Discrimination and classification

Abstract

One of the most widely used multivariate statistical techniques for modelling binary response variables is logistic regression. The goal of logistic regression is to find the parsimonious model which describes the relationship between the response variable and a set of independent variables. Once a logistic regression model is obtained, the predicted probabilities for each subject/object in a sample may be used to classify these subjects/objects into the distinct groups to which they most likely belong. The kernel method provides an alternative way of estimating these probabilities so that they may subsequently be used for discrimination purposes. The greatest difficulty in kernel estimation is that of finding the optimal estimator of the smoothing parameter. An estimator due to Aitchison and Aitken and another one due to Hall shall be presented in this thesis. A Parkinson's dataset obtained from the Laboratory of Molecular Genetics at the Department of Physiology and Biochemistry, University of Malta is investigated, relationships of various risk factors associated with Parkinson's are modelled through the technique of logistic regression and finally, classification of individuals into cases or controls, based on probabilities obtained through logistic regression and through the kernel method is carried out