Model-Assisted Inference for Ordinal Evaluation Data: A Bayesian Latent Mixed Effects Location–Scale Model

Student evaluations of teaching (SETs) are a common measure of teaching quality in higher education, yet valid inference from such data remains challenging. Hierarchical dependencies among observations, variation in response styles, and measurement error in predictors complicate interpretation, while traditional analyses based on mean ratings often fail to distinguish teaching-related effects from correlated, non-teaching influences. This study introduces a Bayesian mixed-effects location–scale probit model as a model-assisted inferential framework for ordinal SET data. The model jointly estimates effects on the latent mean evaluation (location) and on latent response variability (scale), incorporating hierarchical random effects and correcting for measurement error in multi-item predictors. The framework is illustrated using four semesters of SET data from more than 5,000 students in psychology, pedagogy, and teacher education programs at a German university. The application is intended as a methodological demonstration rather than a population-level generalization. Within this context, didactic quality and lecturer likeability emerged as the strongest predictors of overall evaluations. An interaction effect suggested that comprehensibility receives higher ratings when lecturers are viewed as likeable. Beyond mean effects, substantial heterogeneity was observed at the student, lecturer, and course levels, along with systematic differences in rating precision linked to individual response tendencies. These findings highlight that robust inference from SET data requires models capturing both location and scale heterogeneity. More broadly, the proposed Bayesian approach demonstrates how location-scale modeling can improve the analysis of ordinal data with hierarchical dependencies and measurement error.