Tests of covariate effects under finite Gaussian mixture regression models

Mixture of regression model is widely used to cluster subjects from a suspected heterogeneous population due to differential relationships between response and covariates over unobserved subpopulations. In such applications, statistical evidence pertaining to the significance of a hypothesis is important yet missing to substantiate the findings. In this case, one may wish to test hypotheses regarding the effect of a covariate such as its overall significance. If confirmed, a further test of whether its effects are different in different subpopulations might be performed. This paper is motivated by the analysis of Chiroptera dataset, in which, we are interested in knowing how forearm length development of bat species is influenced by precipitation within their habitats and living regions using finite Gaussian mixture regression (GMR) model. Since precipitation may have different effects on the evolutionary development of the forearm across the underlying subpopulations among bat species worldwide, we propose several testing procedures for hypotheses regarding the effect of precipitation on forearm length under finite GMR models. In addition to the real analysis of Chiroptera data, through simulation studies, we examine the performances of these testing procedures on their type I error rate, power, and consequently, the accuracy of clustering analysis.