Item Response Analysis of a Structured Mixture Item Response Model with mirt Package in R

Abstract

Structured mixture item response models (StrMixIRMs) are a special type of constrained confirmatory mixture item response theory (IRT) model for detecting latent performance differences in a measurement instrument by characteristic item groups, and classifying respondents according to these differences. In light of limited software options for estimating StrMixIRMs under existing frameworks, this paper proposes reparameterizing it as a confirmatory mixture IRT model using interaction effects between latent classes and item groups. The reparameterization allows for easier implementation of StrMixIRMs with multiple software programs that have mixture modeling capabilities, including open-source ones. This widens the accessibility to these models to a broad range of users and thus can facilitate research and applications of StrMixIRMs. This paper serves two main goals: First, we introduce StrMixIRMs, focusing on the proposed reparameterization based on interaction effects and its various extensions. Second, we illustrate use cases of this novel reparameterization within the mirt 1.41 package in R by employing two empirical datasets. Detailed R code with notes are provided for the applications along with an interpretation of the outputs.