rasch.copula.Rd
This function handles local dependence by specifying copulas for residuals in multidimensional item response models for dichotomous item responses (Braeken, 2011; Braeken, Tuerlinckx & de Boeck, 2007; Schroeders, Robitzsch & Schipolowski, 2014). Estimation is allowed for item difficulties, item slopes and a generalized logistic link function (Stukel, 1988).
The function rasch.copula3
allows the estimation of multidimensional
models while rasch.copula2
only handles unidimensional models.
rasch.copula2(dat, itemcluster, weights=NULL, copula.type="bound.mixt", progress=TRUE, mmliter=1000, delta=NULL, theta.k=seq(-4, 4, len=21), alpha1=0, alpha2=0, numdiff.parm=1e-06, est.b=seq(1, ncol(dat)), est.a=rep(1, ncol(dat)), est.delta=NULL, b.init=NULL, a.init=NULL, est.alpha=FALSE, glob.conv=0.0001, alpha.conv=1e-04, conv1=0.001, dev.crit=.2, increment.factor=1.01) rasch.copula3(dat, itemcluster, dims=NULL, copula.type="bound.mixt", progress=TRUE, mmliter=1000, delta=NULL, theta.k=seq(-4, 4, len=21), alpha1=0, alpha2=0, numdiff.parm=1e-06, est.b=seq(1, ncol(dat)), est.a=rep(1, ncol(dat)), est.delta=NULL, b.init=NULL, a.init=NULL, est.alpha=FALSE, glob.conv=0.0001, alpha.conv=1e-04, conv1=0.001, dev.crit=.2, rho.init=.5, increment.factor=1.01) # S3 method for rasch.copula2 summary(object, file=NULL, digits=3, ...) # S3 method for rasch.copula3 summary(object, file=NULL, digits=3, ...) # S3 method for rasch.copula2 anova(object,...) # S3 method for rasch.copula3 anova(object,...) # S3 method for rasch.copula2 logLik(object,...) # S3 method for rasch.copula3 logLik(object,...) # S3 method for rasch.copula2 IRT.likelihood(object,...) # S3 method for rasch.copula3 IRT.likelihood(object,...) # S3 method for rasch.copula2 IRT.posterior(object,...) # S3 method for rasch.copula3 IRT.posterior(object,...)
dat | An \(N \times I\) data frame. Cases with only missing responses are removed from the analysis. |
---|---|
itemcluster | An integer vector of length \(I\) (number of items). Items with the same integers define a joint item cluster of (positively) locally dependent items. Values of zero indicate that the corresponding item is not included in any item cluster of dependent responses. |
weights | Optional vector of sampling weights |
dims | A vector indicating to which dimension an item is allocated. The default is that all items load on the first dimension. |
copula.type | A character or a vector containing one of the following copula
types: |
progress | Print progress? Default is |
mmliter | Maximum number of iterations. |
delta | An optional vector of starting values for the dependency parameter |
theta.k | Discretized trait distribution |
alpha1 |
|
alpha2 |
|
numdiff.parm | Parameter for numerical differentiation |
est.b | Integer vector of item difficulties to be estimated |
est.a | Integer vector of item discriminations to be estimated |
est.delta | Integer vector of length |
b.init | Initial \(b\) parameters |
a.init | Initial \(a\) parameters |
est.alpha | Should both alpha parameters be estimated? Default is |
glob.conv | Convergence criterion for all parameters |
alpha.conv | Maximal change in alpha parameters for convergence |
conv1 | Maximal change in item parameters for convergence |
dev.crit | Maximal change in the deviance. Default is |
rho.init | Initial value for off-diagonal elements in correlation matrix |
increment.factor | A numeric value larger than one which controls the size of increments in iterations. To stabilize convergence, choose values 1.05 or 1.1 in some situations. |
object | Object of class |
file | Optional file name for |
digits | Number of digits after decimal in |
... | Further arguments to be passed |
A list with following entries
Number of item clusters
Estimated item parameters
Number of iterations
Deviance
Estimated dependency parameters \(\delta\)
Estimated item difficulties
Estimated item slopes
Mean
Standard deviation
Parameter \(\alpha_1\) in the generalized item response model
Parameter \(\alpha_2\) in the generalized item response model
Information criteria
Discretized ability distribution
Fixed \(\theta\) distribution
Deviance
Item response patterns with frequencies and posterior distribution
Data frame with person parameters
List of generated data frames during estimation
Reliability of the EAP
Type of copula
Summary for estimated \(\delta\) parameters
Individual posterior
Individual likelihood
Further values
Braeken, J. (2011). A boundary mixture approach to violations of conditional independence. Psychometrika, 76(1), 57-76. doi: 10.1007/s11336-010-9190-4
Braeken, J., Kuppens, P., De Boeck, P., & Tuerlinckx, F. (2013). Contextualized personality questionnaires: A case for copulas in structural equation models for categorical data. Multivariate Behavioral Research, 48(6), 845-870. doi: 10.1080/00273171.2013.827965
Braeken, J., & Tuerlinckx, F. (2009). Investigating latent constructs with item response models: A MATLAB IRTm toolbox. Behavior Research Methods, 41(4), 1127-1137.
Braeken, J., Tuerlinckx, F., & De Boeck, P. (2007). Copula functions for residual dependency. Psychometrika, 72(3), 393-411. doi: 10.1007/s11336-007-9005-4
Schroeders, U., Robitzsch, A., & Schipolowski, S. (2014). A comparison of different psychometric approaches to modeling testlet structures: An example with C-tests. Journal of Educational Measurement, 51(4), 400-418. doi: 10.1111/jedm.12054
Stukel, T. A. (1988). Generalized logistic models. Journal of the American Statistical Association, 83(402), 426-431. doi: 10.1080/01621459.1988.10478613
For a summary see summary.rasch.copula2
.
For simulating locally dependent item responses see sim.rasch.dep
.
Person parameters estimates are obtained by person.parameter.rasch.copula
.
See rasch.mml2
for the generalized logistic link function.
See also Braeken and Tuerlinckx (2009) for alternative (and more expanded) copula models implemented in the MATLAB software. See https://ppw.kuleuven.be/okp/software/irtm/.
See Braeken, Kuppens, De Boeck and Tuerlinckx (2013) for an extension of the copula modeling approach to polytomous data.