This function performs fixed ability parameter calibration (FAPC), often called Stocking's (1988) Method A, which is the maximum likelihood estimation of item parameters given ability estimates (Baker & Kim, 2004; Ban et al., 2001; Stocking, 1988). 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, 17)),
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. Ifx = NULL, bothmodelandcatsarguments must be specified. Seeest_irt()orsimdat()for more details about the item metadata. Default isNULL.- data
A matrix of examinees' item responses corresponding to the items specified in the
xargument. Rows represent examinees and columns represent items.- score
A numeric vector of examinees' ability estimates (theta values). The length of this vector must match the number of rows in the response data.
- 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 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"serves as a general label covering all three dichotomous IRT models. 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, IDs are generated automatically. Whenfipc = TRUE, a provideditem.idwill override any IDs present inx. 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. 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.- 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.- control
A named list of options passed directly to
stats::nlminb(). These parameters define settings for the item parameter estimation process, such as the maximum number of iterations. 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.
- 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 based on the observed information functions
- pos.par
A data frame indicating the position of each item parameter within the estimation vector. Useful for interpreting the variance-covariance matrix.
- covariance
A variance-covariance matrix of the item parameter estimates.
- loglikelihood
The total log-likelihood value computed across all estimated items based on the complete response data.
- data
A data frame of examinees' response data.
- 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 total number of items in the response data.
- deleted.item
Items with no response data. These items are excluded from the item parameter estimation.
- npar.est
The total number of parameters estimated.
- n.response
An integer vector indicating the number of valid responses for each item used in the item parameter estimation.
- TotalTime
Total computation time in seconds.
Note that you can easily extract components from the output using the
getirt() function.
Details
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.
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.
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, 17)), 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,
#> 17)), use.startval = FALSE)
#>
#> Fixed ability parameter calibration (Stocking's Method A).
#> All item parameters were successfully converged.
#>
#> Log-likelihood: -15830.66
#>
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,
#> 17)), 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: 0.47
#>
#> Convergence of Solution
#> All item parameters were successfully converged.
#>
#> Summary of Estimation Results
#> -2loglikelihood: 31661.31
#> 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 0.88 0.17 1.03 0.23 0.13 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 1.35 0.34 1.31 0.17 0.17 0.04 NA NA
#> 14 CMC14 2 3PLM 1.36 0.31 0.15 0.24 0.24 0.08 NA NA
#> 15 CMC15 2 3PLM 1.53 0.27 0.01 0.17 0.20 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 0.15 -0.41 0.22 0.16 0.07 NA NA
#> 18 CMC18 2 3PLM 1.27 0.38 1.42 0.20 0.22 0.05 NA NA
#> 19 CMC19 2 3PLM 2.25 0.32 -1.11 0.14 0.17 0.07 NA NA
#> 20 CMC20 2 3PLM 1.47 0.22 -1.74 0.22 0.18 0.08 NA NA
#> 21 CMC21 2 3PLM 1.38 0.21 -1.25 0.23 0.20 0.08 NA NA
#> 22 CMC22 2 3PLM 0.92 0.16 -0.55 0.28 0.19 0.08 NA NA
#> 23 CMC23 2 3PLM 1.10 0.22 -0.12 0.27 0.22 0.09 NA NA
#> 24 CMC24 2 3PLM 1.21 0.34 1.43 0.21 0.22 0.05 NA NA
#> 25 CMC25 2 3PLM 0.83 0.16 -1.51 0.40 0.21 0.09 NA NA
#> 26 CMC26 2 3PLM 1.07 0.18 -2.16 0.35 0.19 0.08 NA NA
#> 27 CMC27 2 3PLM 1.18 0.18 0.09 0.17 0.14 0.06 NA NA
#> 28 CMC28 2 3PLM 2.19 0.31 -0.17 0.11 0.19 0.05 NA NA
#> 29 CMC29 2 3PLM 2.48 0.54 -0.81 0.20 0.38 0.09 NA NA
#> 30 CMC30 2 3PLM 1.88 0.45 0.69 0.15 0.34 0.05 NA NA
#> 31 CMC31 2 3PLM 0.70 0.16 1.00 0.32 0.16 0.07 NA NA
#> 32 CMC32 2 3PLM 1.73 0.30 -0.78 0.21 0.26 0.09 NA NA
#> 33 CMC33 2 3PLM 1.07 0.17 -1.45 0.28 0.19 0.08 NA NA
#> 34 CMC34 2 3PLM 1.04 0.17 0.21 0.20 0.16 0.06 NA NA
#> 35 CMC35 2 3PLM 1.36 0.19 -0.45 0.17 0.16 0.06 NA NA
#> 36 CMC36 2 3PLM 0.88 0.17 0.97 0.23 0.14 0.05 NA NA
#> 37 CMC37 2 3PLM 2.13 0.26 -0.25 0.09 0.13 0.05 NA NA
#> 38 CMC38 2 3PLM 0.87 0.17 -0.31 0.32 0.20 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 1.81 0.39 0.74 0.14 0.28 0.05 NA NA
#> 42 AMC2 2 3PLM 1.70 0.25 -1.59 0.20 0.19 0.08 NA NA
#> 43 AMC3 2 3PLM 1.30 0.25 0.68 0.16 0.16 0.05 NA NA
#> 44 AMC4 2 3PLM 0.94 0.17 -0.18 0.26 0.18 0.07 NA NA
#> 45 AMC5 2 3PLM 1.69 0.65 2.11 0.26 0.19 0.03 NA NA
#> 46 AMC6 2 3PLM 2.83 0.64 1.44 0.10 0.15 0.02 NA NA
#> 47 AMC7 2 3PLM 1.69 0.41 0.37 0.18 0.25 0.07 NA NA
#> 48 AMC8 2 3PLM 1.65 0.29 0.39 0.14 0.20 0.05 NA NA
#> 49 AMC9 2 3PLM 1.55 0.26 0.49 0.13 0.15 0.05 NA NA
#> 50 AMC10 2 3PLM 2.48 0.51 1.31 0.10 0.13 0.02 NA NA
#> 51 AMC11 2 3PLM 1.73 0.23 -1.02 0.15 0.16 0.07 NA NA
#> 52 AMC12 2 3PLM 0.95 0.20 -0.83 0.38 0.24 0.10 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 1.601332202 NA NA NA
#> 2 CMC2 2 1PLM 1.0185279 -1.063754095 NA NA NA
#> 3 CMC3 2 1PLM 1.0185279 0.396517677 NA NA NA
#> 4 CMC4 2 2PLM 0.9627020 -0.425593384 NA NA NA
#> 5 CMC5 2 1PLM 1.0185279 -0.250363868 NA NA NA
#> 6 CMC6 2 3PLM 1.8799184 0.671716274 0.1030566 NA NA
#> 7 CMC7 2 3PLM 0.8814907 1.027532298 0.1344986 NA NA
#> 8 CMC8 2 2PLM 0.9232153 0.865152105 NA NA NA
#> 9 CMC9 2 2PLM 1.0043493 0.892276674 NA NA NA
#> 10 CMC10 2 2PLM 1.6128253 0.092530217 NA NA NA
#> 11 CMC11 2 2PLM 1.0684709 -0.373791037 NA NA NA
#> 12 CMC12 2 2PLM 0.9377669 1.096465720 NA NA NA
#> 13 CMC13 2 3PLM 1.3517210 1.310901882 0.1679386 NA NA
#> 14 CMC14 2 3PLM 1.3633891 0.148678889 0.2381220 NA NA
#> 15 CMC15 2 3PLM 1.5260724 0.006963704 0.2014372 NA NA
#> 16 CMC16 2 3PLM 2.0983557 0.039632481 0.1024467 NA NA
#> 17 CMC17 2 3PLM 1.0182338 -0.410450918 0.1596037 NA NA
#> 18 CMC18 2 3PLM 1.2670142 1.423951501 0.2216976 NA NA
#> 19 CMC19 2 3PLM 2.2480817 -1.110500323 0.1713341 NA NA
#> 20 CMC20 2 3PLM 1.4661194 -1.736037297 0.1808714 NA NA
#> 21 CMC21 2 3PLM 1.3829158 -1.251268609 0.2003236 NA NA
#> 22 CMC22 2 3PLM 0.9246240 -0.550518227 0.1901104 NA NA
#> 23 CMC23 2 3PLM 1.1035700 -0.119211336 0.2161302 NA NA
#> 24 CMC24 2 3PLM 1.2149156 1.433332519 0.2175768 NA NA
#> 25 CMC25 2 3PLM 0.8260590 -1.506818565 0.2126189 NA NA
#> 26 CMC26 2 3PLM 1.0651606 -2.157381967 0.1905922 NA NA
#> 27 CMC27 2 3PLM 1.1784410 0.087234898 0.1431743 NA NA
#> 28 CMC28 2 3PLM 2.1935809 -0.168868628 0.1910359 NA NA
#> 29 CMC29 2 3PLM 2.4827570 -0.810059744 0.3832586 NA NA
#> 30 CMC30 2 3PLM 1.8822455 0.693193770 0.3367413 NA NA
#> 31 CMC31 2 3PLM 0.6992865 1.001048202 0.1588988 NA NA
#> 32 CMC32 2 3PLM 1.7343873 -0.783189247 0.2575467 NA NA
#> 33 CMC33 2 3PLM 1.0695257 -1.448547191 0.1902857 NA NA
#> 34 CMC34 2 3PLM 1.0448545 0.210734195 0.1566960 NA NA
#> 35 CMC35 2 3PLM 1.3588210 -0.447313405 0.1579927 NA NA
#> 36 CMC36 2 3PLM 0.8813308 0.967252482 0.1390619 NA NA
#> 37 CMC37 2 3PLM 2.1252131 -0.246234819 0.1285889 NA NA
#> 38 CMC38 2 3PLM 0.8710093 -0.314317203 0.2036931 NA NA
#> 39 CFR1 5 GRM 2.0000867 -1.882481406 -1.2545794 -0.7031275 -0.2324418
#> 40 CFR2 5 GRM 1.3885998 -0.796583085 -0.1288726 0.6012371 1.0859619
#> 41 AMC1 2 3PLM 1.8103262 0.735519975 0.2756669 NA NA
#> 42 AMC2 2 3PLM 1.7047488 -1.593681876 0.1864312 NA NA
#> 43 AMC3 2 3PLM 1.3037867 0.677356694 0.1580301 NA NA
#> 44 AMC4 2 3PLM 0.9414845 -0.175796355 0.1844536 NA NA
#> 45 AMC5 2 3PLM 1.6874360 2.107853698 0.1899503 NA NA
#> 46 AMC6 2 3PLM 2.8301910 1.444309538 0.1536947 NA NA
#> 47 AMC7 2 3PLM 1.6902164 0.371603972 0.2524593 NA NA
#> 48 AMC8 2 3PLM 1.6456775 0.389081754 0.1999853 NA NA
#> 49 AMC9 2 3PLM 1.5475943 0.487734230 0.1516041 NA NA
#> 50 AMC10 2 3PLM 2.4831968 1.310828955 0.1287528 NA NA
#> 51 AMC11 2 3PLM 1.7344800 -1.020301934 0.1636095 NA NA
#> 52 AMC12 2 3PLM 0.9513776 -0.828671559 0.2401560 NA NA
#> 53 AFR1 5 GRM 1.1355459 -0.300165699 0.3028394 0.9182795 1.3525597
#> 54 AFR2 5 GPCM 1.3267609 -1.994449888 -1.3127161 -0.7196856 -0.2068705
#> 55 AFR3 5 GPCM 0.8941751 -0.795427791 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, 17)), 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, 17)), use.startval = FALSE)
#>
#> Fixed ability parameter calibration (Stocking's Method A).
#> All item parameters were successfully converged.
#>
#> Log-likelihood: -15830.7
#>
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, 17)), 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: 31661.4
#> 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 0.88 0.17 1.03 0.23 0.13 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 1.35 0.34 1.31 0.17 0.17 0.04 NA NA
#> 14 CMC14 2 3PLM 1.36 0.31 0.15 0.24 0.24 0.08 NA NA
#> 15 CMC15 2 3PLM 1.53 0.27 0.01 0.17 0.20 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 0.15 -0.41 0.22 0.16 0.07 NA NA
#> 18 CMC18 2 3PLM 1.27 0.38 1.42 0.20 0.22 0.05 NA NA
#> 19 CMC19 2 3PLM 2.25 0.32 -1.11 0.14 0.17 0.07 NA NA
#> 20 CMC20 2 3PLM 1.47 0.22 -1.74 0.22 0.18 0.08 NA NA
#> 21 CMC21 2 3PLM 1.38 0.21 -1.25 0.23 0.20 0.08 NA NA
#> 22 CMC22 2 3PLM 0.92 0.16 -0.55 0.28 0.19 0.08 NA NA
#> 23 CMC23 2 3PLM 1.10 0.22 -0.12 0.27 0.22 0.09 NA NA
#> 24 CMC24 2 3PLM 1.21 0.34 1.43 0.21 0.22 0.05 NA NA
#> 25 CMC25 2 3PLM 0.83 0.16 -1.51 0.40 0.21 0.09 NA NA
#> 26 CMC26 2 3PLM 1.07 0.18 -2.16 0.35 0.19 0.08 NA NA
#> 27 CMC27 2 3PLM 1.18 0.18 0.09 0.17 0.14 0.06 NA NA
#> 28 CMC28 2 3PLM 2.19 0.31 -0.17 0.11 0.19 0.05 NA NA
#> 29 CMC29 2 3PLM 2.48 0.54 -0.81 0.20 0.38 0.09 NA NA
#> 30 CMC30 2 3PLM 1.88 0.45 0.69 0.15 0.34 0.05 NA NA
#> 31 CMC31 2 3PLM 0.70 0.16 1.00 0.32 0.16 0.07 NA NA
#> 32 CMC32 2 3PLM 1.73 0.30 -0.78 0.21 0.26 0.09 NA NA
#> 33 CMC33 2 3PLM 1.07 0.17 -1.45 0.28 0.19 0.08 NA NA
#> 34 CMC34 2 3PLM 1.04 0.17 0.21 0.20 0.16 0.06 NA NA
#> 35 CMC35 2 3PLM 1.36 0.19 -0.45 0.17 0.16 0.06 NA NA
#> 36 CMC36 2 3PLM 0.88 0.17 0.97 0.23 0.14 0.05 NA NA
#> 37 CMC37 2 3PLM 2.13 0.26 -0.25 0.09 0.13 0.05 NA NA
#> 38 CMC38 2 3PLM 0.87 0.17 -0.31 0.32 0.20 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 1.81 0.39 0.74 0.14 0.28 0.05 NA NA
#> 42 AMC2 2 3PLM 1.70 0.25 -1.59 0.20 0.19 0.08 NA NA
#> 43 AMC3 2 3PLM 1.30 0.25 0.68 0.16 0.16 0.05 NA NA
#> 44 AMC4 2 3PLM 0.94 0.17 -0.18 0.26 0.18 0.07 NA NA
#> 45 AMC5 2 3PLM 1.69 0.65 2.11 0.26 0.19 0.03 NA NA
#> 46 AMC6 2 3PLM 2.83 0.64 1.44 0.10 0.15 0.02 NA NA
#> 47 AMC7 2 3PLM 1.69 0.41 0.37 0.18 0.25 0.07 NA NA
#> 48 AMC8 2 3PLM 1.65 0.29 0.39 0.14 0.20 0.05 NA NA
#> 49 AMC9 2 3PLM 1.55 0.26 0.49 0.13 0.15 0.05 NA NA
#> 50 AMC10 2 3PLM 2.48 0.51 1.31 0.10 0.13 0.02 NA NA
#> 51 AMC11 2 3PLM 1.73 0.23 -1.02 0.15 0.16 0.07 NA NA
#> 52 AMC12 2 3PLM 0.95 0.20 -0.83 0.38 0.24 0.10 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 0.26592875 0.09223933 0.03126001 NA NA
#> 7 CMC7 2 3PLM 0.17007216 0.22868364 0.05043985 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 0.33543956 0.16922355 0.04476102 NA NA
#> 14 CMC14 2 3PLM 0.31025933 0.23821549 0.08293693 NA NA
#> 15 CMC15 2 3PLM 0.26615652 0.17322453 0.06684887 NA NA
#> 16 CMC16 2 3PLM 0.24782824 0.08378912 0.03671343 NA NA
#> 17 CMC17 2 3PLM 0.15336572 0.21797789 0.06861050 NA NA
#> 18 CMC18 2 3PLM 0.37951683 0.20475893 0.05152830 NA NA
#> 19 CMC19 2 3PLM 0.31575318 0.13854698 0.07248859 NA NA
#> 20 CMC20 2 3PLM 0.21769602 0.22444579 0.07986432 NA NA
#> 21 CMC21 2 3PLM 0.20918112 0.22563675 0.08356158 NA NA
#> 22 CMC22 2 3PLM 0.15632987 0.27810767 0.07985413 NA NA
#> 23 CMC23 2 3PLM 0.21812942 0.27395715 0.08641957 NA NA
#> 24 CMC24 2 3PLM 0.33644706 0.21099243 0.04799483 NA NA
#> 25 CMC25 2 3PLM 0.15706343 0.40435671 0.09407396 NA NA
#> 26 CMC26 2 3PLM 0.18446052 0.34745444 0.08484835 NA NA
#> 27 CMC27 2 3PLM 0.17645756 0.16891064 0.05657179 NA NA
#> 28 CMC28 2 3PLM 0.31487828 0.10951574 0.05247206 NA NA
#> 29 CMC29 2 3PLM 0.54086125 0.19720209 0.08789680 NA NA
#> 30 CMC30 2 3PLM 0.44551859 0.15180550 0.04975419 NA NA
#> 31 CMC31 2 3PLM 0.15959759 0.32384772 0.06560236 NA NA
#> 32 CMC32 2 3PLM 0.30476277 0.21153602 0.08816621 NA NA
#> 33 CMC33 2 3PLM 0.16888358 0.27816088 0.08298992 NA NA
#> 34 CMC34 2 3PLM 0.16969347 0.19516848 0.05936051 NA NA
#> 35 CMC35 2 3PLM 0.18844135 0.16666456 0.06387891 NA NA
#> 36 CMC36 2 3PLM 0.17198087 0.23078825 0.05312022 NA NA
#> 37 CMC37 2 3PLM 0.25992108 0.09456053 0.04537614 NA NA
#> 38 CMC38 2 3PLM 0.16843257 0.31736545 0.08539489 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 0.38772085 0.14321180 0.04820526 NA NA
#> 42 AMC2 2 3PLM 0.25187572 0.19813671 0.08045500 NA NA
#> 43 AMC3 2 3PLM 0.24782407 0.16413179 0.05395429 NA NA
#> 44 AMC4 2 3PLM 0.16675130 0.25922208 0.07498779 NA NA
#> 45 AMC5 2 3PLM 0.64524089 0.26375779 0.03021145 NA NA
#> 46 AMC6 2 3PLM 0.63645971 0.09751124 0.02218408 NA NA
#> 47 AMC7 2 3PLM 0.40524702 0.18202698 0.06837224 NA NA
#> 48 AMC8 2 3PLM 0.29111839 0.13833114 0.05205826 NA NA
#> 49 AMC9 2 3PLM 0.25875454 0.13232181 0.04830486 NA NA
#> 50 AMC10 2 3PLM 0.50849974 0.09515461 0.02399167 NA NA
#> 51 AMC11 2 3PLM 0.22749532 0.15400610 0.06996146 NA NA
#> 52 AMC12 2 3PLM 0.19683738 0.38464459 0.10437009 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: 0.27
#>
#> 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(mod2, 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 1.8799184 0.26592875 0.671716274 0.09223933 0.1030566
#> 7 CMC7 2 3PLM 0.8814907 0.17007216 1.027532298 0.22868364 0.1344986
#> 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 1.3517210 0.33543956 1.310901882 0.16922355 0.1679386
#> 14 CMC14 2 3PLM 1.3633891 0.31025933 0.148678889 0.23821549 0.2381220
#> 15 CMC15 2 3PLM 1.5260724 0.26615652 0.006963704 0.17322453 0.2014372
#> 16 CMC16 2 3PLM 2.0983557 0.24782824 0.039632481 0.08378912 0.1024467
#> 17 CMC17 2 3PLM 1.0182338 0.15336572 -0.410450918 0.21797789 0.1596037
#> 18 CMC18 2 3PLM 1.2670142 0.37951683 1.423951501 0.20475893 0.2216976
#> 19 CMC19 2 3PLM 2.2480817 0.31575318 -1.110500323 0.13854698 0.1713341
#> 20 CMC20 2 3PLM 1.4661194 0.21769602 -1.736037297 0.22444579 0.1808714
#> 21 CMC21 2 3PLM 1.3829158 0.20918112 -1.251268609 0.22563675 0.2003236
#> 22 CMC22 2 3PLM 0.9246240 0.15632987 -0.550518227 0.27810767 0.1901104
#> 23 CMC23 2 3PLM 1.1035700 0.21812942 -0.119211336 0.27395715 0.2161302
#> 24 CMC24 2 3PLM 1.2149156 0.33644706 1.433332519 0.21099243 0.2175768
#> 25 CMC25 2 3PLM 0.8260590 0.15706343 -1.506818565 0.40435671 0.2126189
#> 26 CMC26 2 3PLM 1.0651606 0.18446052 -2.157381967 0.34745444 0.1905922
#> 27 CMC27 2 3PLM 1.1784410 0.17645756 0.087234898 0.16891064 0.1431743
#> 28 CMC28 2 3PLM 2.1935809 0.31487828 -0.168868628 0.10951574 0.1910359
#> 29 CMC29 2 3PLM 2.4827570 0.54086125 -0.810059744 0.19720209 0.3832586
#> 30 CMC30 2 3PLM 1.8822455 0.44551859 0.693193770 0.15180550 0.3367413
#> 31 CMC31 2 3PLM 0.6992865 0.15959759 1.001048202 0.32384772 0.1588988
#> 32 CMC32 2 3PLM 1.7343873 0.30476277 -0.783189247 0.21153602 0.2575467
#> 33 CMC33 2 3PLM 1.0695257 0.16888358 -1.448547191 0.27816088 0.1902857
#> 34 CMC34 2 3PLM 1.0448545 0.16969347 0.210734195 0.19516848 0.1566960
#> 35 CMC35 2 3PLM 1.3588210 0.18844135 -0.447313405 0.16666456 0.1579927
#> 36 CMC36 2 3PLM 0.8813308 0.17198087 0.967252482 0.23078825 0.1390619
#> 37 CMC37 2 3PLM 2.1252131 0.25992108 -0.246234819 0.09456053 0.1285889
#> 38 CMC38 2 3PLM 0.8710093 0.16843257 -0.314317203 0.31736545 0.2036931
#> 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 1.8103262 0.38772085 0.735519975 0.14321180 0.2756669
#> 42 AMC2 2 3PLM 1.7047488 0.25187572 -1.593681876 0.19813671 0.1864312
#> 43 AMC3 2 3PLM 1.3037867 0.24782407 0.677356694 0.16413179 0.1580301
#> 44 AMC4 2 3PLM 0.9414845 0.16675130 -0.175796355 0.25922208 0.1844536
#> 45 AMC5 2 3PLM 1.6874360 0.64524089 2.107853698 0.26375779 0.1899503
#> 46 AMC6 2 3PLM 2.8301910 0.63645971 1.444309538 0.09751124 0.1536947
#> 47 AMC7 2 3PLM 1.6902164 0.40524702 0.371603972 0.18202698 0.2524593
#> 48 AMC8 2 3PLM 1.6456775 0.29111839 0.389081754 0.13833114 0.1999853
#> 49 AMC9 2 3PLM 1.5475943 0.25875454 0.487734230 0.13232181 0.1516041
#> 50 AMC10 2 3PLM 2.4831968 0.50849974 1.310828955 0.09515461 0.1287528
#> 51 AMC11 2 3PLM 1.7344800 0.22749532 -1.020301934 0.15400610 0.1636095
#> 52 AMC12 2 3PLM 0.9513776 0.19683738 -0.828671559 0.38464459 0.2401560
#> 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 0.03126001 NA NA NA NA
#> 7 0.05043985 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 0.04476102 NA NA NA NA
#> 14 0.08293693 NA NA NA NA
#> 15 0.06684887 NA NA NA NA
#> 16 0.03671343 NA NA NA NA
#> 17 0.06861050 NA NA NA NA
#> 18 0.05152830 NA NA NA NA
#> 19 0.07248859 NA NA NA NA
#> 20 0.07986432 NA NA NA NA
#> 21 0.08356158 NA NA NA NA
#> 22 0.07985413 NA NA NA NA
#> 23 0.08641957 NA NA NA NA
#> 24 0.04799483 NA NA NA NA
#> 25 0.09407396 NA NA NA NA
#> 26 0.08484835 NA NA NA NA
#> 27 0.05657179 NA NA NA NA
#> 28 0.05247206 NA NA NA NA
#> 29 0.08789680 NA NA NA NA
#> 30 0.04975419 NA NA NA NA
#> 31 0.06560236 NA NA NA NA
#> 32 0.08816621 NA NA NA NA
#> 33 0.08298992 NA NA NA NA
#> 34 0.05936051 NA NA NA NA
#> 35 0.06387891 NA NA NA NA
#> 36 0.05312022 NA NA NA NA
#> 37 0.04537614 NA NA NA NA
#> 38 0.08539489 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 0.04820526 NA NA NA NA
#> 42 0.08045500 NA NA NA NA
#> 43 0.05395429 NA NA NA NA
#> 44 0.07498779 NA NA NA NA
#> 45 0.03021145 NA NA NA NA
#> 46 0.02218408 NA NA NA NA
#> 47 0.06837224 NA NA NA NA
#> 48 0.05205826 NA NA NA NA
#> 49 0.04830486 NA NA NA NA
#> 50 0.02399167 NA NA NA NA
#> 51 0.06996146 NA NA NA NA
#> 52 0.10437009 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
# }