Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso. - Wheeler, David C. (Environment & Planning A, 2009)
A penalized form of geographically weighted regression (GWR), called the “geographically weighted lasso” (GWL), is presented. The GWL limits the magnitude of the estimated regression coefficients to constrain the impact of explanatory-variable correlation. It also conducts local model selection by potentially reducing some of the estimated regression coefficients to zero in some locations of the study area. Two types of GWL are introduced: one designed to enhance prediction of the response variable, and one more geared toward limiting regression coefficients for inference. The application of the GWL to simulated and real datasets demonstrates how it stabilizes regression coefficients in the presence of collinearity. The GWL also yields lower prediction and estimation error of the response variable than does GWR and another constrained version of GWR called geographically weighted ridge regression.