Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 2, Pages 67-86
doi:10.1155/S1173912604000057
A non-iterative alternative to ordinal Log-Linear models
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.
Abstract
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.