Latent Variable Selection for Multidimensional Item Response Theory Models via \(L_{1}\) Regularization

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• 作者：Jianan Sun ; Yunxiao Chen ; Jingchen Liu ; Zhiliang Ying ; Tao Xin
• 关键词：latent variable selection ; multidimensional item response theory model ; \(L_{1}\) ; regularization ; expectation–maximization ; BIC
• 刊名：Psychometrika
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：81
• 期：4
• 页码：921-939
• 全文大小：
• 刊物主题：Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Statistical Theory and Methods;
• 出版者：Springer US
• ISSN：1860-0980
• 卷排序：81

文摘

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 \(L_{1}\) 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.