Local Classification of Discrete Variables by Latent Class Models

"Global" classifiers may fail to distinguish classes adequately in discrimination problems with inhomogeneous groups. Instead, local methods that consider latent subclasses can be adopted in this case. Three different models for local discrimination of categorical variables are presented in this work. They are based on Latent Class Models, which represent discrete finite mixture distributions. Therefore, they can be estimated via the EM algorithm. A corresponding model is constructed analogously to the Mixture Discriminant Analysis by class conditional Latent Class Models. Two other techniques are based on the idea of Common Components Models. Applicable model selection criteria and measures for the classification capability are suggested. In a simulation study, discriminative performance of the methods is compared to that of decision trees and the Na ve Bayes classifier. It turns out that the MDA-type classifier can be seen as a localization of the Naive Bayes method. Additionally the procedures have been applied to a SNP data set.