Generalized Additive Models with Spatio-temporal Data

Generalized additive models (GAMs) have been widely used. While the procedure for fitting a generalized additive model to independent data has been well established, not as much work has been done when the data are correlated. The currently available methods are not completely satisfactory in practice. A new approach is proposed to fit generalized additive models with spatio-temporal data via the penalized likelihood approach which estimates the smooth functions and covariance parameters by iteratively maximizing the penalized log likelihood. Both maximum likelihood (ML) and restricted maximum likelihood (REML) estimation schemes are developed. Also, conditions for asymptotic posterior normality are investigated for the case of separable spatio-temporal data with fixed spatial covariate structure and no temporal dependence. We propose a new model selection criterion for comparing models with and without spatial correlation. The proposed methods are illustrated by both simulation study and real data analysis.