Partially Ordered Logistic Regression

Abstract

Partially ordered sets arise frequently in classification problems. Classification models that are currently used tend to either ignore the partial orderedness of the data by fitting nominal models or apply a strict ordering to the data by fitting ordinal models. In both cases, valuable information about the data is lost or overvalued in the model. Zhang and Ip created a framework for a multistep process in which a series of models can be used to classify data from partially ordered sets while maintaining the underlying structure of the data. While the framework of the model exists, it is not widely used. In this thesis, we provide an algorithm that fits the framework along with pseudocode to assist with implementation of the model. We then show an example of an application to a rare disease, SCN8A, which has a partially ordered structure of disease state.