On the use of the generalized linear exponential cluster-weighted model to asses local linear independence in bivariate data

The generalized linear exponential cluster-weighted model is a recentmixturebased approach which allows for flexible clustering and distribution estimation of a bivariate random vector composed by a response and by a covariate, regardless from the support of these variables. Examples concern a count response and a covariate taking values on the positive real line. With respect to the exponential-exponential latent class model, which is based on the assumption of local independence, the present approach assumes that, in each mixture component, there is a (generalized) linear dependence of the response given the covariate. Since the two models can be considered as nested, in this paper the BIC will be adopted to select the best assumption for data at hand. The procedure is illustrated through an application to real data from a survey on fair-trade coffee consumers interviewed at stores.