Multidimensional Latent Class (LC) Item Response Theory (IRT) Models

Description

This package provides a flexible framework for the Item Response Theory (IRT) analysis of dichotomous and ordinal polytomous outcomes under the assumption of 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 parameterizations. The package also allows for the inclusion individual covariates affecting the class weights.

Details

Function est_multi_poly performs the parameter estimation of the following IRT models, allowing for one or more latent traits:

- Binary responses: Rasch model, 2-Parameter Logistic (2PL) model;

- Ordinal polythomous responses: Samejima's Graded Response Model (GRM) and constrained versions with fixed discrimination parameters and/or additive decomposition of difficulty parameters (rating scale parameterization); Muraki's Generalized Partial Credit Model and constrained versions with fixed discrimination parameters and/or additive decomposition of difficulty parameters, such as Partial Credit Model and Rating Scale Model.

The basic input arguments for est_multi_poly are the person-item matrix of available response configurations and the corresponding frequencies, the number of latent classes, the type of link function, the specification of constraints on the discriminating and difficulty item parameters, and the allocation of items to the latent traits. Missing responses are coded with 999, and units and items without responses are automatically removed.

Function test_dim performs a likelihood ratio test to choose the optimal number of latent traits (or dimensions) by comparing nested models that differ in the number of latent traits, being all the other elements let equal (i.e., number of latent classes, type of link function, constraints on item parameters). The basic input arguments for test_dim are similar as those for est_multi_poly.

Function class_item performs a hierarchical clustering of items based on a specified LC IRT model. The basic input arguments are given by the number of latent classes, the type of model, and the constraints on the item parameters (only for polythomous responses). An allocation of items to the different latent traits is obtained depending on the cut-point of the resulting dendrogram.

Author(s)

Francesco Bartolucci, Silvia Bacci, Michela Gnaldi - University of Perugia (IT)

Maintainer: Francesco Bartolucci <bart@stat.unipg.it>

References

Bartolucci, F. (2007), A class of multidimensional IRT models for testing unidimensionality and clustering items, Psychometrika, 72, 141-157.

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

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.

Examples

## Estimation of different Multidimensional LC IRT models with binary
## responses
# Aggregate data
data(naep)
X = as.matrix(naep)
out = aggr_data(X)
S = out$data_dis
yv = out$freq
# Define matrix to allocate each item on one dimension 
multi1 = rbind(c(1,2,9,10),c(3,5,8,11),c(4,6,7,12))
# Three-dimensional LC Rasch model with 4 latent classes
# less severe tolerance level to check convergence (to be modified)
out1 = est_multi_poly(S,yv,k=4,start=0,link=1,multi=multi1,tol=10^-6)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(MultiLCIRT)
Loading required package: MASS
Loading required package: limSolve
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MultiLCIRT/MultiLCIRT-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: MultiLCIRT-package
> ### Title: Multidimensional Latent Class (LC) Item Response Theory (IRT)
> ###   Models
> ### Aliases: MultiLCIRT-package MultiLCIRT
> ### Keywords: package
> 
> ### ** Examples
> 
> ## Estimation of different Multidimensional LC IRT models with binary
> ## responses
> # Aggregate data
> data(naep)
> X = as.matrix(naep)
> out = aggr_data(X)
> S = out$data_dis
> yv = out$freq
> # Define matrix to allocate each item on one dimension 
> multi1 = rbind(c(1,2,9,10),c(3,5,8,11),c(4,6,7,12))
> # Three-dimensional LC Rasch model with 4 latent classes
> # less severe tolerance level to check convergence (to be modified)
> out1 = est_multi_poly(S,yv,k=4,start=0,link=1,multi=multi1,tol=10^-6)
*-------------------------------------------------------------------------------*
Model with multidimensional structure
            [,1] [,2] [,3] [,4]
Dimension 1    1    2    9   10
Dimension 2    3    5    8   11
Dimension 3    4    6    7   12
Link of type =                  1 
Discrimination index =          0 
Constraints on the difficulty = 0 
Type of initialization =        0 
*-------------------------------------------------------------------------------*
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>