Criteria for model selection in model-based clustering
Model-based clustering, or finite mixture models, are important classification methods, and wide range of theoretical and applied researches have been made. One of the most useful advantages of these methods are the applicability of model selection criteria for choosing the number of clusters, selecting variables, selecting structure of model parameters and so on. One might use some basic information criteria, e.g., AIC or BIC. However, regularity conditions for deriving these criteria do not hold in finite mixture -- these are called models -- and these criteria do not have theoretical justification at all. In this study, we compare the performance of WAIC and WBIC, information criteria applicable for singular models, with the basic criteria numerically in some problem of the model-based clustering.