Multiple group logistic discrimination

Abstract

Logistic discrimination is a partially parametric method for classifying multivariate observations x into one of several populations, H 1,…, H g . It is based on the assumption that posterior probabilities have the form (Anderson, 1972): pr ( H s | x) = exp ( z s )/ Σ s exp ( z s ), where z s = α s T · x ( s = 1,…, g) and z g = 0. This assumption is satisfied by a wide variety of families of distributions involving either continuous or discrete variables or a mixture of both. Maximum-likelihood estimates of the model parameters are obtained by an iterative procedure and, except for certain data configurations (complete, quasi-complete or partial separation), they are finite and unique. Using large sample theory of ML estimates, tests can be performed on the estimated coefficients, and improved measures of the correct classification rate can be derived that account for sampling variation. Diagnostic checks should be performed to verify the appropriateness of the logistic model and to detect outlying or influential observations. Multiple group logistic discrimination has many potential extensions.