Regression with spatially misaligned data

L. Madsen, D. Ruppert, N. S. Altman

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We present a simple approach to the problem of estimating the regression slope parameter from spatially misaligned point data. We assume a linear regression model with errors and covariates from two independent Gaussian spatial processes where covariate and response are observed at different locations. Correlation in the covariate is exploited to predict unobserved covariates via kriging. Kriged values are used to find weighted least squares estimates of regression parameters in a 'krige-and-regress' (KR) procedure. The variance of this estimator is calculated, and a variance estimator is proposed. Because the model and assumptions make it possible to write down the joint likelihood of the data, a maximum likelihood (ML) estimator can be found. Under regularity conditions, this estimator is asymptotically normal with asymptotic variance given by the inverse information matrix, which yields a variance estimator for the ML estimator of the regression parameters. The KR and ML estimators are compared in an example using Environmental Protection Agency data and a simulation study is conducted. While the ML estimator of the slope parameter has a smaller variance than the KR estimator, the ML variance estimator is too small to be used for inference whereas the KR variance estimator gives approximately correct inference.

Original languageEnglish (US)
Pages (from-to)453-467
Number of pages15
JournalEnvironmetrics
Volume19
Issue number5
DOIs
StatePublished - Aug 1 2008

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Maximum Likelihood Estimator
Variance Estimator
Maximum likelihood
Regression
Covariates
Estimator
Slope
Weighted Estimates
kriging
Spatial Process
Least Squares Estimate
Information Matrix
Inverse matrix
Weighted Least Squares
Kriging
Environmental Protection Agency
Asymptotic Variance
Linear Regression Model
Regularity Conditions
Gaussian Process

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Ecological Modeling

Cite this

Madsen, L., Ruppert, D., & Altman, N. S. (2008). Regression with spatially misaligned data. Environmetrics, 19(5), 453-467. https://doi.org/10.1002/env.888
Madsen, L. ; Ruppert, D. ; Altman, N. S. / Regression with spatially misaligned data. In: Environmetrics. 2008 ; Vol. 19, No. 5. pp. 453-467.
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Madsen, L, Ruppert, D & Altman, NS 2008, 'Regression with spatially misaligned data', Environmetrics, vol. 19, no. 5, pp. 453-467. https://doi.org/10.1002/env.888

Regression with spatially misaligned data. / Madsen, L.; Ruppert, D.; Altman, N. S.

In: Environmetrics, Vol. 19, No. 5, 01.08.2008, p. 453-467.

Research output: Contribution to journalArticle

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Madsen L, Ruppert D, Altman NS. Regression with spatially misaligned data. Environmetrics. 2008 Aug 1;19(5):453-467. https://doi.org/10.1002/env.888