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.

This paper focuses on the robust classification procedures in two group discriminant analysis with multivariate binary variables. A normal distribution based data set is generated using the R-software statistical analysis system 2.15.3 using Barlett"s approximation to chi-square, the data set was found to be homogenous and was subjected to five linear classifiers namely: maximum likelihood discriminant function, fisher"s linear discriminant function, likelihood ratio function, full multinomial function and nearest neighbour function rule. To judge the performance of these procedures, the apparent error rates for each procedure are obtained for different sample sizes. The results obtained ranked the procedures as follows: fisher"s linear discriminant function, maximum likelihood, full multinomial, likelihood function and nearest neigbour function.

The performance of four discriminant analysis procedures for the classification of observations from unknown populations was examined by Monte Carlo methods. The procedures examined were the Fisher Linear discriminant function, the quadratic discriminant function, a polynomial discriminant function and A-B linear procedure designed for use in situations where covariance matrices are equal. Each procedure was observed under conditions of equal sample sizes, equal covariance matrices, and in conditions where the sample was drawn from populations that have a multivariate normal distribution. When the population covariance matrices were equal, or not greatly different, the quadratic discriminant function performed similarly or marginally the same like Linear procedures. In all cases the polynomial discriminate function demonstrated the poorest, linear discriminant function performed much better than the other procedures. All of the procedures were greatly affected by non-normality and tended to make many more errors in the classification of one group than the other, suggesting that data be standardized when non-normality is suspected.