A simulation study in the performance of parametric and nonparametric discriminant methods for varying data distribution, group dispersion, and training sample size

Discriminant analysis predicts or classifies observations or subjects into mutually exclusive groups, based on a set of predictor variables. This is accomplished by developing a discriminant rule or function using the predictor variables of known group members and using that function to classify new group members. The method used to develop the discriminant function will depend on the type or condition of the data. Many discriminant methods assume the groups to be multivariate normal and equally dispersed. This research determined the best method of predicting group membership when the assumptions of multivariate normality and homogeneity of variance-covariance matrices were violated. In addition this research determined which discriminant methods worked best with small, medium, and large sample sizes. The discriminant methods employed in this study were two parametric and two nonparametric methods. The parametric methods were Fisher\u27s linear discriminant function (FLDF) and Smith\u27 s quadratic discriminant function (QDF). The nonparametric methods were linear programming methods: the minimize the sum of distances (MSD) and the least absolute deviation (LAD) regression methods. A simulation study was conducted for two groups of data to determine the classification performance of each of the four discriminant methods when the parameters of data distribution, group dispersion, and training sample size were varied. The data distributions were the multivariate normal, uniform continuous, and uniform discrete distributions. The two groups were homogeneous, moderately heterogeneous, and strongly heterogeneous. The sample sizes used to develop the discriminant functions were 20, 50, and 100 observations. The research found that the best classification performance for heterogeneous groups was achieved by the QDF method. The MSD method also classified heterogeneous groups well and performed exceptionally well with uniform discrete data. Both the FLDF and QDF methods required only medium size samples of 50 observations to develop a discriminant rule, whereas the MSD required a large sample. The LAD method, however, demonstrated that it was an inferior method of discrimination