Multilevel models for ordinal data

This chapter is devoted to regression models for ordinal responses with special emphasis on random effects models for multilevel or clustered data. After a brief discussion on ordinal variables in the first section, the second section reviews the most common regression models for ordinal responses focusing on cumulative models, namely models based on cumulative probabilities. The third section deals with random effects cumulative models for multilevel data, discussing several issues peculiar to the random effects extension such as the distinction between marginal and conditional effects, the measures of unobserved cluster- level heterogeneity, the consequences of adding covariates, and the main types of predicted probabilities. The last part of the third section deals with estimation, inference and prediction, with a brief look on available software. The fourth section presents an application of random effects cumulative models to the analysis of student ratings on university courses.