Testing for genuine multimodality in finite mixture models: Application to linear regression models

Abstract

Identifiability problems can be encountered when fitting finite mixture models and their presence should be investigated by model diagnostics. In this paper we propose diagnostic tools to check for identifiability problems based on the fact that they induce multiple (global) modes in the distribution of the parameterizations of the maximum likelihood models depending on the data generating process. The parametric bootstrap is used to approximate this distribution. In order to investigate the presence of multiple (global) modes the congruence between the results of information-based methods based on asymptotic theory and those derived using the models fitted to the bootstrap samples with initalization in the solution as well as random initialization is assessed. The methods are illustrated using a finite mixture of Gaussian regression models on data from a study on spread of viral infection.