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

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 penalty term to the log-likelihood. The computation is carried out by the expectationmaximization algorithm combined with the coordinate descent algorithm. To the authors’ best knowledge, this is the first study investigating a data-driven latent structure in the literature of item response theory. Simulation studies show that the resulting estimator provides an effective way in correctly identifying the latent structures. The method is applied to a real data set involving the Eysenck Personality Questionaire.