Misclassification among methods used for multiple group discrimination--the effects of distributional properties.

Methods of multiple group discriminant analysis have not been fully studied with respect to classification into more than two populations when the covariate distributions are normal or non-normal. The present study examines the classification performance of several multiple discrimination methods under a variety of simulated continuous normal and non-normal covariate distributions. The methods include polychotomous logistic regression, multiple group linear discriminant analysis, kernel density estimation, and rank transformations of the data as input into the linear function. The parameters of interest were distance among populations, configuration of population mean vectors (collinear or forming the vertices of a regular simplex), skewness, kurtosis and bimodality. Simulation of the last three parameters was by log-normal, sinh-1 normal and a two-component mixture of normal distributions, respectively. Results with three trivariate populations show that for all distributions, logistic discrimination classifies close to the optimal under Neyman-Pearson allocation. These results suggest that logistic discrimination is preferable to other widely-used methods for multiple group classification with non-normal data, and is comparable to classification by multiple linear discrimination with normal data.