Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions
Hierarchical Bayesian models are used in data modeling in different areas in which hierarchical structures are reflected through random effects.Usually the Normal distribution is used to model the random effects. The Inverse-gamma(ε , ε ) distribution is used as prior distribution for scale pa...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2022
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13655 |
| _version_ | 1801706352037330944 |
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| author | Rojas Mora, Jessica Maria Ramírez Guevara, Isabel |
| author_facet | Rojas Mora, Jessica Maria Ramírez Guevara, Isabel |
| author_sort | Rojas Mora, Jessica Maria |
| collection | OJS |
| description |
Hierarchical Bayesian models are used in data modeling in different areas in which hierarchical structures are reflected through random effects.Usually the Normal distribution is used to model the random
effects. The Inverse-gamma(ε , ε ) distribution is used as prior distribution for scale parameters with very small ε values, this selection has been criticized, some authors comment that unstable posterior distributions can be obtained, which causes not robust inference. Distributions such as half -Cauchy, Scaled Beta2 (SBeta2) and Uniform are considered as alternatives by many authors to model the scale parameter. In the present research work, the behavior of the random effects estimators in a hierarchical model with a Baye- sian approach was examined. It was assumed random effects distribution t-Student and scale parameter distributions half -Cauchy, SBeta2 and Uniform. A simulation study was carry on to evaluate the behavior of the random effects estimators. Based on the obtained results, and under differen scenarios, it was possible to examine the shrinkage of the posterior parameters of the model. We concluded that in presence of atypical values, the shrinkage is lower when the effects are modeled with a t-Student distribution compared with those obtained when a Normal distribution is associated to the random effects, under the same prior distribution for the scale parameter.
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| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-13655 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2022 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-136552023-06-26T20:42:54Z Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions Análisis de las estimaciones de los efectos aleatorios de un modelo jerárquico con distribuciones a priori de colas pesadas Rojas Mora, Jessica Maria Ramírez Guevara, Isabel Inferencia bayesiana Modelo jerárquico Parámetro de escala Distribución t-Student Bayesian Inference Hierarchical model Scale parameter t-Student distribution Hierarchical Bayesian models are used in data modeling in different areas in which hierarchical structures are reflected through random effects.Usually the Normal distribution is used to model the random effects. The Inverse-gamma(ε , ε ) distribution is used as prior distribution for scale parameters with very small ε values, this selection has been criticized, some authors comment that unstable posterior distributions can be obtained, which causes not robust inference. Distributions such as half -Cauchy, Scaled Beta2 (SBeta2) and Uniform are considered as alternatives by many authors to model the scale parameter. In the present research work, the behavior of the random effects estimators in a hierarchical model with a Baye- sian approach was examined. It was assumed random effects distribution t-Student and scale parameter distributions half -Cauchy, SBeta2 and Uniform. A simulation study was carry on to evaluate the behavior of the random effects estimators. Based on the obtained results, and under differen scenarios, it was possible to examine the shrinkage of the posterior parameters of the model. We concluded that in presence of atypical values, the shrinkage is lower when the effects are modeled with a t-Student distribution compared with those obtained when a Normal distribution is associated to the random effects, under the same prior distribution for the scale parameter. Los modelos jerárquicos Bayesianos son utilizados en la modelación de datos en diferentes áreas en las cuales las estructuras jerárquicas se reflejan a través de efectos aleatorios. La distribución de probabilidad considerada como elección natural para el modelamiento de los efectos aleatorios es la Normal. Como distribución a priori para el parámetro de escala regularmente se utiliza Gamma-inversa (ε,ε) (IG) con valores de ε muy pequeños y esta selección ha tenido críticas, algunos autores comentan que se pueden obtener distribuciones posteriores inestables, lo cual ocasiona que la inferencia no sea robusta. Distri- buciones como half -Cauchy, Beta2 escalada (SBeta2) y Uniforme son consideradas como alternativas por diversos autores para modelar el parámetro de escala. En el presente trabajo de investigación se examinó el comportamiento de las estimaciones de los efectos aleatorios de un modelo jerárquico con un enfoque Bayesiano. Se asumió efectos aleatorios distribuidos t-Student y parámetro de escala distribuidos half - Cauchy, SBeta2 y Uniforme. Se llevó a cabo un estudio de simulación para evaluar el comportamiento del error de estimación de los efectos del modelo. Con base a los resultados obtenidos, y bajo los diferentes escenarios en consideración, fue posible examinar el encogimiento de los parámetros a posteriori del mo- delo y se pudo establecer que en presencia de valores atípicos, esta medida es menor cuando los efectos se modelan con una distribución t de Student comparados con los obtenidos cuando se le asocia a los efectos una distribución Normal bajo las misma distribuciones a priori para el parámetro de escala. 3 Universidad Pedagógica y Tecnológica de Colombia 2022-01-29 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion text texto application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13655 10.19053/01217488.v13.n1.2022.13655 Ciencia En Desarrollo; Vol. 13 No. 1 (2022): Vol. 13 Núm. 1 (2022): Vol 13, Núm.1 (2022): Enero-Junio; 65-78 Ciencia en Desarrollo; Vol. 13 Núm. 1 (2022): Vol. 13 Núm. 1 (2022): Vol 13, Núm.1 (2022): Enero-Junio; 65-78 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13655/12522 |
| spellingShingle | Inferencia bayesiana Modelo jerárquico Parámetro de escala Distribución t-Student Bayesian Inference Hierarchical model Scale parameter t-Student distribution Rojas Mora, Jessica Maria Ramírez Guevara, Isabel Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title | Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title_alt | Análisis de las estimaciones de los efectos aleatorios de un modelo jerárquico con distribuciones a priori de colas pesadas |
| title_full | Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title_fullStr | Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title_full_unstemmed | Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title_short | Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| title_sort | analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions |
| topic | Inferencia bayesiana Modelo jerárquico Parámetro de escala Distribución t-Student Bayesian Inference Hierarchical model Scale parameter t-Student distribution |
| topic_facet | Inferencia bayesiana Modelo jerárquico Parámetro de escala Distribución t-Student Bayesian Inference Hierarchical model Scale parameter t-Student distribution |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/13655 |
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