The Improved EMS Algorithm for Latent Variable Selection in M3PL Model

One of the main concerns in multidimensional item response theory (MIRT) is to detect the relationship between items and latent traits, which can be treated as a latent variable selection problem. An attractive method for latent variable selection in multidimensional 2-parameter logistic (M2PL) model is to minimize the observed Bayesian information criterion (BIC) by the expectation model selection (EMS) algorithm. The EMS algorithm extends the EM algorithm and allows the updates of the model (e.g., the loading structure in MIRT) in the iterations along with the parameters under the model. As an extension of the M2PL model, the multidimensional 3-parameter logistic (M3PL) model introduces an additional guessing parameter which makes the latent variable selection more challenging. In this paper, a well-designed EMS algorithm, named improved EMS (IEMS), is proposed to accurately and efficiently detect the underlying true loading structure in the M3PL model, which also works for the M2PL model. In simulation studies, we compare the IEMS algorithm with several state-of-art methods and the IEMS is of competitiveness in terms of model recovery, estimation precision, and computational efficiency. The IEMS algorithm is illustrated by its application to two real data sets.