Improving estimation for beta regression models via EM-algorithm and related diagnostic tools

In this paper we propose an alternative procedure for estimating the parameters of the beta regression model. This alternative estimation procedure is based on the EM-algorithm. For this, we took advantage of the stochastic representation of the beta random variable through ratio of independent gamm...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2017-09, Vol.87 (14), p.2847-2867
Main Authors: Barreto-Souza, Wagner, Simas, Alexandre B.
Format: Article
Language:English
Subjects:
Algorithms
Bounded data
Computer simulation
Diagnostic software
Diagnostic systems
diagnostic tools
Economic models
Independent variables
inference
latent variables
maximum likelihood estimators
Monte Carlo simulation
Parameter estimation
Probability theory
Random variables
Randomness
Regression
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Summary:In this paper we propose an alternative procedure for estimating the parameters of the beta regression model. This alternative estimation procedure is based on the EM-algorithm. For this, we took advantage of the stochastic representation of the beta random variable through ratio of independent gamma random variables. We present a complete approach based on the EM-algorithm. More specifically, this approach includes point and interval estimations and diagnostic tools for detecting outlying observations. As it will be illustrated in this paper, the EM-algorithm approach provides a better estimation of the precision parameter when compared to the direct maximum likelihood (ML) approach. We present the results of Monte Carlo simulations to compare EM-algorithm and direct ML. Finally, two empirical examples illustrate the full EM-algorithm approach for the beta regression model. This paper contains a Supplementary Material.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2017.1350679