Spatial design and strength of spatial signal: Effects on covariance estimation

Journal of Agricultural, Biological, and Environmental Statistics
By: , and 

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Abstract

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Spatial design and strength of spatial signal: Effects on covariance estimation
Series title Journal of Agricultural, Biological, and Environmental Statistics
DOI 10.1198/108571107X249799
Volume 12
Issue 4
Year Published 2007
Language English
Publisher Springer
Contributing office(s) Northern Rocky Mountain Science Center
Description 20 p.
First page 450
Last page 469
Online Only (Y/N) N
Additional Online Files (Y/N) N