Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics.
Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences whe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2021-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0253349 |
| _version_ | 1818834616301125632 |
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| author | Ana C Guedes Francisco Cribari-Neto Patrícia L Espinheira |
| author_facet | Ana C Guedes Francisco Cribari-Neto Patrícia L Espinheira |
| author_sort | Ana C Guedes |
| collection | DOAJ |
| description | Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed. |
| first_indexed | 2024-12-19T02:37:39Z |
| format | Article |
| id | doaj.art-a7ba3e203e9e4cec88571deb92fac450 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-19T02:37:39Z |
| publishDate | 2021-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-a7ba3e203e9e4cec88571deb92fac4502022-12-21T20:39:19ZengPublic Library of Science (PLoS)PLoS ONE1932-62032021-01-01166e025334910.1371/journal.pone.0253349Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics.Ana C GuedesFrancisco Cribari-NetoPatrícia L EspinheiraBeta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed.https://doi.org/10.1371/journal.pone.0253349 |
| spellingShingle | Ana C Guedes Francisco Cribari-Neto Patrícia L Espinheira Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. PLoS ONE |
| title | Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. |
| title_full | Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. |
| title_fullStr | Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. |
| title_full_unstemmed | Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. |
| title_short | Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics. |
| title_sort | bartlett corrected tests for varying precision beta regressions with application to environmental biometrics |
| url | https://doi.org/10.1371/journal.pone.0253349 |
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