Classification of multivariate count data with multivariate log-linear conditional Poisson distribution

A classification model is proposed for distinguishing between several subpopulations using a multivariate count dataset. The classification rule, which minimizes the probability of misclassification, is obtained under the distributional hypothesis of a multivariate log-linear conditional Poisson distribution. A sample classification rule is defined based on the maximum likelihood estimators of the distributional parameters. This rule is based on functions associated with each one of the subpopulations, or equivalently, on the estimated posterior probabilities. Additionally, the likelihood ratio test of equality of the parameters for all the subpopulations is analyzed, providing a measure of the power to discriminate between subpopulations. Furthermore, an algorithm to determine the most suitable subset of counting variables for classification is proposed. Finally, actual and simulated datasets are considered to illustrate the application of the methodology.