  Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling
the joint probability of data coming from a heterogeneous population as a
weighted sum of the products of marginal distributions and conditional
distributions. In this paper, we introduce a wide family of Cluster Weighted
models in which the conditional distributions are assumed to belong to the
exponential family with canonical links which will be referred to as
Generalized Linear Gaussian Cluster Weighted Models. Moreover, we show that, in
a suitable sense, mixtures of generalized linear models can be considered as
nested in Generalized Linear Gaussian Cluster Weighted Models. The proposal is
illustrated through many numerical studies based on both simulated and real
data sets.
