Predicting ordinal outcomes: options and assumptions

There are a number of methods of analyzing data that consists of several distinct categories, with the categories ordered in some manner. Analysis of such data is commonly based on a generalized linear model of the cumulative response probability, either the cumulative odds model (ologit) or the continuation ratio model (ocratio). However, these models assume a particular relationship between the predictor variables and the outcome. If these assumptions are not met, a multinomial model, which does not make such assumptions, can be fitted instead. This effectively ignores the ordering of the categories. It has the disadvantage that it requires more parameters than the above models, which makes it more difficult to interpret. An alternative model for ordinal data is the stereotype model. This has been little used in the past, as it is quite difficult to fit. It can be thought of as a constrained multinomial model, although some of the constraints applied are nonlinear. An ado-file to fit this model in Stata has recently been developed. I will present analyses of a radiographic dataset, where the aim was to predict the severity of joint damage. All four of the above models were fitted to the data. The assumptions of the cumulative odds and continuation ratio models were not satisfied. A highly constrained stereotype model provided a good fit. Importantly, it showed that different variables were important for discriminating between different levels of the outcome variable.