The location model for mixtures of categorical and continuous variables

Recent research into graphical association models has focussed interest on the conditional Gaussian distribution for analyzing mixtures of categorical and continuous variables. A special case of such models, utilizing the homogeneous conditional Gaussian distribution, has in fact been known since 1961 as the location model, and for the past 30 years has provided a basis for the multivariate analysis of mixed categorical and continuous variables. Extensive development of this model took place throughout the 1970’s and 1980’s in the context of discrimination and classification, and comprehensive methodology is now available for such analysis of mixed variables. This paper surveys these developments and summarizes current capabilities in the area. Topics include distances between groups, discriminant analysis, error rates and their estimation, model and feature selection, and the handling of missing data.