A Multidimensional Latent Class IRT Model for Non-Ignorable Missing Responses

22 Pages Posted: 9 Feb 2013

See all articles by Silvia Bacci

Silvia Bacci

University of Perugia - Department of Economics, Finance and Statistics

Francesco Bartolucci

Università di Perugia - Finanza e Statistica - Dipartimento di Economia

Date Written: February 7, 2013

Abstract

A relevant problem in applications of Item Response Theory (IRT) models is due to non- ignorable missing responses. We propose a multidimensional latent class IRT model for binary items in which the missingness mechanism is driven by a latent variable (propensity to answer) correlated with the latent variable for the ability (or latent variables for the abilities) measured by the test items. These latent variables are assumed to have a joint discrete distribution. This assumption is convenient both from the point of view of estimation, since the manifest distribution of the responses may be simply obtained, and for the decisional process, since individuals are classified in homogeneous groups having common latent variable values. Moreover, this assumption avoids parametric formulations for the distribution of the latent variables, giving rise to a semiparametric model. The basic model, which can be expressed in terms of a Rasch or a two-parameters logistic parameterization, is also extended to allow for covariates that influence the weights of latent classes. The resulting model may be efficiently estimated through the discrete marginal maximum likelihood method, making use of the Expectation-Maximization algorithm. The proposed approach is illustrated through an application to data coming from a Students’ Entry Test for the admission to the courses in Economics in an Italian University.

Keywords: EM algorithm, finite mixture models, semiparametric inference, Students’ Entry Test

JEL Classification: C10, I20

Suggested Citation

Bacci, Silvia and Bartolucci, Francesco, A Multidimensional Latent Class IRT Model for Non-Ignorable Missing Responses (February 7, 2013). Available at SSRN: https://ssrn.com/abstract=2213721 or http://dx.doi.org/10.2139/ssrn.2213721

Silvia Bacci (Contact Author)

University of Perugia - Department of Economics, Finance and Statistics ( email )

Italy

Francesco Bartolucci

Università di Perugia - Finanza e Statistica - Dipartimento di Economia ( email )

06123

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