Title: Longitudinal multiple-group IRT modelling: covariance pattern selection using MCMC and RJMCMC

Authors: Caio L.N. Azevedo; Jean-Paul Fox; Dalton F. Andrade

Addresses: Department of Statistics, State University of Campinas, Campinas, SP, Brazil ' Department of Research Methodology, Measurement and Data Analysis, University of Twente, Enschede, Netherlands ' Department of Informatic and Statistics, Federal University of Santa Catarina, Florianópolis, Brazil

Abstract: Longitudinal studies in psychometric assessment are often focused on latent traits of subjects, who are clustered in different groups (e.g., gender, grade, social level). The corresponding type of data can be characterised as longitudinal multiple-group item responses. For this type of data, a longitudinal multiple-group IRT (LMGIRT) model is proposed, where group-specific dependencies between latent traits can be modelled using the appropriate covariance structure. The multiple-group specification together with the developed MCMC-based algorithms make it possible to handle the scaling process simultaneously with the estimation of latent traits, item and population parameters. Also, a reversible-jump MCMC (RJMCMC) algorithm is proposed for joint parameter estimation and covariance matrix selection for a single-group longitudinal IRT model. The MCMC-based algorithms can handle identification rules, scaling issues and selection between restricted covariance structures. Simulation studies reveal that not only all parameters are accurately recovered, but also the correct underlying covariance pattern model is selected. Two real datasets are used to illustrate the longitudinal IRT models and the MCMC algorithms for estimation and model fit assessment. One study concerns the health condition of Dutch students from Amsterdam Growth and Health Longitudinal Study (AGHLS) and the other study a longitudinal research program of the Brazilian federal government.

Keywords: longitudinal data; multi-group IRT; item response theory; IRT modelling; Bayesian inference; Markov chain Monte Carlo; reversible-jump MCMC; RJMCMC; joint parameter estimation; covariance matrix selection; psychometrics; identification rules; scaling issues; restricted covariance structure selection; simulation.

DOI: 10.1504/IJQRE.2015.071737

International Journal of Quantitative Research in Education, 2015 Vol.2 No.3/4, pp.213 - 243

Received: 03 Dec 2014
Accepted: 20 May 2015
Published online: 16 Sep 2015 *

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