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Geostatistical mixed beta regression: a Bayesian approach

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Abstract

This paper develops regression techniques for geostatistical data, with an emphasis in proportions measured on a continuous scale. Specifically, it deals with Beta regression models with mixed effects to control the spatial variability from a Bayesian approach. We use a suitable parametrization of the Beta distribution in terms of its mean and the precision parameter, allowing for both parameters to be modeled through regression structures that may involve fixed and random effects. Specification of prior distributions is discussed, computational implementation via Gibbs sampling is provided, and the methodology is illustrated using simulated and real data.

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Acknowledgments

The authors would like to acknowledge the following partial financial support. The first author thanks the VRID grant 216.014.026-1.0, from University of Concepción. The second author thanks the Fondecyt grant 11130483, and the third author the Advanced Mining Technology Center, University of Chile and CSIRO-Chile for having provided the facilities and equipment in which the data were simulated. Finally, the fourth author thanks the grants MTM2013-43917-P from the Spanish Ministry of Science and Education, and P1-1B2015-40.

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Authors and Affiliations

  1. Department of Statistics, University of Concepción, Concepción, Chile

    Bernardo M. Lagos-Álvarez & Jorge Figueroa-Zúñiga

  2. Department of Mining Engineering, University of Chile, Santiago, Chile

    Roberto Fustos-Toribio

  3. Advanced Mining Technology Center, University of Chile, Santiago, Chile

    Roberto Fustos-Toribio

  4. CSIRO-Chile International Center of Excellence in Mining and Mineral Processing, Santiago, Chile

    Roberto Fustos-Toribio

  5. Department of Mathematics, Universitat Jaume I, Castellón de la Plana, Spain

    Jorge Mateu

Authors
  1. Bernardo M. Lagos-Álvarez
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  2. Roberto Fustos-Toribio
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  3. Jorge Figueroa-Zúñiga
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  4. Jorge Mateu
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Corresponding author

Correspondence to Bernardo M. Lagos-Álvarez.

Appendix

Appendix

R-code used with the library compositions of the R software for the compositional analysis.

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Lagos-Álvarez, B.M., Fustos-Toribio, R., Figueroa-Zúñiga, J. et al. Geostatistical mixed beta regression: a Bayesian approach. Stoch Environ Res Risk Assess 31, 571–584 (2017). https://doi.org/10.1007/s00477-016-1308-5

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  • DOI: https://doi.org/10.1007/s00477-016-1308-5

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