The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach
Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1459524 |
| _version_ | 1827077577774202880 |
|---|---|
| author | Endris Assen Ebrahim Mehmet Ali Cengiz Erol Terzi |
| author_facet | Endris Assen Ebrahim Mehmet Ali Cengiz Erol Terzi |
| author_sort | Endris Assen Ebrahim |
| collection | DOAJ |
| description | Both frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct. Many regression model selection criteria are considered, including the maximum likelihood (ML) point estimation of the parameter and the logarithm of the likelihood of the dataset. This paper demonstrates the information complexity (ICOMP), Bayesian deviance information, or the widely applicable information criterion (WAIC) of the BRMS to hierarchical linear models fitted with repeated measures with a simulation and two real data examples. The Fisher information matrix for the Bayesian hierarchical model considering fixed and random parameters under maximizing a posterior estimation is derived. Using Gibbs sampling and Hybrid Hamiltonian Monte Carlo approaches, six different models were fitted for three distinct application datasets. The best-fitted candidate models were identified under each application dataset with the two MCMC approaches. In this case, the Bayesian hierarchical (mixed effect) linear model with random intercepts and random slopes estimated using the Hamiltonian Monte Carlo method best fits the two application datasets. Information complexity (ICOMP) is a better indicator of the best-fitted models than DIC and WAIC. In addition, the information complexity criterion showed that hierarchical models with gradient-based Hamiltonian Monte Carlo estimation are the best fit and have supper convergence relative to the gradient-free Gibbs sampling methods. |
| first_indexed | 2024-03-08T04:09:42Z |
| format | Article |
| id | doaj.art-87eacc8286cc4c23bf4c7cdb8eae8927 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2025-03-20T02:15:59Z |
| publishDate | 2024-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-87eacc8286cc4c23bf4c7cdb8eae89272024-10-03T07:51:41ZengHindawi LimitedJournal of Mathematics2314-47852024-01-01202410.1155/2024/1459524The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC ApproachEndris Assen Ebrahim0Mehmet Ali Cengiz1Erol Terzi2Debre Tabor UniversityOndokuz Mayis UniversityOndokuz Mayis UniversityBoth frequentist and Bayesian statistics schools have improved statistical tools and model choices for the collected data or measurements. Model selection approaches have advanced due to the difficulty of comparing complicated hierarchical models in which linear predictors vary by grouping variables, and the number of model parameters is not distinct. Many regression model selection criteria are considered, including the maximum likelihood (ML) point estimation of the parameter and the logarithm of the likelihood of the dataset. This paper demonstrates the information complexity (ICOMP), Bayesian deviance information, or the widely applicable information criterion (WAIC) of the BRMS to hierarchical linear models fitted with repeated measures with a simulation and two real data examples. The Fisher information matrix for the Bayesian hierarchical model considering fixed and random parameters under maximizing a posterior estimation is derived. Using Gibbs sampling and Hybrid Hamiltonian Monte Carlo approaches, six different models were fitted for three distinct application datasets. The best-fitted candidate models were identified under each application dataset with the two MCMC approaches. In this case, the Bayesian hierarchical (mixed effect) linear model with random intercepts and random slopes estimated using the Hamiltonian Monte Carlo method best fits the two application datasets. Information complexity (ICOMP) is a better indicator of the best-fitted models than DIC and WAIC. In addition, the information complexity criterion showed that hierarchical models with gradient-based Hamiltonian Monte Carlo estimation are the best fit and have supper convergence relative to the gradient-free Gibbs sampling methods.http://dx.doi.org/10.1155/2024/1459524 |
| spellingShingle | Endris Assen Ebrahim Mehmet Ali Cengiz Erol Terzi The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach Journal of Mathematics |
| title | The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach |
| title_full | The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach |
| title_fullStr | The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach |
| title_full_unstemmed | The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach |
| title_short | The Best Fit Bayesian Hierarchical Generalized Linear Model Selection Using Information Complexity Criteria in the MCMC Approach |
| title_sort | best fit bayesian hierarchical generalized linear model selection using information complexity criteria in the mcmc approach |
| url | http://dx.doi.org/10.1155/2024/1459524 |
| work_keys_str_mv | AT endrisassenebrahim thebestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach AT mehmetalicengiz thebestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach AT erolterzi thebestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach AT endrisassenebrahim bestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach AT mehmetalicengiz bestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach AT erolterzi bestfitbayesianhierarchicalgeneralizedlinearmodelselectionusinginformationcomplexitycriteriainthemcmcapproach |