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A comparison of errors in variables methods for use in regression models with spatially misaligned data.

Kenneth K Lopiano1, Linda J Young, Carol A Gotway

  • 1Department of Statistics, University of Florida, Florida, USA. klopiano@ufl.edu

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This study addresses spatial misalignment between predictor (X) and response (Y) variables. It compares methods for accurate standard errors in regression when X is predicted, finding naive errors are too small.

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Area of Science:

  • Spatial statistics
  • Geostatistics
  • Statistical modeling

Background:

  • Spatial data often involves variables measured at different locations or scales.
  • This spatial misalignment complicates inference on variable associations.

Purpose of the Study:

  • To compare methods for calculating accurate standard errors in regression when predictor variables are spatially misaligned with response variables.
  • To evaluate these methods in both point-referenced and change-of-support settings.

Main Methods:

  • Two simulation studies were conducted to compare standard error estimation methods.
  • Methods were extended and tested for the change-of-support problem (point-to-area data).

Main Results:

  • Regression parameter estimates are unbiased when using predicted predictor values (e.g., via kriging).
  • Naive standard errors for these parameters are underestimated, leading to potentially incorrect statistical inference.

Conclusions:

  • Accurate standard error estimation is crucial for valid statistical inference in spatially misaligned data.
  • The study provides a comparison of methods for addressing this challenge in geostatistics.