A multidimensional latent class IRT model for non-ignorable missing responses

TL;DR

This paper introduces a multidimensional latent class IRT model that accounts for non-ignorable missing responses in binary data, using a discrete latent structure and efficient EM estimation, demonstrated through simulations and a university test application.

Contribution

It presents a novel latent class IRT model for non-ignorable missing data that incorporates covariates and uses a discrete latent distribution for efficient estimation.

Findings

Model effectively handles non-ignorable missing responses.

Simulation confirms reliable parameter estimation.

Application demonstrates practical utility in educational testing.

Abstract

We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with non-ignorable missingness. The missingness mechanism is driven by two sets of latent variables: one describing the propensity to respond and the other referred to the abilities measured by the test items. These latent variables are assumed to have a discrete distribution, so as to reduce the number of parametric assumptions regarding the latent structure of the model. Individual covariates may also be included through a multinomial logistic parametrization of the probabilities of each support point of the distribution of the latent variables. Given the discrete nature of this distribution, the proposed model is efficiently estimated by the Expectation-Maximization algorithm. A simulation study is performed to evaluate the finite sample properties of the parameter estimates. Moreover, an application is illustrated to data coming from a Students' Entry Test for the admission to some university courses.