Model selection with misspecified spatial covariance structure

Abstract

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square (${\overline{R}}_{\alpha }^2$), and overall RIC performs well.

Keywords:

• spatial data analysis
• information criterion
• correlation function
• variance function
• mean function

Acknowledgements

We wish to thank the review team for their detailed comments and suggestions that have led to significant improvement of our work.

Funding

The research was partially supported by [PCSIRT, NECT-11-0616], [NSFC 11171058], and the Australian Research Council Discovery Project [DP130100766].