Alternative parameterization of polychotomous models: theory and application to matched case-control studies

A method is proposed for transforming a class of models having an outcome variable with more than two levels into an equivalent binary model. The polychotomous logistic model is used to demonstrate the method. The equivalency to a simple logistic regression model after some data transformation (augmentation) is shown. The method is applied to the data from two case-control studies each with two control groups, and further applications are indicated.