Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 340415, 12 pages
Research Article

On Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models: A Computational Study

1School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia
2School of Veterinary Medicine, University of California, Davis, Davis, CA 95616, USA

Received 17 January 2012; Accepted 5 March 2012

Academic Editors: T. Allahviranloo, H. J. Ruskin, P. B. Vasconcelos, and Q.-W. Wang

Copyright © 2012 Eric J. Beh and Thomas B. Farver. 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.


Estimating linear-by-linear association has long been an important topic in the analysis of contingency tables. For ordinal variables, log-linear models may be used to detect the strength and magnitude of the association between such variables, and iterative procedures are traditionally used. Recently, studies have shown, by way of example, three non-iterative techniques can be used to quickly and accurately estimate the parameter. This paper provides a computational study of these procedures, and the results show that they are extremely accurate when compared with estimates obtained using Newton’s unidimensional method.