Investigating Within-Person Variation in Response Processes for Likert-Scale Data with a Response-Level Mixture IRTree Model

Self-report scales are central to psychological and behavioral science, yet most analyses assume a single response process. In practice, respondents may follow cognitively distinct processes to answer the same item, and a respondent may switch processes across items. Ignoring between-person and/or within-person heterogeneity in item response process may bias item parameter estimates and person scores. In this study, we introduce a response-level mixture model, namely, MIX-R. The proposed model represents two or more distinct response processes using item response trees and specifies the probability that a specific process is used with a prevalence model, which includes additive person and item effects and optional covariates. We fit MIX-R in a fully Bayesian framework. Applied to three-category items from the verbal aggression questionnaire, MIX-R reveals distinct process-specific item functioning so that expected scores of the same item vary across response processes. As shown in our simulation studies, MIX-R exhibits better model fit when it is consistent with the data-generating process and does not overfit. In addition, it accurately recovers person-level and item-level process prevalence and item parameters. We conclude this study by discussing its limitations and outlining directions for future research.