Performance relative des règles linéaire, quadratique et logistique en analyse discriminante

Monte Carlo study is achieved to compare linear, quadratic and logistic classification rules for two groups, in 480 situations related to the type of distribution, the overlap of the populations, the number of variables, the sample size and the heteroscedasticity degree of the model, which is measured by a parameter gamma defined in the study. The results of this study show that the quadratic rule is the best only for severe heteroscedastic normal or moderate non-normal models with high overlap. The linear rule is the best for homoscedastic normal or moderate non-normal models with low overlap. The logistic rule is the best for severe non-normal models except when homoscedasticity occurs. In the order situations linear and logistic rules have almost the same performance. By considering the parameters computed on the data samples, the linear rule gives the best performance for high values of r whereas logistic rule performs is best for low or moderate values of the same parameter.