Module 9: Single-level and multilevel models for ordinal responses (Concepts)

n Module 6 we saw how multiple regression models for continuous responses can be generalised to handle binary responses, and in Module 7 these models were further extended for the analysis of binary data with a two-level hierarchical structure. This module considers standard (single-level) and multilevel models for ordinal categorical response variables, where the numeric codes assigned to categories imply some ordering. We begin with a cription of two approaches for the analysis of single-level ordinal data:

the cumulative logit model which is appropriate for variables such as Likert scale items, where respondents are asked to indicate their strength of agreement with a statement from 'strongly agree' to 'strongly disagree', and educational tests where marks are available as grades rather than percentage scores; and
the continuation ratio model for ordinal responses that can be viewed as the result of a series of sequential decisions or actions (e.g. highest level of educational qualifications).
We then show how the cumulative logit model can be extended for the analysis of data with a two-level hierarchical structure.