Augmented mixed beta regression models with skew-normal independent distributions: Bayesian analysis of labor force data

References

• Andrews, D. R., and C. L. Mallows. 1974. Scale mixtures of normal distributions. Journal of the Royal Statistical Society, Series B 36:99–102.
   Google Scholar
• Arellano-Valle, R. B., H. Bolfarine, and V. H. Lachos. 2005. Skew-normal linear mixed models. Journal of Data Science 3:415–38.
   Google Scholar
• Arellano-Valle, B., H. Bolfarine, and V. H. Lachos. 2007. Bayesian inference for skew-normal linear mixed models. Journal of Applied Statistics 34 (6):663–82.
   Web of Science ®Google Scholar
• Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12:171–78.
   Web of Science ®Google Scholar
• Azzalini, A. 2014. The skew-normal and related families. Cambridge: Cambridge University Press.
   Google Scholar
• Azzalini, A., and A. Capitanio. 1996. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Statistical Society, Series B 65: 367–89.
   Google Scholar
• Azzalini, A., and A. Dalla Valle. 1996. The multivariate skew-normal distribution. Biometrika 83:715–26.
   Web of Science ®Google Scholar
• Azzalini, A., and M. G. Genton. 2008. Robust likelihood methods based on the skew-t and related distributions. International Statistical Review 76 (1):106–29.
   Web of Science ®Google Scholar
• Baghfalaki, T., M. Ganjali, and D. Berridge. 2014. Joint modeling of multivariate longitudinal mixed measurements and time to event data using a Bayesian approach. Journal of Applied Statistics 41 (9):1934–55.
   Web of Science ®Google Scholar
• Branscum, A. J., W. O. Johnson, and M. Thurmond. 2007. Bayesian beta regression: Applications to houshold expenditure data and genetic distance between food and mouth dieseas viruses. Australian and New Zealand Journal of Statistics 49 (3):287–301.
   Web of Science ®Google Scholar
• Carlin, B. P., and T. A. Louis. 2008. Bayesian methods fordata analysis. Texas: Chapman & Hall/CRC Press..
   Google Scholar
• Cribari-Neto, F., and A. Zeileis. 2010. Beta regression in R. Journal of Statistical Software 34 (2):1–24.
   Web of Science ®Google Scholar
• Ferrari, S., and F. Cribari-Neto. 2004. Beta regression for modelling rates and proportions. Journal of Applied Statistics 31 (7):799–815.
   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 and Data Analysis 61:137–47.
   Web of Science ®Google Scholar
• Galvis, D. M., D. Bandyopadhyay, and V. H. Lachos. 2014. Augmented mixed beta regression models for periodontal proportion data. Statistics in medicine 33 (21):3759–71.
   PubMed Web of Science ®Google Scholar
• Gelfand, A. E., and D. K. Dey. 1994. Bayesian model choice: Asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B (Methodological) 56 (3):501–14.
   Google Scholar
• Gelfand, A. E., D. K. Dey, and H. Chang. 1992. Model determination using predictive distributions with implementation via sampling-based methods. Report No. 462, STANFORD UNIV CA DEPT OF STATISTICS 147–67.
   Google Scholar
• Gelman, A., and D. B. Rubin. 1992. Inference from iterative simulation using multiple sequences. Statistical science 457–511.
   Google Scholar
• Ghidey, W., E. Lesaffre, and P. Eilers. 2004. Smooth random effects distribution in a linear mixed model. Biometrics 60 (4):945–53.
   PubMed Web of Science ®Google Scholar
• Gupta, A. K. 2004. Multivariate skew t-distribution. Statistics: A Journal of Theoretical and Applied Statistics 37 (4):359–63.
   Google Scholar
• Hall, D. B., and K. S. Berenhaut. 2002. Score tests for heterogeneity and over dispersion in zero-inflated Poisson and binomial regression models. Canadian Journal of Statistics 30 (3):415–30.
   Web of Science ®Google Scholar
• ILO. 1998. Guidelines concerning dissemination practices for labour statistics. Sixteenth International Conference of Labour Statisticians Geneva.
   Google Scholar
• Kieschnick, R., and B. D. McCullough. 2003. Regression analysis of variates observed on (0,1): Percentages, proportions and fractions. Statistical modelling 3 (3):193–213.
   Web of Science ®Google Scholar
• Lachenbruch, P. A. 2002. Analysis of data with excess zeros. Statistical methods in medical research 11 (4):297–302.
   PubMed Web of Science ®Google Scholar
• Lachos, V. H., D. K. Dey, and V. G. Cancho. 2009. Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective. Journal of Statistical Planning and Inference 139 (12):4098–110.
   Web of Science ®Google Scholar
• Lange, K., and J. S. Sinsheimer. 1993. Normal/independent distributions and their applications in robust regression. Journal of Computational and Graphical Statistics 2 (2):175–98.
   Google Scholar
• Li, N., R. M. Elashoff, and G. Li. 2010. Robust joint modeling of longitudinal measurements and competing risks failure time data. Biometrical Journal 51 (1):19–30.
   Web of Science ®Google Scholar
• Lin, T. I., J. C. Lee, and W. J. Hsieh. 2007. Robust mixture modeling using the skew t distribution. Statistics and Computing 17 (2):81–92.
   Web of Science ®Google Scholar
• Liu, C. 1996. Bayesian robust multivariate linear regression with incomplete data. Journal of the American Statistical Association 91 (435):1219–27.
   Web of Science ®Google Scholar
• Ospina, R., and S. L. Ferrari. 2010. Inflated beta distributions. Statistical Papers 51 (1):111–26.
   Web of Science ®Google Scholar
• Ospina, R., and S. L. Ferrari. 2012. A general class of zero-or-one inflated beta regression models. Computational Statistics & Data Analysis 56 (6):1609–23.
   Web of Science ®Google Scholar
• Paolino, P. 2001. Maximum likelihood estimation of models with beta-distributed dependent variables. Political Analysis 9 (4):325–46.
   Google Scholar
• Rosa, G. J., C. R. Padovani, and D. Gianola. 2003. Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation. Biometrical Journal 45 (5):573–90.
   Web of Science ®Google Scholar
• Smithson, M., and J. Verkuilen. 2006. A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological methods 11 (1):54.
   PubMed Web of Science ®Google Scholar
• Verbeke, G., and E. Lesaffre. 1997. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Computational Statistics & Data Analysis 23 (4):541–56.
   Web of Science ®Google Scholar
• Verkuilen, J., and M. Smithson. 2012. Mixed and mixture regression models for continuous bounded responses using the beta distribution. Journal of Educational and Behavioral Statistics 37 (1):82–113.
   Web of Science ®Google Scholar
• Wang, J., and M. G. Genton. 2006. The multivariate skew-slash distribution. Journal of Statistical Planning and Inference 136 (1):209–20.
   Web of Science ®Google Scholar
• Zhang, D., and M. Davidian. 2001. Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics 57 (3):795–802.
   PubMed Web of Science ®Google Scholar