A two-stage estimation method with bootstrap inference for semi-parametric geographically weighted generalized linear models

ABSTRACT Semi-parametric geographically weighted generalized linear models (S-GWGLMs) are a useful tool in modeling a regression relationship where the impact of certain explanatory variables on a non-Gaussian distributed response variable is global while that of others is spatially varying. In this article, we propose for S-GWGLMs a new estimation method, called two-stage geographically weighted maximum likelihood estimation, and further develop a likelihood ratio statistic-based bootstrap test to determine constant coefficients in the models. The performance of the estimation and test methods is then evaluated by simulations. The results show that the proposed estimation method performs as well as the existing method in estimating both constant and spatially varying coefficients but it is more efficient in terms of computation time; the bootstrap test is of accurate size under the null hypothesis and satisfactory power in identifying spatially varying coefficients. A real-world data set is finally analyzed to demonstrate the application of the proposed estimation and test methods.

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