On comparing some algorithms for finding the optimal bandwidth in Geographically Weighted Regression

Abstract Geographically Weighted Regression (GWR) models are sensitive to the choice of the bandwidth, and this choice is traditionally made through the golden section search algorithm. This algorithm is applied in a function, known as Cross-Validation (CV), which quantifies the efficiency of the model, therefore looking for the optimal parameter that results in the best model. In this paper, the behavior of the CV function was studied, and it was verified that when it is not strictly convex, the golden section search algorithm converges to local minimums instead of the global one. Three algorithms have been used to find the optimal bandwidth: the lightning search algorithm, the harmony search algorithm and an adaptation of the golden section search algorithm. In addition, comparisons were made between them to check the suitability of each one in GWR models. It was found that the golden section search algorithm is not the most adequate in this situation because, in more than one simulation, it resulted in a value too far from the optimal bandwidth. It was also verified that the models with the bandwidth far from the optimal value showed differences in the significance of the parameter estimates compared to the models with the optimal bandwidth.

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