Abstract:
|
In many application areas, data are collected on a count or binary response with spatial covariate information. In this talk, we introduce a class of generalized additive models (GAMs) for spatial data distributed over complex domains. Through a link function, the GAM assumes that the mean of the response variable depends on additive univariate functions of explanatory variables and a bivariate function to adjust for geographic location. We propose a two-step approach for estimation and simultaneous inference of the components in the GAM. In the first step, the univariate and bivariate components in the model are approximated using univariate polynomial splines and bivariate penalized splines over triangulation, respectively. In the second step, local polynomial smoothing is then applied to the data, which enables us to construct simultaneous confidence bands and make inferences about the component functions. The performance of the method is evaluated by simulation studies. We apply the proposed method to the crash counts data in the Tampa Bay Area in Florida.
|