Jessica Rothman, Emory University
Authors: Jessica E. Rothman, Monica C. Jackson, Kimberly F. Sellers, Talithia Williams, Subhash R. Lele, and Lance A. Waller
2023 AWM Research Symposium
Meet Researchers Behind the Real-Life Examples of Elementary Statistics: A Guide to Data Analysis Using R [Organized by Nancy Griesinger]

Residual spatial correlation in linear regression 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 nonunique decomposition of mixed models into mixed 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. Through the use of semivariograms of the residuals, we found that in comparing reduced models to the full postulated model, the semivariance is higher in the reduced models and decreases as the model is more accurately specified. Essentially, larger semivariance is found when misspecification of the model is present. 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.

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