Classification with discrete and continuous variables via general mixed-data models

Abstract

We study the problem of classifying an individual into one of several populations based on mixed nominal, continuous, and ordinal data. Specifically, we obtain a classification procedure as an extension to the so-called location linear discriminant function, by specifying a general mixed-data model for the joint distribution of the mixed discrete and continuous variables. We outline methods for estimating misclassification error rates. Results of simulations of the performance of proposed classification rules in various settings vis-à-vis a robust mixed-data discrimination method are reported as well. We give an example utilizing data on croup in children.

Keywords:

• error rate
• general location model
• grouped continuous model
• maximum likelihood
• measurement level
• minimum distance probability
• misclassification probability
• plug-in estimates

Acknowledgements

This research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. A.S. was an NSERC summer research student when this research was completed. T.W. was supported by a Studentship Award from the Alberta Heritage Foundation for Medical Research. The authors are grateful to Prof. J. Oller, Universitat de Barcelona, for providing the MDP program, and to G. Duggan and J. Owoc for computational help. They are thankful to several anonymous reviewers for insightful comments leading to an improved article. This work was partially carried out while A.R.L. was enjoying the hospitality of the School of Statistics, University of the Philippines.