A Constrained Confirmatory Mixture IRT Model: Extensions and Estimation of the Saltus model using Mplus

Abstract

In this paper, I will discuss applications, extensions, and estimation of the Saltus model, a specialized confirmatory mixture IRT model. The Saltus model is confirmatory because the number/nature of latent classes is pre-specified and prior item information is utilized for class differentiation. Such a confirmatory model has not been fully utilized in applied research due to two main misconceptions: (1) the model is designed for specific purposes only and (2) a specialized software package is required to estimate the model. In this study, I will discuss that (1) such a confirmatory approach is applicable to various applications of mixture IRT modeling, (2) the model can actually be parameterized as a constrained mixture IRT model and (3) the model can be readily extended and estimated with regular, off-the-shelf mixture IRT software packages that allow for linear constraints on model parameters. An application and estimation of the constrained confirmatory IRT model is illustrated with an empirical example.