A Finite Mixture Item Response Theory Model for Continuous Measurement Outcomes

Abstract

A mixture extension of Samejima’s continuous response model for continuous measurement outcomes and its estimation through a heuristic approach based on limited-information factor analysis is introduced. Using an empirical data set, it is shown that two groups of respondents that differ both qualitatively and quantitatively in their response behavior can be revealed. In addition to the real data application, the effectiveness of the heuristic estimation approach under real data analytic conditions was examined through a Monte Carlo simulation study. The results showed that the heuristic estimation approach provided reliable parameter estimates and the model successfully converged above 80% when the sample size was 250 and above 90% when the sample size was 500 or 1,000 for most conditions.