Abstract
Consider a set of categorical variables P where at least one, denoted by Y, is binary. The loglinear model that describes the contingency table counts implies a logistic regression model, with outcome Y. Extending results from Christensen (1997, Loglinear models and logistic regression, 2nd edn. New York, NY, Springer), we prove that the maximumlikelihood estimates (MLE) of the logistic regression parameters equals the MLE for the corresponding loglinear 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 loglinear 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 loglinear 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.
Original language  English 

Article number  191483 
Number of pages  13 
Journal  Royal Society Open Science 
Volume  7 
Issue number  1 
DOIs  
Publication status  Published  15 Jan 2020 
Keywords
 Contingency table
 Generalized linear modelling
 Categorical variables
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Michail Papathomas
 Statistics  Senior Lecturer
 Centre for Research into Ecological & Environmental Modelling
Person: Academic, Academic  Research