Model-based clustering from finite mixtures of generalized linear models is a challenging issue which has undergone many recent developments. In practice, the model selection step is usually performed by using AIC or BIC penalized criteria. Though, simulations show that they tend to overestimate the actual dimension of the model. These evidence led us to consider a new criterion close to ICL, firstly introduced in Baudry (2009). Its definition requires to introduce a contrast embedding an entropic term: using concentration inequalities, we derive key properties about the convergence of the associated M-estimator. The consistency of the corresponding classification criterion then follows depending on some classical requirements on the penalty term. Finally a simulation study enables to corroborate our theoretical results, and shows the effectiveness of the method in a clustering perspective.
