On the estimation of the stereotype regression model

Regression models for discrete responses with more than two categories are well established in applied statistics nowadays, where the Proportional odds model is mainly used for ordinal and the Multinomial logistic model for nominal responses. Anderson's Stereotype regression model has been used less. It is a mixture of the aforementioned models that has fewer parameters than the Multinomial model and models the assumed ordinality of the response in terms of the covariates. The main reason for the rare application of the Stereotype model might have been the enhanced mathematical complexity due to multiplicative parameters in the linear predictor and the lack of standard software. Two methods are shown that estimate the model with standard software and the SAS system is used for illustration. The first method interprets the Stereotype model as a nonlinear model with a multivariate response, and thus embeds it in a well-known and mature statistical class of models. The second method maximizes the likelihood function directly. An example on occupational hand eczema in the car industry is used to introduce the model and the different possibilities for computation. Results from a small simulation study, inspired by the hand eczema data set, are given which demonstrate that the estimation of the Stereotype model by the two proposed methods indeed yields valid results in terms of empirical size and power.