Contributions to Discriminant Analysis using Qualitative Data

Abstract

Many practical problems of classification have qualitative data. In such cases, it may be more natural to assume underlying qualitative structures and proceed with discriminant techniques based on such characterizations. One of the main important approaches developed for this case is the Full Multinomial approach which is considered in the literature of Discrete Discriminant Analysis as a standard procedure.

This study suggests a mathematical programming methodology to solve the discriminant analysis problems using qualitative data by introducing a new class of models that not only overcomes the drawbacks of the Full Multinomial approach but also allows the decision maker to assign priorities to some important states.. The thesis also employs the Nearest Neighbour approach to reduce the number of states of the problem, and objectively handle the problems of zero and/or of equal relative frequencies. These models aim at minimizing the total expected cost of misclassification for the case of two-group classification problem using qualitative data. Using illustrative numerical examples for comparing the suggested models with the Full Multinomial approach disregarding its drawbacks, shows that the suggested models have approximately the same total efficiency of classification as the Full Multinomial approach.

The problem of discriminating between unemployed and employed women in the urban governorates of Egypt is used as a real-life application. The Full Multinomial approach as well as the mixed integer linear programming model are applied using the Egypt Demographic and Health Surveys (EDHS, 1995 data and EDHS, 2000 data), to discriminate between unemployed and employed women in the Urban Governorates of Egypt. Each of the two models is, firstly, applied on EDHS, 1995 data to obtain the classification rule, which is used with the EDHS, 2000 data to examine the ability of the suggested model to correctly allocate new observations. The total efficiency of classification was 80% in 1995 and 74% in 2000.