Regression Modeling Strategies with Applications to Linear Models, Logistic Regression and Survival Analysis. Frank E. Harrell, Jun, Springer-Verlag, New York, 2001. No. of pages: 568. ISBN 0-387-95232-2

2003 ◽  
Vol 22 (15) ◽  
pp. 2531-2532 ◽  
Author(s):  
Per Kragh Andersen
Keyword(s):  
New York ◽  
Logistic Regression ◽  
Survival Analysis ◽  
Linear Models ◽  
Regression Modeling

scholarly journals On the correspondence of deviances and maximum-likelihood and interval estimates from log-linear to logistic regression modelling

2020 ◽  
Vol 7 (1) ◽  
pp. 191483
Author(s):  
W. Jing ◽  
M. Papathomas
Keyword(s):  
New York ◽  
Logistic Regression ◽  
Maximum Likelihood ◽  
Linear Model ◽  
Contingency Table ◽  
Linear Models ◽  
Maximum Likelihood Estimates ◽  
Categorical Variables ◽  
Model Parameters ◽  
Log Linear

Consider 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.

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