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This summary is machine-generated.

This study introduces new tools for analyzing linear mixed models with Gaussian processes (GPs). These methods enhance understanding of how data influences estimates and assess covariate effects on GP and error components.

Keywords:
Added variable plotGaussian processLack of fitLinear mixed modelMissing predictorSpectral approximation

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Geostatistics

Background:

  • Gaussian processes (GPs) are integral to linear mixed models (LMMs).
  • Current fitting methods include restricted likelihood and Bayesian analysis.
  • Understanding data's influence on GP estimates is crucial.

Purpose of the Study:

  • Develop tools to understand data's role in GP-based LMM estimates.
  • Propose methods to assess covariate support and impact on model components.
  • Adapt techniques for both regular and irregular spatial data.

Main Methods:

  • Spectral basis approximation of GPs for LMMs.
  • Equating restricted likelihood to a gamma-errors GLM likelihood.
  • Application of Added Variable Plots (AVPs) in spectral and observation domains.

Main Results:

  • Spectral approximation simplifies GP analysis and links to GLMs.
  • AVPs in different domains reveal covariate effects on GP and error terms.
  • Methods are adaptable to irregular data via smoothing.

Conclusions:

  • The proposed spectral approximation and AVPs offer novel insights into GP-based LMMs.
  • These tools improve the understanding of covariate influence on model components.
  • The methodology is practical for analyzing spatial data, including forest biomass data.