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Spatial auto-correlation and auto-regressive models estimation from sample survey data.

Roberto Benedetti1, Thomas Suesse2, Federica Piersimoni3

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This study introduces a maximum marginal likelihood approach for spatial population models, enhancing estimation efficiency by incorporating both sample and population data. This method proves more precise than traditional sample-only techniques for spatial auto-regressive models.

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maximum marginal likelihoodmissing datanoninformative samplingspatial sampling

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Area of Science:

  • Spatial statistics
  • Statistical modeling
  • Survey methodology

Background:

  • Maximum likelihood estimation (MLE) is standard for spatial population models with non-informative sampling.
  • Naive MLE using only sample data can yield inconsistent estimates for certain models, like spatial auto-regressive models.
  • Existing methods often neglect spatial information from non-sampled units.

Purpose of the Study:

  • To develop and evaluate a maximum marginal likelihood (MML) approach for spatial population models.
  • To improve estimation efficiency by utilizing both sample and population data.
  • To compare the MML approach with traditional sample-only methods.

Main Methods:

  • Developed a maximum marginal likelihood (MML) framework for spatial population models.
  • Incorporated spatial information from both sampled and non-sampled units.
  • Conducted extensive simulation experiments to assess performance.

Main Results:

  • The MML approach yields more efficient and precise estimates compared to methods using only sample data.
  • Performance is influenced by spatial sampling design, auto-correlation, and sample size.
  • The MML approach effectively utilizes spatial information from the entire population.

Conclusions:

  • The maximum marginal likelihood approach offers a significant improvement in precision for spatial population modeling.
  • This method is particularly beneficial for spatial auto-regressive models where naive MLE fails.
  • Integrating population-level spatial data enhances the accuracy of statistical inference.