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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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