A Comparison of the Optimal Classification Rule and Maximum Likelihood Rule for Binary Variables

I Egbo,S I Onyeagu,Dan Dan Ekezie ,O Peter

doi:10.5539/jmr.v6n4p124

Abstract

Optimal classification rule and maximum likelihood rules have the largest possible posterior probability of correct allocation with respect to the prior. They have a ‘nice’ optimal property and appropriate for the development of linear classification models. In this paper we consider the problem of choosing between the two methods and set some guidelines for proper choice. The comparison between the methods is based on several measures of predictive accuracy. The performance of the methods is studied by simulations.

Highlights

Optimal classification rules and maximum likelihood rule are widely used multivariate statistical methods for analysis of data with categorical outcome variables. Both of them are appropriate for the development of linear classification models, i.e. models associated with linear boundaries between the groups
Classification is of broad interest in science because it permeates many scientific studies and arises in the contexts of many applications (Panel on Discriminant Analysis, Classification and Clustering, 1989)
Social and behavioural sciences include identifying children in kindergarten at risk for future reading difficulties (Catts, Fey, Zhang and Tomblin (2001), identifying individuals at risk for addiction (Robinson, 2002) and predicting the crimes that male juvenile offenders may commit according to their personality characteristics (Glaser, Calhoun and Petrocelli, 2002)

Summary

Introduction

Optimal classification rules and maximum likelihood rule are widely used multivariate statistical methods for analysis of data with categorical outcome variables. Both of them are appropriate for the development of linear classification models, i.e. models associated with linear boundaries between the groups. In practice, the assumptions are nearly always violated and we have tried to check the performance of both methods with simulations This kind of research demands a careful control, so we have decided to study just a few chosen situations, trying to find a logic in the behaviour and think about the expansion onto more general cases.

The Optimal Classification Rule Independent Random Variables

Optimal Rules for a Case of Four Variables in Two Group Classifications

Probability of Misclassification

Evaluating the Probability of Misclassification for the Optimal Rule Ropt

Simulation Experiments and Results

Conclusion