Correlation induced by missing spatial covariates: a connection between variance components models and kriging

Jessica Rothman¹, Monica C. Jackson², Kimberly F. Sellers³, Talithia Williams⁴, Subhash R. Lele⁵, and Lance A. Waller⁶

1. Department of Biostatistics, Yale University, New Haven, CT 06510.
2. Department of Mathematics and Statistics, American University, Washington, DC 20016. Corresponding author: monica@american.edu.
3. Department of Mathematics and Statistics, Georgetown University, Washington, DC 20057.
4. Department of Mathematics, Harvey Mudd College, Claremont, CA 91711.
5. Department of Mathematical and Statistical Sciences, University of Alberta, University of Alberta Edmonton, AB, Canada.
6. Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA 30322.

Abstract: Residual spatial correlation in linear models of environmental data is often attributed to spatial patterns in related covariates omitted from the fitted model. We connect the nonunique decomposition of error in geostatistical models into trend and covariance components to the similarly non-unique decomposition of mixed models into fixed and random effects. We specify spatial correlation induced by missing spatial covariates as a function of the strength of association and (spatial) covariation of the missing covariates. The connection with variance components models provides insight into estimation procedures. We showed how missing covariates in spatial linear models actually induces spatial autocorrelation in the covariates. This finding was confirmed through the use of simulated data and the Binary Steve dataset.

Keywords: geostatistics, spatial regression, variable selection, semi-variogram, spatial auto-correlation.

Pages: 333 – 344 | Full PDF Paper