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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.2 Bogotá July/Dec. 2022 Epub Feb 01, 2023
https://doi.org/10.15446/rce.v45n2.98988
Artículos originales de investigación
Some Developments in Bayesian Hierarchical Linear Regression Modeling
Algunos desarrollos en modelos de regresión lineal jerárquicos bayesianos
1 Departamento de Estadistíca, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia
2 Facultad de Administración de Empresas, Universidad Externado de Colombia, Bogotá, Colombia
Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the full conditional distribution for each model parameter. Under our hierarchical extensions, we allow the mean of the second stage of the model to have a linear dependency on a set of covariates. The Gibbs sampling algorithms used to obtain samples when fitting the models are fully described and derived. In addition, we consider a case study in which the plant size is characterized as a function of nitrogen soil concentration and a grouping factor (farm).
Key words: Bayesian inference; Clustering; Gibbs Sampling; Hierarchical model; Linear regression
Considerando la flexibilidad y aplicabilidad del modelamiento Bayesiano, en este trabajo se revisan las principales características de dos modelos jerárquicos en un escenario de regresión. Se estudia la estructura probabilística completa de los modelos junto con la distribución condicional completa para cada parámetro del modelo. Las extensiones jerárquicas que se presentan permiten que la media de la segunda etapa del modelo tenga una dependencia lineal de un conjunto de covariables. Se describen y derivan completamente los algoritmos de muestreo de Gibbs para ajustar los modelos. Además, se considera un caso de estudio en el que se caracteriza el tamaño de plantas en función de la concentración de nitrógeno en el suelo y un factor de agrupación (fincas).
Palabras clave: Agrupamiento; Inferencia bayesiana; Muestreador de Gibbs; Modelo jerárquico; Regresión lineal
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Received: October 2021; Accepted: February 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
