scholarly journals PARAMETER REDUNDANCY AND THE EXISTENCE OF MAXIMUM LIKELIHOOD ESTIMATES IN LOG-LINEAR MODELS

2021 ◽  
Author(s):  
Serveh Sharifi Far ◽  
Michail Papathomas ◽  
Ruth King
Keyword(s):  
Maximum Likelihood ◽  
Linear Models ◽  
Maximum Likelihood Estimates ◽  
Parameter Redundancy ◽  
Log Linear

scholarly journals A non-iterative alternative to ordinal Log-Linear models

2004 ◽  
Vol 8 (2) ◽  
pp. 67-86 ◽  
Author(s):  
Eric J. Beh ◽  
Pamela J. Davy
Keyword(s):  
Maximum Likelihood ◽  
Linear Models ◽  
Contingency Tables ◽  
Model Fitting ◽  
Maximum Likelihood Estimates ◽  
Order Effects ◽  
Parameter Estimates ◽  
Linear Modeling ◽  
Statistical Tool ◽  
Log Linear

Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic and higher order effects can readily be included, in contrast to conventional log-linear models which incorporate linear terms only.The focus of the discussion is the application of the new parameter estimation technique to multi-way contingency tables with at least one ordered variable. This will also be done by considering singly and doubly ordered two-way contingency tables. It will be shown by example that the resulting parameter estimates are numerically similar to corresponding maximum likelihood estimates for ordinal log-linear models.

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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