The Efficiency of Multinomial Logistic Regression Compared with Multiple Group Discriminant Analysis
Abstract Multinomial logistic regression (also referred to as polychotomous logistic regression) is frequently used for the analysis of categorical response data with continuous or categorical explanatory variables. Parameter estimates are usually obtained through direct maximum likelihood estimation. Normal discriminant analysis has been used as an alternative approach to this methodology, although it is strictly appropriate only when the usual normal discriminant assumptions concerning the explanatory variables are valid. Comparative evaluations of the two procedures, including the investigation of bias and efficiency in parameter estimation, have been almost entirely limited to the case of two response groups for both normal and nonnormal explanatory variables. Bull and Donner (1987) extended the comparison of logistic regression and normal discrimination in the normal case to more than two response groups, deriving the large sample distribution of the slope parameter estimates for each of the two proc...