Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models

In this paper, we introduce two semiparametric single-index models for spatially and temporally correlated data. Our first model has spatially and temporally correlated random effects that are additive to the nonparametric function, which we refer to as the “semiparametric spatio-temporal single-index model (ST-SIM)”. The second model integrates the spatially correlated effects into the nonparametric function, and the time random effects are additive to the single-index function. We refer to our second model as the “semiparametric integrated spatio-temporal single-index model (IST-SIM)”. Two algorithms based on a Markov chain expectation maximization are introduced to simultaneously estimate the model parameters, spatial effects, and time effects of the two models. We compare the performance of our models using several simulation studies. The proposed models are then applied to mortality data from six major cities in South Korea. Our results suggest that IST-SIM (1) is more flexible than ST-SIM because the former can estimate various nonparametric functions for different locations, while ST-SIM enforces the mortality functions having the same shape over locations; (2) provides better estimation and prediction, and (3) does not need restrictions for the single-index coefficients to fix the identifiability problem.