NA NA NA NA
#> 3 CMC3 2 1PLM 1.00 NA 0.40 0.10 NA NA NA NA
#> 4 CMC4 2 2PLM 0.96 0.12 -0.43 0.11 NA NA NA NA
#> 5 CMC5 2 1PLM 1.00 NA -0.25 0.10 NA NA NA NA
#> 6 CMC6 2 3PLM 2.25 0.29 0.83 0.08 0.20 NA NA NA
#> 7 CMC7 2 3PLM 1.00 0.17 1.22 0.19 0.20 NA NA NA
#> 8 CMC8 2 2PLM 0.92 0.12 0.87 0.13 NA NA NA NA
#> 9 CMC9 2 2PLM 1.00 0.12 0.89 0.13 NA NA NA NA
#> 10 CMC10 2 2PLM 1.61 0.15 0.09 0.07 NA NA NA NA
#> 11 CMC11 2 2PLM 1.07 0.12 -0.37 0.10 NA NA NA NA
#> 12 CMC12 2 2PLM 0.94 0.12 1.10 0.15 NA NA NA NA
#> 13 CMC13 2 3PLM 1.53 0.28 1.37 0.15 0.20 NA NA NA
#> 14 CMC14 2 3PLM 1.26 0.18 0.05 0.10 0.20 NA NA NA
#> 15 CMC15 2 3PLM 1.52 0.20 0.00 0.09 0.20 NA NA NA
#> 16 CMC16 2 3PLM 2.36 0.27 0.18 0.07 0.20 NA NA NA
#> 17 CMC17 2 3PLM 1.06 0.15 -0.30 0.12 0.20 NA NA NA
#> 18 CMC18 2 3PLM 1.16 0.23 1.38 0.19 0.20 NA NA NA
#> 19 CMC19 2 3PLM 2.30 0.30 -1.07 0.10 0.20 NA NA NA
#> 20 CMC20 2 3PLM 1.48 0.22 -1.71 0.19 0.20 NA NA NA
#> 21 CMC21 2 3PLM 1.38 0.19 -1.25 0.16 0.20 NA NA NA
#> 22 CMC22 2 3PLM 0.93 0.14 -0.52 0.15 0.20 NA NA NA
#> 23 CMC23 2 3PLM 1.08 0.16 -0.17 0.12 0.20 NA NA NA
#> 24 CMC24 2 3PLM 1.13 0.23 1.40 0.19 0.20 NA NA NA
#> 25 CMC25 2 3PLM 0.82 0.15 -1.55 0.28 0.20 NA NA NA
#> 26 CMC26 2 3PLM 1.07 0.18 -2.14 0.31 0.20 NA NA NA
#> 27 CMC27 2 3PLM 1.27 0.17 0.22 0.10 0.20 NA NA NA
#> 28 CMC28 2 3PLM 2.22 0.27 -0.15 0.07 0.20 NA NA NA
#> 29 CMC29 2 3PLM 1.84 0.28 -1.19 0.14 0.20 NA NA NA
#> 30 CMC30 2 3PLM 1.19 0.20 0.35 0.11 0.20 NA NA NA
#> 31 CMC31 2 3PLM 0.76 0.15 1.15 0.23 0.20 NA NA NA
#> 32 CMC32 2 3PLM 1.62 0.22 -0.90 0.12 0.20 NA NA NA
#> 33 CMC33 2 3PLM 1.07 0.16 -1.43 0.21 0.20 NA NA NA
#> 34 CMC34 2 3PLM 1.11 0.16 0.33 0.12 0.20 NA NA NA
#> 35 CMC35 2 3PLM 1.42 0.18 -0.36 0.10 0.20 NA NA NA
#> 36 CMC36 2 3PLM 1.00 0.17 1.15 0.18 0.20 NA NA NA
#> 37 CMC37 2 3PLM 2.30 0.27 -0.15 0.07 0.20 NA NA NA
#> 38 CMC38 2 3PLM 0.87 0.14 -0.33 0.15 0.20 NA NA NA
#> 39 CFR1 5 GRM 2.00 0.14 -1.88 0.12 -1.25 0.08 -0.70 0.06
#> 40 CFR2 5 GRM 1.39 0.11 -0.80 0.09 -0.13 0.07 0.60 0.08
#> 41 AMC1 2 3PLM 1.45 0.22 0.57 0.10 0.20 NA NA NA
#> 42 AMC2 2 3PLM 1.72 0.25 -1.57 0.16 0.20 NA NA NA
#> 43 AMC3 2 3PLM 1.44 0.21 0.77 0.11 0.20 NA NA NA
#> 44 AMC4 2 3PLM 0.96 0.15 -0.13 0.13 0.20 NA NA NA
#> 45 AMC5 2 3PLM 1.83 0.53 2.10 0.25 0.20 NA NA NA
#> 46 AMC6 2 3PLM 3.32 0.68 1.50 0.09 0.20 NA NA NA
#> 47 AMC7 2 3PLM 1.48 0.21 0.25 0.09 0.20 NA NA NA
#> 48 AMC8 2 3PLM 1.65 0.23 0.39 0.09 0.20 NA NA NA
#> 49 AMC9 2 3PLM 1.72 0.23 0.59 0.09 0.20 NA NA NA
#> 50 AMC10 2 3PLM 3.21 0.62 1.40 0.09 0.20 NA NA NA
#> 51 AMC11 2 3PLM 1.78 0.22 -0.96 0.11 0.20 NA NA NA
#> 52 AMC12 2 3PLM 0.91 0.15 -0.96 0.19 0.20 NA NA NA
#> 53 AFR1 5 GRM 1.14 0.10 -0.30 0.09 0.30 0.09 0.92 0.11
#> 54 AFR2 5 GPCM 1.33 0.11 -1.99 0.21 -1.31 0.15 -0.72 0.12
#> 55 AFR3 5 GPCM 0.89 0.07 -0.80 0.15 0.15 0.15 0.46 0.16
#> 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 -0.23 0.06
#> 40 1.09 0.10
#> 41 NA NA
#> 42 NA NA
#> 43 NA NA
#> 44 NA NA
#> 45 NA NA
#> 46 NA NA
#> 47 NA NA
#> 48 NA NA
#> 49 NA NA
#> 50 NA NA
#> 51 NA NA
#> 52 NA NA
#> 53 1.35 0.13
#> 54 -0.21 0.10
#> 55 1.35 0.19
#>
#> Group Parameters:
#> mu sigma
#> 0.03 1.02
#>
# Extract both item parameter and standard error estimates
getirt(mod3, what = "estimates")
#> id cats model par.1 se.1 par.2 se.2 par.3
#> 1 CMC1 2 1PLM 1.0000000 NA 1.621648179 0.11819685 NA
#> 2 CMC2 2 1PLM 1.0000000 NA -1.077997364 0.10825953 NA
#> 3 CMC3 2 1PLM 1.0000000 NA 0.400985408 0.09953834 NA
#> 4 CMC4 2 2PLM 0.9627020 0.11608725 -0.425593384 0.11102431 NA
#> 5 CMC5 2 1PLM 1.0000000 NA -0.254140164 0.09928963 NA
#> 6 CMC6 2 3PLM 2.2500919 0.29270332 0.825828340 0.08036861 0.2000000
#> 7 CMC7 2 3PLM 1.0036741 0.17274098 1.220313782 0.18746678 0.2000000
#> 8 CMC8 2 2PLM 0.9232153 0.11779263 0.865152105 0.13411409 NA
#> 9 CMC9 2 2PLM 1.0043493 0.12280227 0.892276674 0.12623451 NA
#> 10 CMC10 2 2PLM 1.6128253 0.15351879 0.092530217 0.06743190 NA
#> 11 CMC11 2 2PLM 1.0684709 0.12147067 -0.373791037 0.09986851 NA
#> 12 CMC12 2 2PLM 0.9377669 0.12170130 1.096465720 0.14960502 NA
#> 13 CMC13 2 3PLM 1.5326878 0.28020682 1.366583323 0.14630563 0.2000000
#> 14 CMC14 2 3PLM 1.2635859 0.17930997 0.049538517 0.10479586 0.2000000
#> 15 CMC15 2 3PLM 1.5223449 0.20092501 0.003798397 0.09136761 0.2000000
#> 16 CMC16 2 3PLM 2.3649011 0.27209426 0.178716474 0.06633356 0.2000000
#> 17 CMC17 2 3PLM 1.0570158 0.14864138 -0.304921316 0.12499504 0.2000000
#> 18 CMC18 2 3PLM 1.1551459 0.22668006 1.384671872 0.18737538 0.2000000
#> 19 CMC19 2 3PLM 2.2990572 0.30283205 -1.072306197 0.09949557 0.2000000
#> 20 CMC20 2 3PLM 1.4753552 0.21719019 -1.707510827 0.18984250 0.2000000
#> 21 CMC21 2 3PLM 1.3826192 0.19457880 -1.251896849 0.15683875 0.2000000
#> 22 CMC22 2 3PLM 0.9332927 0.14206202 -0.521508774 0.14964036 0.2000000
#> 23 CMC23 2 3PLM 1.0773435 0.15735891 -0.165078858 0.12141497 0.2000000
#> 24 CMC24 2 3PLM 1.1319498 0.22600866 1.401368677 0.19493590 0.2000000
#> 25 CMC25 2 3PLM 0.8189358 0.14565030 -1.546381787 0.27883156 0.2000000
#> 26 CMC26 2 3PLM 1.0677236 0.18389876 -2.139687238 0.30768760 0.2000000
#> 27 CMC27 2 3PLM 1.2708127 0.17146482 0.222497065 0.10270475 0.2000000
#> 28 CMC28 2 3PLM 2.2219254 0.27235680 -0.154819257 0.07177770 0.2000000
#> 29 CMC29 2 3PLM 1.8449880 0.28426198 -1.192296541 0.13973851 0.2000000
#> 30 CMC30 2 3PLM 1.1940175 0.19828372 0.348142434 0.11047643 0.2000000
#> 31 CMC31 2 3PLM 0.7593502 0.14910997 1.149740983 0.22846628 0.2000000
#> 32 CMC32 2 3PLM 1.6206911 0.22154895 -0.900109322 0.12049024 0.2000000
#> 33 CMC33 2 3PLM 1.0748928 0.16403279 -1.426774544 0.20609255 0.2000000
#> 34 CMC34 2 3PLM 1.1091948 0.15973517 0.326310883 0.11584196 0.2000000
#> 35 CMC35 2 3PLM 1.4165401 0.18012321 -0.360663487 0.10144083 0.2000000
#> 36 CMC36 2 3PLM 0.9969002 0.17077471 1.146409605 0.17989819 0.2000000
#> 37 CMC37 2 3PLM 2.3032474 0.26827208 -0.145152052 0.06860776 0.2000000
#> 38 CMC38 2 3PLM 0.8670753 0.14052732 -0.326413178 0.15022224 0.2000000
#> 39 CFR1 5 GRM 2.0000867 0.14447773 -1.882481406 0.11978029 -1.2545794
#> 40 CFR2 5 GRM 1.3885998 0.10798168 -0.796583085 0.09234859 -0.1288726
#> 41 AMC1 2 3PLM 1.4502462 0.22326359 0.566879449 0.09958949 0.2000000
#> 42 AMC2 2 3PLM 1.7151696 0.24723800 -1.574228038 0.16075234 0.2000000
#> 43 AMC3 2 3PLM 1.4433616 0.21355473 0.772806457 0.10784590 0.2000000
#> 44 AMC4 2 3PLM 0.9596890 0.14670104 -0.129486195 0.13092991 0.2000000
#> 45 AMC5 2 3PLM 1.8262781 0.53318392 2.104648144 0.24940051 0.2000000
#> 46 AMC6 2 3PLM 3.3183758 0.68224522 1.496175655 0.09411622 0.2000000
#> 47 AMC7 2 3PLM 1.4760489 0.20992793 0.248178936 0.09366215 0.2000000
#> 48 AMC8 2 3PLM 1.6457292 0.22603729 0.389112025 0.08717637 0.2000000
#> 49 AMC9 2 3PLM 1.7158347 0.23401847 0.585029590 0.08859760 0.2000000
#> 50 AMC10 2 3PLM 3.2051509 0.62156279 1.396831011 0.08801443 0.2000000
#> 51 AMC11 2 3PLM 1.7765368 0.22324501 -0.963904250 0.10962935 0.2000000
#> 52 AMC12 2 3PLM 0.9095976 0.14868993 -0.957678253 0.19188052 0.2000000
#> 53 AFR1 5 GRM 1.1355459 0.10188574 -0.300165699 0.09221751 0.3028394
#> 54 AFR2 5 GPCM 1.3267609 0.10884827 -1.994449888 0.21458427 -1.3127161
#> 55 AFR3 5 GPCM 0.8941751 0.07361344 -0.795427791 0.15373354 0.1540945
#> se.3 par.4 se.4 par.5 se.5
#> 1 NA NA NA NA NA
#> 2 NA NA NA NA NA
#> 3 NA NA NA NA NA
#> 4 NA NA NA NA NA
#> 5 NA NA NA NA NA
#> 6 NA NA NA NA NA
#> 7 NA NA NA NA NA
#> 8 NA NA NA NA NA
#> 9 NA NA NA NA NA
#> 10 NA NA NA NA NA
#> 11 NA NA NA NA NA
#> 12 NA NA NA NA NA
#> 13 NA NA NA NA NA
#> 14 NA NA NA NA NA
#> 15 NA NA NA NA NA
#> 16 NA NA NA NA NA
#> 17 NA NA NA NA NA
#> 18 NA NA NA NA NA
#> 19 NA NA NA NA NA
#> 20 NA NA NA NA NA
#> 21 NA NA NA NA NA
#> 22 NA NA NA NA NA
#> 23 NA NA NA NA NA
#> 24 NA NA NA NA NA
#> 25 NA NA NA NA NA
#> 26 NA NA NA NA NA
#> 27 NA NA NA NA NA
#> 28 NA NA NA NA NA
#> 29 NA NA NA NA NA
#> 30 NA NA NA NA NA
#> 31 NA NA NA NA NA
#> 32 NA NA NA NA NA
#> 33 NA NA NA NA NA
#> 34 NA NA NA NA NA
#> 35 NA NA NA NA NA
#> 36 NA NA NA NA NA
#> 37 NA NA NA NA NA
#> 38 NA NA NA NA NA
#> 39 0.08307182 -0.7031275 0.06307867 -0.2324418 0.05703100
#> 40 0.07429798 0.6012371 0.08110680 1.0859619 0.09995812
#> 41 NA NA NA NA NA
#> 42 NA NA NA NA NA
#> 43 NA NA NA NA NA
#> 44 NA NA NA NA NA
#> 45 NA NA NA NA NA
#> 46 NA NA NA NA NA
#> 47 NA NA NA NA NA
#> 48 NA NA NA NA NA
#> 49 NA NA NA NA NA
#> 50 NA NA NA NA NA
#> 51 NA NA NA NA NA
#> 52 NA NA NA NA NA
#> 53 0.08931676 0.9182795 0.10902552 1.3525597 0.13282858
#> 54 0.15227381 -0.7196856 0.11752786 -0.2068705 0.10041751
#> 55 0.15429938 0.4638485 0.16257565 1.3511384 0.18586806
# }