Mixture-model cluster analysis using information theoretical criteria

The estimation of mixture models has been proposed for quite some time as an approach for cluster analysis. Several variants of the Expectation-Maximization algorithm are currently available for this purpose. Estimation of mixture models simultaneously allows the determination of the number of clusters and yields distributional parameters for clustering base variables. There are several information criteria that help to support the selection of a particular model or clustering structure. However, a question remains concerning the selection of specific criteria that may be more suitable for particular applications. In the present work we analyze the relationship between the performance of information criteria and the type of measurement of clustering variables. In order to study this relationship we perform the analysis of forty-two data sets with known clustering structure and with clustering variables that are categorical, continuous and mixed type. We then compare eleven information-based criteria in their ability to recover the data sets’ clustering structures. As a result, we select AIC3, BIC and ICL-BIC criteria as the best candidates for model selection that refers to models with categorical, continuous and mixed type clustering variables, respectively.