Finite mixture regression models are widely used to capture the heterogeneous effects of covariates on a response variable. Our study, motivated by the analysis of Chiroptera, explores the dynamic effects of various environmental, biological, and human-related covariates on the evolutionary development of bat forearm using finite Gaussian mixture regression (GMR) models. In this paper, we address two key questions: (1) which covariates are associated with the variation in forearm length; and (2) whether the associated covariates have the same effect across all subpopulations. To answer these questions, we propose two stepwise procedures within the finite GMR framework based on the weighted significance test (WEST): (1) a stepwise variable selection procedure to identify relevant influential covariates, and (2) a stepwise effect-type determination procedure to determine each relevant covariate as having either a homogeneous or heterogeneous effect across subpopulations. Based on these procedures, we introduce a stepwise model selection procedure for finite mixture regression, illustrated through finite GMR models. Simulation studies are conducted to assess the performances of our proposed procedures. The proposed procedure will be applied to the Chiroptera dataset.

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