Spatial clustering based on geographically weighted multivariate generalized gamma regression

Abstract

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:

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  A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.

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  Goodness of fit test to test the spatial effects in GWMGGR model.

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  Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.