Multiple group logistic discrimination

Among the many possible approaches suggested for statistical discrimination, the logistic method can be classified midway between fully distributional solutions, of which the assumption of multivariate normality is a classical example[16l, and the distribution-free techniques, using, for instance, kernel or nearest-neighbor methods[l,32]. Therefore it is often called a partially parametric or partially distributional method[l l]. This central position of the logistic model makes it one of the most attractive and widely used tools for solving regression and discrimination problems. Indeed, since there are fewer distributional assumptions than for fully parametric models, the logistic method is applicable to a larger family of multivariate distributions involving both discrete and continuous variables. Moreover, in spite of its wide applicability and generality, the method remains feasible and easy to use, in contrast with nonparametric methods. This paper is intended to review the basic ideas and principles of logistic discrimination[415,22-25] and also to bring additional results to some of the queries raised by Professor Anderson before his death. We restrict our attention to discrimination between qualitatively distinct groups and do not envisage the case where groups are quantitatively distinct or ordered[3,12,14]. We dedicate this paper to our friend and mentor, the late Professor J. A. Anderson, for his fundamental contribution to discriminant analysis and for his continuous support of our research efforts.