Performance of some discriminant analysis techniques

Abstract

This paper re-appraises the use of the minimised sum of deviations by the proportion method (MSDP), the linear discriminant analysis (LDA) embodied in Minitab and the logit discriminant analysis (LoDA), for allocating observations into one of two mutually exclusive groups using some examples. In a recent paper, the MSDP was proposed as a means of generating a discriminant function that separates observations in a training sample (or development sample) of known group membership into specified groups. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The decision rule on group-membership prediction is constructed using the apparent error rate. This study compares the performance of the MSDP with the LDA and LoDA based on their classification accuracy. The obtained results indicate that the LoDA is not suitable for the examples considered and that the MSDP is an appropriate alternative to the LDA.