Semiparametric spatial mixed effects single index models

Abstract

Environmental health studies are of often interest in human research to evaluate the relationship between mortality and temperature by incorporating spatial correlation and other weather variables. Since this relationship cannot be expressed by a parametric model, a nonparametric model is often used to estimate this relationship. A semiparametric integrated-spatial mixed effects single index model is proposed. It can detect subtle changes among spatial effects, covariates, and nonparametric function. This model is not only to estimate this nonparametric relationship but also to incorporate spatial effects and other weather variables. It is useful when the spatial areas are located close to each other because the nonparametric function may not be separated from spatially correlated random effects. Based on the simulation study, the semiparametric integrated-spatial mixed effects single index model provides more accurate estimates of spatial correlation and prediction. The advantage of the semiparametric integrated-spatial mixed effects single index model is further demonstrated using mortality data of six cities in South Korea from January 2000 to December 2007.