Mixture of generalized linear models: identifiability and applications.

We consider finite mixtures of generalized linear models with binary output. We prove that cross moments till order 3 are sufficient to identify all parameters of the model. We propose a least squares estimation method and we prove the consistency and the Gaussian asymptotic behavior of the estimator. An R-package is developed to apply our method, we give numerical experiments to compare with likelihood methods. We then provide new identifiability results for several finite mixtures of generalized linear models with binary output and unknown link function including both continuous and categorical covariates, and possibly longitudinal data.