LASSO-Based Pattern Recognition for Replenished Items With Graded Responses in Multidimensional Computerized Adaptive Testing

Abstract

As a branch of statistical latent variable modeling, multidimensional item response theory (MIRT) plays an important role in psychometrics. Multidimensional graded response model (MGRM) is a key model for the development of multidimensional computerized adaptive testing (MCAT) with graded-response data and multiple traits. This paper explores how to automatically identify the item-trait patterns of replenished items based on the MGRM in MCAT. The problem is solved by developing an exploratory pattern recognition method for graded-response items based on the least absolute shrinkage and selection operator (LASSO), which is named LPRM-GR and facilitates the subsequent parameter estimation of replenished items and helps maintaining the effectiveness of item replenishment in MCAT. In conjunction with the proposed approach, the regular BIC and weighted BIC are applied, respectively, to select the optimal item-trait patterns. Simulation for evaluating the LPRM-GR in pattern recognition accuracy of replenished items and the corresponding item estimation accuracy is conducted under multiple conditions across different numbers with respect to dimensionality, response-category numbers, latent trait correlation, stopping rules, and item selection criteria. Results show that the proposed method with the two types of BIC both have good performance in pattern recognition for item replenishment in the two- to four-dimensional MCAT with the MGRM, for which the weighted BIC is generally superior to the regular BIC. The proposed method has relatively high accuracy and efficiency in identifying the patterns of graded-response items, and has the advantages of easy implementation and practical feasibility.

Keywords: LASSO; item-trait pattern recognition; multidimensional computerized adaptive testing; multidimensional graded response model; replenished items; weighted BIC.