Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 2, Pages 67-86

A non-iterative alternative to ordinal Log-Linear models

Eric J. Beh1 and Pamela J. Davy2

1School of Quantitative Methods and Mathematical Sciences, University of Western Sydney, Australia
2School of Mathematics and Applied Statistics, University of Wollongong, Australia

Copyright © 2004 Eric J. Beh and Pamela J. Davy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.