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Latent variable selection in multidimensional item response theory models using the expectation model selection algorithm |
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| Authors: | Ping-Feng Xu Laixu Shang Qian-Zhen Zheng Na Shan Man-Lai Tang |
| Institution: | 1. Academy for Advanced Interdisciplinary Studies, Northeast Normal University, Changchun, China
School of Mathematics and Statistics, Changchun University of Technology, Changchun, China Contribution: Formal analysis (equal), Funding acquisition (equal), Methodology (equal), Visualization (equal), Writing - original draft (equal), Writing - review & editing (equal);2. School of Mathematics and Statistics, Changchun University of Technology, Changchun, China Contribution: Formal analysis (equal), Methodology (equal), Software (equal), Visualization (equal), Writing - original draft (equal), Writing - review & editing (equal);3. School of Mathematics and Statistics, Changchun University of Technology, Changchun, China Contribution: Methodology (equal), Writing - original draft (equal), Writing - review & editing (equal);4. School of Psychology & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, China;5. Department of Mathematics, College of Engineering, Design & Physical Sciences, Brunel University London, Uxbridge, UK Contribution: Funding acquisition (equal), Writing - original draft (equal), Writing - review & editing (equal) |
| Abstract: | The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L1 regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire. |
| Keywords: | expectation model selection algorithm latent variable selection multidimensional item response theory model Bayesian information criterion |