Table of Contents
ISRN Computational Mathematics
Volume 2012, Article ID 396831, 8 pages
Research Article

A Computational Study Assessing Maximum Likelihood and Noniterative Methods for Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models

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

Received 5 October 2011; Accepted 16 November 2011

Academic Editors: K. T. Miura, 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.


For ordinal log-linear models, the estimation of the parameter reflecting the linear-by-linear measure of association has long been a topic for the analysis of dependence for contingency tables. Typically, iterative procedures (including Newton’s method) are used to determine the maximum likelihood estimate of the parameter. Recently Beh and Farver (2009, ANZJS, 51, 335–352) show by way of example three reliable and accurate noniterative techniques that can be used to estimate the parameter and extended this study by examining their reliability computationally. This paper further investigates the reliability of the non-iterative procedures when compared with Newton’s method for estimating this association parameter and considers the impact of the sample size on the estimate.