Properties of the beta regression model for small area estimation of proportions and application to estimation of poverty rates

References

• Bauder, M., D. Luery, and S. Szelepka. 2015. Small area estimation of health insurance coverage in 2010–2013. Technical report, U. S. Census Bureau. https://www.census.gov/did/www/sahie/methods/files/sahie_tech_2010_to_2013.pdf.
   Google Scholar
• Bonat, W. H., P. J. Ribeiro, Jr., and W. M. Zeviani. 2015. Likelihood analysis for a class of beta mixed models. Journal of Applied Statistics 42(2):252–66. doi:10.1080/02664763.2014.947248.
   Web of Science ®Google Scholar
• Cepeda-Cuervo, E., J. A. Achcar, and L. G. Lopera. 2014. Bivariate beta regression models: joint modeling of the mean, dispersion and association parameters. Journal of Applied Statistics 41 (3):677–87. doi:10.1080/02664763.2013.847071.
   Web of Science ®Google Scholar
• Datta, G. S., P. Lahiri, T. Maiti, and K. L. Lu. 1999. Hierarchical Bayes estimation of unemployment rates for the states of the U. S. Journal of the American Statistical Association 94 (448):1074–82. doi:10.1080/01621459.1999.10473860.
   Web of Science ®Google Scholar
• Dragomir, S. S., R. P. Agarwal, and N. S. Barnett. 2000. Inequalities for the beta and gamma functions via some classical and new integral inequalities. Journal of Inequalities and Applications 5 :103–65.
   Web of Science ®Google Scholar
• Espinheira, P. L., S. L. P. Ferrari, and F. Cribari-Neto. 2008. On beta regression residuals. Journal of Applied Statistics 35 (4):407–19. doi:10.1080/02664760701834931.
   Web of Science ®Google Scholar
• Fabrizi, E., M. R. Ferrante, S. Pacei, and C. Trivisano. 2011. Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains. Computational Statistics & Data Analysis 55(4):1736–47. doi:10.1016/j.csda.2010.11.001.
   Web of Science ®Google Scholar
• Fabrizi, E., and C. Trivisano. 2016. Small area estimation of the Gini concentration coefficient. Computational Statistics & Data Analysis 99 :223–34. doi:10.1016/j.csda.2016.01.010.
   Web of Science ®Google Scholar
• Fay, R. E., and R. A. Herriot. 1979. Estimation of income from small places: an application of James-Stein procedures to census data. Journal of the American Statistical Association 74(366a):269–77. doi:10.1080/01621459.1979.10482505.
   Web of Science ®Google Scholar
• Ferrari, S. L. P., and F. Cribari-Neto. 2004. Beta regression for modelling rates and proportions. Journal of Applied Statistics 31 (7):799–815. doi:10.1080/0266476042000214501.
   Web of Science ®Google Scholar
• Figueroa-Zúñiga, J. I., R. B. Arellano-Valle, and S. L. P. Ferrari. 2013. Mixed beta regression: A bayesian perspective. Computational Statistics & Data Analysis 61 :137–47.
   Web of Science ®Google Scholar
• Grenié, L., and G. Molteni. 2015. Inequalities for the beta function. Mathematical Inequalities & Applications 18 (4):1427–42. doi:10.7153/mia-18-111.
   Web of Science ®Google Scholar
• Kalton, G., J. M. Brick, and T. Le. 2005. Estimating components of design effects for use in sample design. In Household surveys in developing and transition countries, 95–121. New York: United Nations Publications.
   Google Scholar
• Kieschnick, R., and B. D. McCullough. 2003. Regression analysis of variates observed on (0,1): percentages, proportions and fractions. Statistical Modelling 3 :193–213. doi:10.1191/1471082X03st053oa.
   Web of Science ®Google Scholar
• Kish, L. 1992. Weighting for unequal pi. Journal of Official Statistics 8 (2):183–200.
   Google Scholar
• Kish, L., and M. R. Frankel. 1974. Inference from complex samples. Journal of the Royal Statistical Society. Series B 36 :1–37. doi:10.1111/j.2517-6161.1974.tb00981.x.
   Google Scholar
• Lagos-Álvarez, B. M., R. Fustos-Toribio, J. Figueroa-Zúñiga, and J. Mateu. 2017. Geostatistical mixed beta regression: a Bayesian approach. Stochastic Environmental Research and Risk Assessment 31(2):571–84. doi:10.1007/s00477-016-1308-5.
   Web of Science ®Google Scholar
• Li, X., and C.-P. Chen. 2007. Inequalities for the gamma function. Journal of Inequalities in Pure and Applied Mathematics 8 (electronic).
   Google Scholar
• Liu, B., P. Lahiri, and G. Kalton. 2014. Hierarchical Bayes modeling of survey-weighted small area proportions. Survey Methodology 40 (1):1–13.
   Web of Science ®Google Scholar
• Luery, D. M. 2010. Small area income and poverty estimates program. Technical report, U. S. Census Bureau. Available at https://www.census.gov/did/www/saipe/publications/files/luery.pdf.
   Google Scholar
• Plummer, M. 2016. rjags: Bayesian graphical models using MCMC. R package version 4-6.
   Google Scholar
• R Core Team 2013. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Wieczorek, J., and S. Hawala. 2011. A Bayesian zero-one inflated Beta model for estimating poverty in U. S. counties. Technical report, U. S. Census Bureau. https://www.census.gov/did/www/saipe/publications/files/wieczorekhawalajsm2011.pdf.
   Google Scholar
• You, Y., and J. N. K. Rao. 2002. Small area estimation using unmatched sampling and linking models. Canadian Journal of Statistics 30(1):3–15. doi:10.2307/3315862.
   Web of Science ®Google Scholar