Latent Variable Selection for Multidimensional Item Response Theory Models via L1 Regularization

Abstract

We develop a latent variable selection method for multidimensional item response theory models. The proposed method identifies latent traits probed by items of a multidimensional test. Its basic strategy is to impose an L1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{1}$$\end{document} penalty term to the log-likelihood. The computation is carried out by the expectation–maximization algorithm combined with the coordinate descent algorithm. Simulation studies show that the resulting estimator provides an effective way in correctly identifying the latent structures. The method is applied to a real dataset involving the Eysenck Personality Questionnaire.

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