In this paper, Professors Prasad Naik and Chih-Ling Tsai, with co-author Peide Shi from Nuclear Safety Solutions Ltd., examine the problem of jointly selecting the number of components and variables in finite mixture regression models.

The authors find that the Akaike information criterion is unsatisfactory for this purpose because it overestimates the number of components, which in turn results in incorrect variables being retained in the model. Therefore, they derive a new information criterion, the mixture regression criterion (MRC), that yields marked improvement in model selection due to what they call the “clustering penalty function.”