Efficient estimation and prediction for the Bayesian binary spatial model with flexible link functions

Biometrics
Vivekananda RoyZhengyuan Zhu

Abstract

Spatial generalized linear mixed models (SGLMMs) are popular models for spatial data with a non-Gaussian response. Binomial SGLMMs with logit or probit link functions are often used to model spatially dependent binomial random variables. It is known that for independent binomial data, the robit regression model provides a more robust (against extreme observations) alternative to the more popular logistic and probit models. In this article, we introduce a Bayesian spatial robit model for spatially dependent binomial data. Since constructing a meaningful prior on the link function parameter as well as the spatial correlation parameters in SGLMMs is difficult, we propose an empirical Bayes (EB) approach for the estimation of these parameters as well as for the prediction of the random effects. The EB methodology is implemented by efficient importance sampling methods based on Markov chain Monte Carlo (MCMC) algorithms. Our simulation study shows that the robit model is robust against model misspecification, and our EB method results in estimates with less bias than full Bayesian (FB) analysis. The methodology is applied to a Celastrus Orbiculatus data, and a Rhizoctonia root data. For the former, which is known to contain outlying...Continue Reading

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