Geographically weighted Poisson regression models with different kernels: application to road traffic accident data

Geographically weighted Poisson regression models (GWPR) are the class of spatial count regression models that capture the localisation effect on various influencing factors on the dependent variable. The main challenge with the GWPR models is to set appropriate kernel function to give weights for each neighbouring point during the model calibration. In this paper, we consider GWPR models for many different kernel functions, including box-car, bi-square, tri-cube, exponential and Gaussian function. Likelihood function, parameter estimation and model selection criteria have been shown in details. We applied the model formulation to the road traffic accident data in Oman as the country is one of the largest road traffic accident-prone countries in the Gulf region. Akaike information criterion (AIC), corrected Akaike information criterion (AICc) and geographically weighted deviance (GWD) have been used to assess the model fitting. The model with the exponential kernel weighted function provides the best fit for the data and captures the spatial heterogeneity and factors better with the exponential kernel weighting function.