Estimation and Selection for Spatial Regression When Fixed Effects and Random Effects Are Correlated

• Activity Number: 190 - Contributed Poster Presentations: Section on Statistics and the Environment
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Chun-Shu Chen* and Hong-Ding Yang and Yung-Huei Chiou
• Companies: National Changhua University of Education and National Changhua University of Education and National Changhua University of Education
• Keywords: Conditional information criterion; Mean squared prediction error; Spatial prediction; Variable selection

Abstract

The spatial random effects model is popular in analyzing spatially referenced data. The model includes observable spatial covariates and unobservable spatial random effects, which if not deal properly with the confounding effect between the two components, parameter estimation and spatial prediction had been demonstrated to be unreliable. In this research, we focus on discussing the estimation of regression coefficients and the selection of covariates for spatial regression under the presence of spatial confounding. We first introduce an adjusted estimation method of regression coefficients and the corresponding spatial predictor when spatial confounding exists. From a prediction point of view, we then propose a generalized conditional Akaike information criterion to select a subset of covariates, resulting in variable selection and spatial prediction those are satisfactory. Statistical inferences of the proposed methodology are justified theoretically and numerically.