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On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling
Consider a set of categorical variables [Formula: see text] where at least one, denoted by Y, is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Log-linear models and logistic regr...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7029921/ https://www.ncbi.nlm.nih.gov/pubmed/32218966 http://dx.doi.org/10.1098/rsos.191483 |
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author | Jing, W. Papathomas, M. |
author_facet | Jing, W. Papathomas, M. |
author_sort | Jing, W. |
collection | PubMed |
description | Consider a set of categorical variables [Formula: see text] where at least one, denoted by Y, is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Log-linear models and logistic regression, 2nd edn. New York, NY, Springer), we prove that the maximum-likelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding log-linear model parameters, also considering the case where contingency table factors are not present in the corresponding logistic regression and some of the contingency table cells are collapsed together. We prove that, asymptotically, standard errors are also equal. These results demonstrate the extent to which inferences from the log-linear framework translate to inferences within the logistic regression framework, on the magnitude of main effects and interactions. Finally, we prove that the deviance of the log-linear model is equal to the deviance of the corresponding logistic regression, provided that no cell observations are collapsed together when one or more factors in [Formula: see text] become obsolete. We illustrate the derived results with the analysis of a real dataset. |
format | Online Article Text |
id | pubmed-7029921 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-70299212020-03-26 On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling Jing, W. Papathomas, M. R Soc Open Sci Mathematics Consider a set of categorical variables [Formula: see text] where at least one, denoted by Y, is binary. The log-linear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Log-linear models and logistic regression, 2nd edn. New York, NY, Springer), we prove that the maximum-likelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding log-linear model parameters, also considering the case where contingency table factors are not present in the corresponding logistic regression and some of the contingency table cells are collapsed together. We prove that, asymptotically, standard errors are also equal. These results demonstrate the extent to which inferences from the log-linear framework translate to inferences within the logistic regression framework, on the magnitude of main effects and interactions. Finally, we prove that the deviance of the log-linear model is equal to the deviance of the corresponding logistic regression, provided that no cell observations are collapsed together when one or more factors in [Formula: see text] become obsolete. We illustrate the derived results with the analysis of a real dataset. The Royal Society 2020-01-15 /pmc/articles/PMC7029921/ /pubmed/32218966 http://dx.doi.org/10.1098/rsos.191483 Text en © 2020 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Mathematics Jing, W. Papathomas, M. On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title | On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title_full | On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title_fullStr | On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title_full_unstemmed | On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title_short | On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
title_sort | on the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling |
topic | Mathematics |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7029921/ https://www.ncbi.nlm.nih.gov/pubmed/32218966 http://dx.doi.org/10.1098/rsos.191483 |
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