Extracts internal components from an object of class est_irt
(from est_irt()), est_mg (from est_mg()), or est_item
(from est_item()).
Usage
getirt(x, ...)
# S3 method for class 'est_irt'
getirt(x, what, ...)
# S3 method for class 'est_mg'
getirt(x, what, ...)
# S3 method for class 'est_item'
getirt(x, what, ...)Arguments
- x
An object of class
est_irt,est_mg, orest_itemas returned byest_irt(),est_mg(), orest_item(), respectively.- ...
Additional arguments passed to or from other methods.
- what
A character string specifying the name of the internal component to extract.
Value
The internal component extracted from an object of class est_irt, est_mg, or est_item,
depending on the input to the x argument.
Details
The following components can be extracted from an object of class est_irt
created by est_irt():
- estimates
A data frame containing both the item parameter estimates and their corresponding standard errors.
- par.est
A data frame containing only the item parameter estimates.
- se.est
A data frame containing the standard errors of the item parameter estimates, calculated using the cross-product approximation method (Meilijson, 1989).
- pos.par
A data frame indicating the position index of each estimated item parameter. This is useful when interpreting the variance-covariance matrix.
- covariance
A variance-covariance matrix of the item parameter estimates.
- loglikelihood
The total marginal log-likelihood value summed across all items.
- aic
Akaike Information Criterion (AIC) based on the marginal log-likelihood.
- bic
Bayesian Information Criterion (BIC) based on the marginal log-likelihood.
- group.par
A data frame containing the mean, variance, and standard deviation of the latent variable's prior distribution.
- weights
A two-column data frame containing quadrature points (first column) and corresponding weights (second column) of the (updated) latent trait prior.
- posterior.dist
A matrix of normalized posterior densities for all response patterns at each quadrature point. Rows represent examinees, and columns represent quadrature points.
- data
A data frame of the examinee response dataset used in estimation.
- scale.D
The scaling constant (usually 1 or 1.7) used in the IRT model.
- ncase
The number of unique response patterns.
- nitem
The number of items included in the dataset.
- Etol
The convergence criterion used for the E-step in the EM algorithm.
- MaxE
The maximum number of E-steps allowed during EM estimation.
- aprior
A list describing the prior distribution for item slope parameters.
- bprior
A list describing the prior distribution for item difficulty (or threshold) parameters.
- gprior
A list describing the prior distribution for item guessing parameters.
- npar.est
The total number of parameters estimated.
- niter
The number of EM cycles completed.
- maxpar.diff
The maximum change in parameter estimates at convergence.
- EMtime
Computation time (in seconds) for the EM algorithm.
- SEtime
Computation time (in seconds) for estimating standard errors.
- TotalTime
Total computation time (in seconds) for model estimation.
- test.1
Result of the first-order test indicating whether the gradients were sufficiently close to zero.
- test.2
Result of the second-order test indicating whether the information matrix was positive definite (a condition for maximum likelihood).
- var.note
A note indicating whether the variance-covariance matrix was successfully derived from the information matrix.
- fipc
Logical value indicating whether Fixed Item Parameter Calibration (FIPC) was applied.
- fipc.method
The specific method used for FIPC.
- fix.loc
An integer vector indicating the positions of fixed items used during FIPC.
Components that can be extracted from an object of class est_mg created by
est_mg() include:
- estimates
A list with two components:
overallandgroup.overall: A data frame containing item parameter estimates and their standard errors, based on the combined data set across all groups.group: A list of group-specific data frames containing item parameter estimates and standard errors for each group.
- par.est
Same structure as
estimates, but containing only the item parameter estimates (without standard errors).- se.est
Same structure as
estimates, but containing only the standard errors of the item parameter estimates. The standard errors are computed using the cross-product approximation method (Meilijson, 1989).- pos.par
A data frame indicating the position index of each estimated parameter. This index is based on the combined item set across all groups and is useful when interpreting the variance-covariance matrix.
- covariance
A variance-covariance matrix for the item parameter estimates based on the combined data from all groups.
- loglikelihood
A list with
overallandgroupcomponents:overall: The marginal log-likelihood summed over all unique items across all groups.group: Group-specific marginal log-likelihood values.
- aic
Akaike Information Criterion (AIC) computed from the overall log-likelihood.
- bic
Bayesian Information Criterion (BIC) computed from the overall log-likelihood.
- group.par
A list of group-specific summary statistics (mean, variance, and standard deviation) of the latent trait prior distribution.
- weights
A list of two-column data frames (one per group) containing the quadrature points (first column) and the corresponding weights (second column) for the updated prior distributions.
- posterior.dist
A matrix of normalized posterior densities for all response patterns at each quadrature point. Rows correspond to individuals, and columns to quadrature points.
- data
A list with
overallandgroupcomponents, each containing examinee response data.- scale.D
The scaling constant used in the IRT model (typically 1 or 1.7).
- ncase
A list with
overallandgroupcomponents indicating the number of response patterns in each.- nitem
A list with
overallandgroupcomponents indicating the number of items in the respective response sets.- Etol
Convergence criterion used for the E-step in the EM algorithm.
- MaxE
Maximum number of E-steps allowed in the EM algorithm.
- aprior
A list describing the prior distribution for item slope parameters.
- gprior
A list describing the prior distribution for item guessing parameters.
- npar.est
Total number of parameters estimated across all unique items.
- niter
Number of EM cycles completed.
- maxpar.diff
Maximum change in item parameter estimates at convergence.
- EMtime
Computation time (in seconds) for EM estimation.
- SEtime
Computation time (in seconds) for estimating standard errors.
- TotalTime
Total computation time (in seconds) for model estimation.
- test.1
First-order condition test result indicating whether gradients converged sufficiently.
- test.2
Second-order condition test result indicating whether the information matrix is positive definite.
- var.note
A note indicating whether the variance-covariance matrix was successfully derived from the information matrix.
- fipc
Logical value indicating whether Fixed Item Parameter Calibration (FIPC) was used.
- fipc.method
The method used for FIPC.
- fix.loc
A list with
overallandgroupcomponents specifying the locations of fixed items when FIPC was applied.
Components that can be extracted from an object of class est_item created by
est_item() include:
- estimates
A data frame containing both the item parameter estimates and their corresponding standard errors.
- par.est
A data frame containing only the item parameter estimates.
- se.est
A data frame containing the standard errors of the item parameter estimates, computed using observed information functions.
- pos.par
A data frame indicating the position index of each estimated item parameter. This is useful when interpreting the variance-covariance matrix.
- covariance
A variance-covariance matrix of the item parameter estimates.
- loglikelihood
The sum of log-likelihood values across all items in the complete data set.
- data
A data frame of examinee response data.
- score
A numeric vector of examinees' ability values used as fixed effects during estimation.
- scale.D
The scaling constant (typically 1 or 1.7) used in the IRT model.
- convergence
A character string indicating the convergence status of the item parameter estimation.
- nitem
The total number of items included in the response data.
- deleted.item
Items that contained no response data and were excluded from estimation.
- npar.est
The total number of estimated item parameters.
- n.response
An integer vector indicating the number of responses used to estimate parameters for each item.
- TotalTime
Total computation time (in seconds) for the estimation process.
See est_irt(), est_mg(), and est_item() for more details.
Methods (by class)
getirt(est_irt): An object created by the functionest_irt().getirt(est_mg): An object created by the functionest_mg().getirt(est_item): An object created by the functionest_item().
Author
Hwanggyu Lim hglim83@gmail.com
Examples
# \donttest{
# Fit a 2PL model to the LSAT6 data
mod.2pl <- est_irt(data = LSAT6, D = 1, model = "2PLM", cats = 2)
#> Parsing input...
#> Estimating item parameters...
#>
EM iteration: 1, Loglike: -3182.3860, Max-Change: 0.390402
EM iteration: 2, Loglike: -2561.0478, Max-Change: 0.00000
#> Computing item parameter var-covariance matrix...
#> Estimation is finished in 0.07 seconds.
# Extract item parameter estimates
(est.par <- getirt(mod.2pl, what = "par.est"))
#> id cats model par.1 par.2 par.3
#> 1 V1 2 2PLM 0.8851380 -2.872384950 NA
#> 2 V2 2 2PLM 0.8780243 -0.890284439 NA
#> 3 V3 2 2PLM 0.9305760 0.003668382 NA
#> 4 V4 2 2PLM 0.8617347 -1.269897767 NA
#> 5 V5 2 2PLM 0.8410096 -2.250964712 NA
# Extract standard error estimates
(est.se <- getirt(mod.2pl, what = "se.est"))
#> id cats model par.1 par.2 par.3
#> 1 V1 2 2PLM 0.2452172 0.67487124 NA
#> 2 V2 2 2PLM 0.1905223 0.18450934 NA
#> 3 V3 2 2PLM 0.2020198 0.08146577 NA
#> 4 V4 2 2PLM 0.1919434 0.25426752 NA
#> 5 V5 2 2PLM 0.2087045 0.48313552 NA
# Extract the variance-covariance matrix of item parameter estimates
(cov.mat <- getirt(mod.2pl, what = "covariance"))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0601314833 0.161626270 -0.0051257769 -0.0044224511 -0.002071661
#> [2,] 0.1616262701 0.455451195 -0.0136565487 -0.0103462255 -0.005500742
#> [3,] -0.0051257769 -0.013656549 0.0362987519 0.0305074017 -0.007660103
#> [4,] -0.0044224511 -0.010346225 0.0305074017 0.0340436966 -0.005426263
#> [5,] -0.0020716614 -0.005500742 -0.0076601034 -0.0054262631 0.040812001
#> [6,] 0.0003284084 0.001904617 0.0005559771 0.0017297229 0.001821232
#> [7,] -0.0019311592 -0.003705538 -0.0009465802 0.0006292671 -0.008775219
#> [8,] -0.0020030971 -0.001814204 0.0008034353 0.0040386727 -0.010316758
#> [9,] 0.0015223739 0.006454168 -0.0032010354 -0.0020718831 -0.003243842
#> [10,] 0.0049990824 0.020820838 -0.0064320092 -0.0026824700 -0.005159683
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] 3.284084e-04 -1.931159e-03 -0.0020030971 0.0015223739 0.004999082
#> [2,] 1.904617e-03 -3.705538e-03 -0.0018142036 0.0064541683 0.020820838
#> [3,] 5.559771e-04 -9.465802e-04 0.0008034353 -0.0032010354 -0.006432009
#> [4,] 1.729723e-03 6.292671e-04 0.0040386727 -0.0020718831 -0.002682470
#> [5,] 1.821232e-03 -8.775219e-03 -0.0103167581 -0.0032438424 -0.005159683
#> [6,] 6.636672e-03 -5.923696e-05 0.0011872961 0.0003003195 0.002347453
#> [7,] -5.923696e-05 3.684226e-02 0.0450056386 -0.0031576436 -0.007049767
#> [8,] 1.187296e-03 4.500564e-02 0.0646519738 -0.0034621648 -0.006508739
#> [9,] 3.003195e-04 -3.157644e-03 -0.0034621648 0.0435575616 0.097528414
#> [10,] 2.347453e-03 -7.049767e-03 -0.0065087390 0.0975284136 0.233419934
# }