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dc.contributor.authorJing, Wei
dc.contributor.authorPapathomas, Michail
dc.identifier.citationJing , W & Papathomas , M 2020 , ' On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling ' , Royal Society Open Science , vol. 7 , no. 1 , 191483 .
dc.identifier.otherORCID: /0000-0002-5897-695X/work/67525883
dc.descriptionFunding: The first author would like to acknowledge the support of the School of Mathematics and Statistics, as well as CREEM, at the University of St Andrews, and the University of St Andrews St Leonard’s 7th Century Scholarship.en
dc.description.abstractConsider a set of categorical variables P 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 P∖{Y} become obsolete. We illustrate the derived results with the analysis of a real dataset.
dc.relation.ispartofRoyal Society Open Scienceen
dc.subjectContingency tableen
dc.subjectGeneralized linear modellingen
dc.subjectCategorical variablesen
dc.subjectQA Mathematicsen
dc.titleOn the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modellingen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Research into Ecological & Environmental Modellingen
dc.description.statusPeer revieweden

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