Regularization of the location model in discrimination with mixed discrete and continuous variables

Regularized techniques in discriminant analysis with mixed discrete and continuous variables for generalized location model (GLOM) are presented. Three extensions are considered: constraining models, combining standard techniques and flexible Bayesian methods. The first approach is based on the flexibility in modelling the relationship among cell covariance matrices while at the same time keeping the number of unknown parameters reasonably small. The second approach is a regularized cell covariance matrices which takes a compromise between standard linear methods using two regularized parameters. The third approach develops a range of flexible Bayesian methods based on a conjugate and hierarchical covariance prior distributions akin to regularized GLOM. To assess the efficiency of these regularized versions, three real data sets are used for illustrations. The proposed methods compare very favourably with the classical GLOM. (C) 2003 Elsevier B.V. All rights reserved.