Some Developments in Bayesian Hierarchical Linear Regression Modeling

• Autores: Juan Sosa, Jeimy-Paola Aristizabal
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 45, Nº. 2, 2022, págs. 231-255
• Idioma: inglés
• DOI: 10.15446/rce.v45n2.98988
• Títulos paralelos:
  • Algunos desarrollos en modelos de regresión lineal jerárquicos bayesianos
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  • Texto completo
• Resumen
  • español

    Resumen 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).

  • English

    Abstract 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).

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