Published

2022-07-14

Some Developments in Bayesian Hierarchical Linear Regression Modeling

Algunos desarrollos en modelos de regresión lineal jerárquicos bayesianos

DOI:

https://doi.org/10.15446/rce.v45n2.98988

Keywords:

Bayesian Inference, Clustering, Gibbs Sampling, Hierarchical Model, Linear Regression (en)
Agrupamiento, Inferencia bayesiana, Muestreador de Gibb, Modelo jerárquico, Regresión lineal (es)

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Authors

  • Juan Sosa Departamento de Estadistíca, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia
  • Jeimy-Paola Aristizabal 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).

Considerando la exibilidad 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).

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How to Cite

APA

Sosa, J. and Aristizabal, J.-P. (2022). Some Developments in Bayesian Hierarchical Linear Regression Modeling. Revista Colombiana de Estadística, 45(2), 231–255. https://doi.org/10.15446/rce.v45n2.98988

ACM

[1]
Sosa, J. and Aristizabal, J.-P. 2022. Some Developments in Bayesian Hierarchical Linear Regression Modeling. Revista Colombiana de Estadística. 45, 2 (Jul. 2022), 231–255. DOI:https://doi.org/10.15446/rce.v45n2.98988.

ACS

(1)
Sosa, J.; Aristizabal, J.-P. Some Developments in Bayesian Hierarchical Linear Regression Modeling. Rev. colomb. estad. 2022, 45, 231-255.

ABNT

SOSA, J.; ARISTIZABAL, J.-P. Some Developments in Bayesian Hierarchical Linear Regression Modeling. Revista Colombiana de Estadística, [S. l.], v. 45, n. 2, p. 231–255, 2022. DOI: 10.15446/rce.v45n2.98988. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/98988. Acesso em: 14 jan. 2025.

Chicago

Sosa, Juan, and Jeimy-Paola Aristizabal. 2022. “Some Developments in Bayesian Hierarchical Linear Regression Modeling”. Revista Colombiana De Estadística 45 (2):231-55. https://doi.org/10.15446/rce.v45n2.98988.

Harvard

Sosa, J. and Aristizabal, J.-P. (2022) “Some Developments in Bayesian Hierarchical Linear Regression Modeling”, Revista Colombiana de Estadística, 45(2), pp. 231–255. doi: 10.15446/rce.v45n2.98988.

IEEE

[1]
J. Sosa and J.-P. Aristizabal, “Some Developments in Bayesian Hierarchical Linear Regression Modeling”, Rev. colomb. estad., vol. 45, no. 2, pp. 231–255, Jul. 2022.

MLA

Sosa, J., and J.-P. Aristizabal. “Some Developments in Bayesian Hierarchical Linear Regression Modeling”. Revista Colombiana de Estadística, vol. 45, no. 2, July 2022, pp. 231-55, doi:10.15446/rce.v45n2.98988.

Turabian

Sosa, Juan, and Jeimy-Paola Aristizabal. “Some Developments in Bayesian Hierarchical Linear Regression Modeling”. Revista Colombiana de Estadística 45, no. 2 (July 14, 2022): 231–255. Accessed January 14, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/98988.

Vancouver

1.
Sosa J, Aristizabal J-P. Some Developments in Bayesian Hierarchical Linear Regression Modeling. Rev. colomb. estad. [Internet]. 2022 Jul. 14 [cited 2025 Jan. 14];45(2):231-55. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/98988

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