Specification issues in stratified variance component ordinal response models

The paper presents some criteria for the specification of ordinal variance component models when the units are grouped in a limited number of strata. The base model is specified using a latent variable approach, allowing the first level variance, the second level variance, and the thresholds to vary according to the strata. However this model is not identifiable. The paper discusses some alternative assumptions that overcome the identification problem and illustrates a general strategy for model selection. The proposed methodology is applied to the analysis of course programme evaluations based on student ratings, referring to three different schools of the University of Florence. The adopted model takes into account both the ordinal scale of the ratings and the hierarchical nature of the phenomenon. In this framework, the specification of the latent variable distributions is crucial, since a different first level variance among the schools would substantially change the interpretation of model parameters, as confirmed by the limited simulation study presented in the paper.