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The aim of this paper is to propose a generalised framework for semiparametric geographically weighted regression (S-GWR) by combining several theoretical aspects of geographically weighted regression (GWR). In this framework, we can implement model selection in order to judge which explanatory effects on the response variable are globally fixed or geographically varying in generalised linear modelling (GLM). This framework is implemented in a new version of the GWR software (GWR 4.0) which is soon to be released and which will be described.

To date, numerous theoretical and applied studies of GWR have been reported after the first seminal papers of GWR appeared (Fotheringham et al., 1996; Brunsdon et al, 1996). Here, we focus on two important extensions of GWR; geographically weighted generalised linear modelling (GWGLM) and semiparametric extension of GWR. While the original GWR assumes that the response is a continuous variable and the error term follows a Gaussian (normal) distribution, GWGLM enables us to fit generalised linear models with geographically local coefficients to accommodate commonly encountered types of response including count and binomial variables with likelihood functions of non-normal errors.