A Method of Empirical Q-Matrix Validation for Multidimensional Item Response Theory

A Q-matrix is a binary matrix that defines the relationship between items and latent variables and is widely used in diagnostic classification models (DCMs), and can also be adopted in multidimensional item response theory (MIRT) models. The construction process of the Q-matrix is typically carried out by experts in the subject area of the items and statistical procedures can be used to verify its suitability. In DCMs, different approaches have been proposed for validating the Q-matrix through iterative algorithms. This article presents a method of empirical Q-matrix validation for MIRT models. A simulation study and an application to real data of morphology skills of elementary students are conducted to examine the viability of the method. Relevant issues regarding the implementation of the method and the results obtained are discussed.