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Spatial Generalized Linear Models with Non-Gaussian Translation Processes

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  • Robert Richardson

    (Brigham Young University)

Abstract

It is not generally feasible to pick any given marginal distribution and assume there will be a way to apply a link function to add fixed and random effects in a spatial generalized linear model. We introduce an adjustment to spatial copula processes called a non-Gaussian translation process that will allow for the specification of any marginal distribution with a closed-form density function in a single unified framework. While translation processes do not preserve the exact marginal structure, they allow for fixed effects to be included in a non-Gaussian spatial model without needing to define a link function, as well as providing a number of other computational and modeling benefits. Non-Gaussian translation processes are compared theoretically and via simulation with traditional link function approaches and spatial copula processes and are shown to perform similarly in cases where all three models can effectively be used. A daily precipitation data set is analyzed with elevation as a predictor variable that includes a majority of observations being 0. Out-of-sample predictions are evaluated, and it is determined that the model is effective when compared to a two-stage prediction model and a Bayesian power truncated normal model.

Suggested Citation

  • Robert Richardson, 2022. "Spatial Generalized Linear Models with Non-Gaussian Translation Processes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 4-21, March.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:1:d:10.1007_s13253-021-00458-y
    DOI: 10.1007/s13253-021-00458-y
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    References listed on IDEAS

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    1. Hao Zhang, 2002. "On Estimation and Prediction for Spatial Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(1), pages 129-136, March.
    2. Bruno Sansó & Lelys Guenni, 1999. "Venezuelan Rainfall Data Analysed by Using a Bayesian Space–time Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 345-362.
    3. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
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