A Connection between the Logit Model, Normal Discriminant Analysis, and Multivariate Normal Mixtures

A relationship between the logit model, normal discriminant analysis, and mixtures of multivariate normal distributions is discussed.It is shown that the likelihood equations for multivariate normal mixtures can be obtained from the likelihood equations for the normal discriminant analysis model by simply replacing the index variables with weights that are logistic probabilities, and that all three models use the same linear discriminant function to classify observations into different populations.Some implications of these relationships for data analysis are also discussed.