MLCIRTwithin (version 1.1)

MLCIRTwithin-package: Latent Class Item Response Theory (LC-IRT) Models under Within-Item Multidimensionality

Description

This package provides a flexible framework for the Item Response Theory (IRT) analysis of dichotomous and ordinal polytomous outcomes under the assumption of one or more items shared by two latent traits (i.e., within-item multidimensionality) and discreteness of latent traits (abilities). Every level of the abilities identify a latent class of subjects. The fitting algorithms are based on the Expectation-Maximization (EM) paradigm and allow for missing responses and for different item parametrizations. The package also allows for the inclusion of individual covariates affecting the class weights.

Details

Package:

MultiLCIRT

Type:

Package

Version:

1.1

Date:

2016-02-03

License:

GPL (>= 2)

Function est_multi_poly_within performs the parameter estimation of the same model considered in the R package MultiLCIRT when one or more items are shared by two latent traits (within-item multidimensionality).

References

Adams, R., Wilson, M., and Wang, W. (1997), The multidimensional random coefficients multinomial logit, Applied Psychological Measurement, 21, 1-24. Bacci, S. and Bartolucci, F. (2015), A multidimensional finite mixture SEM for non-ignorable missing responses to test items, Structural Equation Modeling, 22, 352-365.

Bacci, S., Bartolucci, F., and Gnaldi, M. (2014), A class of Multidimensional Latent Class IRT models for ordinal polytomous item responses, Communications in Statistics - Theory and Methods, 43, 787-800.

Bartolucci, F. (2007), A class of multidimensional IRT models for testing unidimensionality and clustering items, Psychometrika, 72, 141-157. Bartolucci, F., Bacci, S., and Gnaldi, M. (2015), Statistical Analysis of Questionnaires: A Unified Approach Based on R and Stata, Chapman and Hall/CRC press.

Bartolucci, F., Bacci, S., and Gnaldi, M. (2014), MultiLCIRT: An R package for multidimensional latent class item response models, Computational Statistics and Data Analysis, 71, 971-985. Bock, R.D., Gibbons, R., and Muraki, E. (1988), Full-information item factor analysis, Applied Psychological Measurement, 12, 261-280. Cai, L. (2010), A two-tier full-information item factor analysis model with applications, Psychometrika, 75, 581-612.

Gibbons, R. D., Darrell, R. B., Hedeker, D., Weiss, D. J., Segawa, E., Bhaumik, D. K., and Stover, A. (2007), Full-information item bifactor analysis of graded response data, Applied Psychological Measurement, 31, 4-19. Gibbons, R. D. and Hedeker, D. R. (1992), Full-information item bi-factor analysis, Psychometrika, 57, 423-436.

Examples

## Not run: 
# # Estimation of a LC-IRT model with a within-item multidimensional
# # structure
# data(SF12_nomiss)
# S = SF12_nomiss[,1:12]
# X = SF12_nomiss[,13]
# # Define matrices to allocate each item on the latent variables  
# multi1=rbind(1:6, 7:12)
# multi2=rbind(4:8, c(2:3, 10:12))
# # Graded response model with two primary latent variables, each of them
# # having two dimensions (free discrimination and difficulty parameters;
# # two latent classes for both the latent variables; one covariate):
# tol = 10^-6 # decrease the tolerance to obtain more reliable results
# out1 = est_multi_poly_within(S=S,k1=2,k2=2,X=X,link="global",disc=TRUE,
#                              multi1=multi1,multi2=multi2,tol=tol,
#                              disp=TRUE,out_se=FALSE) 
# # Display output
# summary.est_multi_poly_within(out1)
# ## End(Not run)