A Bayesian Approach to Parameter Estimation in Simplex Regression Model: A Comparison with Beta Regression

Un enfoque bayesiano para la estimación de los parámetros del modelo regresión Simplex: una comparación con la regresión Beta

Some variables are restricted to the open interval (0; 1) and several methods have been developed to work with them under the scheme of the regression analysis. Most of research consider maximum likelihood methods and the use of Beta or Simplex distributions.

 

This paper presents the use of Bayesian techniques to estimate the parameters of the simplex regression supported on the implementation of some simulations and a comparison with Beta regression. We consider both models with constant variance and models with heteroscedasticity.

Algunas variables están restringidas al intervalo abierto (0; 1) y para trabajar con ellas se han desarrollado diversos métodos bajo el esquema del análisis de regresión. La mayoría de ellos han sido concebidos originalmente para ser estimados por métodos de máxima verosimilitud. Los más naturales parecen descansar especialmente sobre las distribuciones Beta o Simplex.

En este trabajo se presenta el uso de técnicas Bayesianas para la estimación de los parámetros de la regresión Simplex respaldada con la aplicación de algunas simulaciones y comparaciones con la regresión Beta. Se presentan resultados para modelos de varianza constante y de varianza heterogénea para cada individuo. Se presenta un ejemplo con datos reales.

 

A Bayesian Approach to Parameter Estimation in Simplex Regression Model: A Comparison with Beta Regression Un enfoque bayesiano para la estimación de los parámetros del modelo regresión Simplex: una comparación con la regresión Beta FREDDY OMAR LÓPEZ¹

¹Universidad de Valparaíso, Valparaíso, Chile. PhD Student. Email: freddy.vate01@gmail.com

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Abstract

Some variables are restricted to the open interval (0,1) and several methods have been developed to work with them under the scheme of the regression analysis. Most of research consider maximum likelihood methods and the use of Beta or Simplex distributions.
This paper presents the use of Bayesian techniques to estimate the parameters of the simplex regression supported on the implementation of some simulations and a comparison with Beta regression. We consider both models with constant variance and models with variance heterogeneity. Regressions are exemplified with heteroscedasticity.

Key words: Beta distribution, Gibbs sampler, Heterogeneous, Proportions, Simplex distribution, Variances.

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Resumen

Algunas variables están restringidas al intervalo abierto (0,1) y para trabajar con ellas se han desarrollado diversos métodos bajo el esquema del análisis de regresión. La mayoría de ellos han sido concebidos originalmente para ser estimados por métodos de máxima verosimilitud. Los más naturales parecen descansar especialmente sobre las distribuciones Beta o Simplex.
En este trabajo se presenta el uso de técnicas Bayesianas para la estimación de los parámetros de la regresión Simplex respaldada con la aplicación de algunas simulaciones y comparaciones con la regresión Beta. Se presentan resultados para modelos de varianza constante y de varianza heterogénea para cada individuo. Se presenta un ejemplo con datos reales.

Palabras clave: distribución beta, distribución simplex, muestreador de Gibbs, proporciones, varianza heterogénea.

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[Recibido en marzo de 2012. Aceptado en enero de 2013]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv36n1a01,
    AUTHOR  = {López, Freddy Omar},
    TITLE   = {{A Bayesian Approach to Parameter Estimation in Simplex Regression Model: A Comparison with Beta Regression}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2013},
    volume  = {36},
    number  = {1},
    pages   = {1-21}
}

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