Additive models with spatio-temporal data

Additive models (AMs) have been widely used in environmental, biological, and ecological studies. While the procedure for fitting an AM to independent data has been well established, the currently available methods for fitting AMs with correlated data are not completely satisfactory in practice. We propose a new approach based on penalized likelihood method to fit AMs for spatio-temporal data. Both maximum likelihood and restricted maximum likelihood estimation schemes are developed. Conditions for asymptotic posterior normality are investigated for the case with fixed spatial correlation structure and no temporal dependence. We also propose a new model selection criterion for comparing AMs with and without spatial correlation. The proposed methods are illustrated by both simulation study and real data analysis on the abundance distribution of Alaska plaice in eastern Bering Sea.