A Mixture IRTree Model for Extreme Response Style: Accounting for Response Process Uncertainty

This paper presents a mixture item response tree (IRTree) model for extreme response style. Unlike traditional applications of single IRTree models, a mixture approach provides a way of representing the mixture of respondents following different underlying response processes (between individuals), as well as the uncertainty present at the individual level (within an individual). Simulation analyses reveal the potential of the mixture approach in identifying subgroups of respondents exhibiting response behavior reflective of different underlying response processes. Application to real data from the Students Like Learning Mathematics (SLM) scale of Trends in International Mathematics and Science Study (TIMSS) 2015 demonstrates the superior comparative fit of the mixture representation, as well as the consequences of applying the mixture on the estimation of content and response style traits. We argue that methodology applied to investigate response styles should attend to the inherent uncertainty of response style influence due to the likely influence of both response styles and the content trait on the selection of extreme response categories.