Prediction of ordinal outcomes when the association between predictors and outcome differs between outcome levels.

There are a number of regression models which are widely used to predict ordinal outcomes. The commonly used models assume that all predictor variables have a similar effect at all levels of the outcome variable. If this is not the case, for example if some variables predict susceptibility to a disease and others predict the severity of the disease, then a more complex model is required. One possibility is the multinomial logistic regression model, which assumes that the predictor variables have different effects at all levels of the outcome variable. An alternative is to use the stereotype family of regression models. A one-dimensional stereotype model makes the assumption that the effect of each predictor is the same at all outcome levels. However, it is possible to fit stereotype models with more than one dimension, up to a maximum of min(k-1, p) where k is the number of outcome categories and p is the number of predictor variables. A stereotype model of this maximum dimension is equivalent to a multinomial logistic regression model, in that it will produce the same predicted values and log-likelihood. If there are sufficient outcome levels and/or predictor variables, there may be a number of stereotype models of differing dimension. The method is illustrated with an example of prediction of damage to joints in rheumatoid arthritis.