Augmented Mixed Beta Regression and Modeling of Employed Proportions in Households

Document Type : Original Paper

Authors

1 Department of Statistics, Tarbiat Modares University

2 Department of Statistics, Tarbiat Modares University, Tehran, Iran

Abstract

The Beta regression model is usually used for modeling the rates or proportions confined in an open interval (0,1). In some studies, the data may also include zero and one. In this paper, an augmented Beta regression model that is a mixture of Beta distribution with two degenerated distributions at 0 and 1 is presented for rates or proportions confined in [0,1]. For the augmented mixed Beta model with reparametrization of Beta distribution, the mean and precision parameters were modeled including fixed and random effects. This is while taking into account that the random effects make these models applicable to correlated data. Here, the augmented mixed Beta model is presented. Then this model is evaluated in a simulation study. Next, the application of this model is shown for analyzing the proportions of employed persons in every household. Finally, conclusion and results are presented.

Keywords

Main Subjects


[1] Paolino, P. (2001). Maximum Likelihood E stimation of Models with Beta-Distributed Dependent Variables, Political Analysis9, 325-346.
 
[2] Kieschnik, R. and McCullough, B.D. (2003). Regression Analysis of Variates Observed on (0,1): Percentage, Proportions and Fractions. Statistical Modelling3,193-213.
[3] Ferrari, S. and Cribari, F. (2004). Beta Regression for ModellingR ates and Proportions, Journal of Applied Statistics31, 799-815.
 
[4] Cepeda, E.D. and Gamerman, D. (2005). Bayesian Methodology for Modeling Parameters in the Two ParameterE xponentialF amily, Revista Estadística57, 168-169.
[5] Smithson, M. and Verkuilen, J. (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables, Psychological Methods11, 54-71.
 
[6] Branscum, A.J., Johnson, W.O. and Thurmond, M. (2007). Baysian Beta Regression Applications to Houshold Expenditure Data and Genetic Distance Between Food and Mouth Dieseas Viruses, Australian & New Zealand Journal of Statistics49, 287-301.
[7] Ospina, R. and Ferrari, S. (2010). Inflated Beta Distributions. Statistical Paper23, 193-213.
 
[8] Ospina, R. and Ferrari, S. (2012). A General Class of Zeror-One Inflated Beta Regression Models. Computational Statistics & Data Analysis56, 1609-1623.
 
[9] Galvis, M.D., Dipankar, B. and Victor, H.L. (2014). Augmented Mixed Beta Regression Models for Periodontal Proportion Data, Preprinted, Statistics in Medicine, 33,3759-3771.
[0] Figueroa-Zúñiga, J.I., Arellano-Valle, R.B. and Ferrari, S.L. (2013). Mixed Beta Regression: A Bayesian Perspective, Computational Statistics & Data Analysis61, 137– 147.
[11] Sturtz, S., Ligges, U. and Gelman, A. (2005). R2winbugs: A Package for Running Winbugs from R, Journal of Statistical Software12, 1–16.
 
[12] نتایج آمارگیری نیروی کار (1392)، مرکز آمار ایران، تهران.
[13] Gelman, A. and Rubin, D.B. (1992). Inference from Iterative Simulation Using Multiple Sequences, Statistical Science 7, 457–511.
[14] Heidelberger, P. and Welch, P.D. (1981). A Spectral Method for Confidence Interval Generation and Run Length Contral in Simulations, Communications of the ACM24, 233-245.
 
[15] Brooks, S.P. and Gelman, A., (1998). General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics 7, 434–455.
 
[16] Plummer, M., Best, N., Cowles, K. and Vines, K., (2006). The coda Package. R Project. http://cran.r-project.org/doc/packages/coda.pdf.