Local-linear likelihood estimation of geographically weighted generalised linear models

Abstract

Geographically weighted generalised linear models are an extension of the geographically weighted regression models in order to handle such types of the response variables that their distributions follow a member of the exponential family of distributions. In view of the advantages of the local-linear fitting technique, we propose in this paper a local-linear likelihood estimation approach for geographically weighted generalised linear models to improve the accuracy of the coefficient estimators. A Fisher scoring algorithm is formulated to compute the estimators of the coefficients. Simulations are conducted for some typical geographically weighted generalised linear models to evaluate the performance of the proposed estimation method and the results show that, compared to the existing local-constant likelihood estimation, the local-linear likelihood method can evidently improve the accuracy of the coefficient estimators. A real-world data-set is finally analysed to demonstrate the application of the proposed approach.

Keywords:

• geographically weighted generalised linear model
• exponential family of distributions
• local-linear likelihood estimation
• spatial non-stationarity
• Fisher scoring algorithm

Acknowledgements

The authors would like to thank the three reviewers and the editor for their valuable comments and suggestions. Especially, the editor’s insightful suggestion has largely simplified the algorithm in the paper.