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This study introduces a robust Bayesian spatial robit model for binomial data, offering improved predictions against extreme values. An empirical Bayes approach enhances estimation and prediction accuracy compared to full Bayesian methods.

Keywords:
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Area of Science:

  • Statistics
  • Spatial Analysis
  • Biostatistics

Background:

  • Spatial generalized linear mixed models (SGLMMs) are widely used for non-Gaussian spatial data.
  • Binomial SGLMMs commonly employ logit or probit links, but are sensitive to extreme observations.
  • Robit regression offers a robust alternative for independent binomial data.

Purpose of the Study:

  • Introduce a Bayesian spatial robit model for spatially dependent binomial data.
  • Develop an empirical Bayes (EB) approach for parameter estimation and random effect prediction in SGLMMs.
  • Address challenges in prior specification for link function and spatial correlation parameters.

Main Methods:

  • Developed a Bayesian spatial robit model for binomial SGLMMs.
  • Implemented an empirical Bayes (EB) methodology using importance sampling and Markov chain Monte Carlo (MCMC).
  • Applied the methodology to invasive species distribution and root disease severity data.

Main Results:

  • The robit model demonstrated robustness against model misspecification in simulations.
  • The EB method yielded less biased estimates than full Bayesian analysis.
  • The model improved prediction for invasive species distribution with outlying data.
  • Performance was comparable to classical models for root disease severity prediction.

Conclusions:

  • The Bayesian spatial robit model with EB estimation is a robust and effective tool for spatial binomial data.
  • The EB methodology is generalizable to other SGLMM types (e.g., Poisson, Gamma).
  • The geoBayes R package provides implementations for various SGLMMs.