Comparison of bandwidth selection in application of geographically weighted regression: a case study

A forest plot with a clustered spatial pattern of tree locations was used to investigate the impacts of different kernel functions (fixed vs. adaptive) and different sizes of bandwidth on model fitting, model performance, and spatial characteristics of the geographically weighted regression (GWR) coefficient estimates and model residuals. Our results indicated that (i) the GWR models with smaller bandwidths fit the data better, yielded smaller model residuals across tree sizes, significantly reduced spatial autocorrelation and heterogeneity for model residuals, and generated better spatial patterns for model residuals; however, smaller bandwidth sizes produced a high level of coefficient variability; (ii) the GWR models based on the fixed spatial kernel function produced smoother spatial distributions for the model coefficients than those based on the adaptive kernel function; and (iii) the GWR cross-validation or Akaike's information criterion (AIC) optimization process may not produce an "optimal'' bandwidth for model fitting and performance. It was evident that the selection of spatial kernel function and bandwidth has a strong impact on the descriptive and predictive power of GWR models.