Multilevel models for ordinal data
This chapter is concerned with regression models for ordinal responses, with special emphasis on random effects models for multilevel or clustered data. After a brief discussion on ordinal variables, it reviews the most common regression models for ordinal responses, focusing on cumulative models, namely models based on cumulative probabilities. It then 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. It also deals with estimation, inference and prediction, with a brief look on available software. Finally, it presents an application of random effects cumulative models to the analysis of student ratings of university courses.
19.1 Ordinal variables
Satisfaction is usually measured using graded scales, also called Likert scales, such as ‘Very dissatisfied’, ‘Dissatisfied’, ‘Satisfied’ and ‘Very satisfied’. The resulting statistical variable Y is ordinal, that is, it has ordered categories. Sometimes a score is associated with each label (e.g., ‘Very dissatisfied’ is 1, ‘Dissatisfied’ is 2, …), but even in this case the variable Y is genuinely ordinal: it is not measured on an interval scale since the distances between the ...