Abstract Discrete variables that have an inherent sense of ordering across outcomes are commonly found in large data sets available to many economists, and are often the focus of research. However, assumptions underlying the standard ordered probit (which is usually used to analyse such variables) are not always justified by the data. This study provides a review of the ways in which the ordered probit might be extended to account for additional heterogeneity. Differing from other reviews in scope, application and relevance in economic settings, a series of issues pertaining to choices of variables, and the economic assumptions underlying each model are discussed in the context of measuring the underlying health of respondents. The models are applied to a wave of the household, income and labour dynamics in Australia survey, in order to check the appropriateness of such assumptions in an applied context.