Bayesian model selection for multilevel models using integrated likelihoods.
Multilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the Bayesian setting, the standard approach is a comparison of models u...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2023-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0280046 |
| _version_ | 1797852105990471680 |
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| author | Tom Edinburgh Ari Ercole Stephen Eglen |
| author_facet | Tom Edinburgh Ari Ercole Stephen Eglen |
| author_sort | Tom Edinburgh |
| collection | DOAJ |
| description | Multilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the Bayesian setting, the standard approach is a comparison of models using the model evidence or the Bayes factor. Explicit expressions for these quantities are available for the simplest linear models with unrealistic priors, but in most cases, direct computation is impossible. In practice, Markov Chain Monte Carlo approaches are widely used, such as sequential Monte Carlo, but it is not always clear how well such techniques perform. We present a method for estimation of the log model evidence, by an intermediate marginalisation over non-variance parameters. This reduces the dimensionality of any Monte Carlo sampling algorithm, which in turn yields more consistent estimates. The aim of this paper is to show how this framework fits together and works in practice, particularly on data with hierarchical structure. We illustrate this method on simulated multilevel data and on a popular dataset containing levels of radon in homes in the US state of Minnesota. |
| first_indexed | 2024-04-09T19:28:43Z |
| format | Article |
| id | doaj.art-491293890f4f4aebb4fd40e58be8f676 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-04-09T19:28:43Z |
| publishDate | 2023-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-491293890f4f4aebb4fd40e58be8f6762023-04-05T05:31:29ZengPublic Library of Science (PLoS)PLoS ONE1932-62032023-01-01182e028004610.1371/journal.pone.0280046Bayesian model selection for multilevel models using integrated likelihoods.Tom EdinburghAri ErcoleStephen EglenMultilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the Bayesian setting, the standard approach is a comparison of models using the model evidence or the Bayes factor. Explicit expressions for these quantities are available for the simplest linear models with unrealistic priors, but in most cases, direct computation is impossible. In practice, Markov Chain Monte Carlo approaches are widely used, such as sequential Monte Carlo, but it is not always clear how well such techniques perform. We present a method for estimation of the log model evidence, by an intermediate marginalisation over non-variance parameters. This reduces the dimensionality of any Monte Carlo sampling algorithm, which in turn yields more consistent estimates. The aim of this paper is to show how this framework fits together and works in practice, particularly on data with hierarchical structure. We illustrate this method on simulated multilevel data and on a popular dataset containing levels of radon in homes in the US state of Minnesota.https://doi.org/10.1371/journal.pone.0280046 |
| spellingShingle | Tom Edinburgh Ari Ercole Stephen Eglen Bayesian model selection for multilevel models using integrated likelihoods. PLoS ONE |
| title | Bayesian model selection for multilevel models using integrated likelihoods. |
| title_full | Bayesian model selection for multilevel models using integrated likelihoods. |
| title_fullStr | Bayesian model selection for multilevel models using integrated likelihoods. |
| title_full_unstemmed | Bayesian model selection for multilevel models using integrated likelihoods. |
| title_short | Bayesian model selection for multilevel models using integrated likelihoods. |
| title_sort | bayesian model selection for multilevel models using integrated likelihoods |
| url | https://doi.org/10.1371/journal.pone.0280046 |
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