An introduction to mixture item response theory models
Affiliation:
1. University of Nebraska, Lincoln, United States;2. Consolidated School District of New Britain, Connecticut, United States;1. Department of Counseling and Human Development, University of Louisville, Louisville, KY, USA;2. Department of Educational Leadership, Evaluation and Organizational Development, University of Louisville, Louisville, KY, USA;1. Roehampton University, United Kingdom;2. Université du Québec à Montréal, Canada;3. Cégep Régional de Lanaudière à Joliette, Canada;1. University of Arizona, United States;2. University of South Florida, United States;3. George Mason University, United States;1. Division of Learning, Development, and Diversity, Faculty of Education, The University of Hong Kong, Hong Kong;2. Department of Curriculum and Instruction, The Education University of Hong Kong , Hong Kong;3. Division of Information Technology Studies, Faculty of Education, The University of Hong Kong, Hong Kong
Abstract:
Mixture item response theory (IRT) allows one to address situations that involve a mixture of latent subpopulations that are qualitatively different but within which a measurement model based on a continuous latent variable holds. In this modeling framework, one can characterize students by both their location on a continuous latent variable as well as by their latent class membership. For example, in a study of risky youth behavior this approach would make it possible to estimate an individual's propensity to engage in risky youth behavior (i.e., on a continuous scale) and to use these estimates to identify youth who might be at the greatest risk given their class membership. Mixture IRT can be used with binary response data (e.g., true/false, agree/disagree, endorsement/not endorsement, correct/incorrect, presence/absence of a behavior), Likert response scales, partial correct scoring, nominal scales, or rating scales. In the following, we present mixture IRT modeling and two examples of its use. Data needed to reproduce analyses in this article are available as supplemental online materials at http://dx.doi.org/10.1016/j.jsp.2016.01.002.
