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ISRN Computational Mathematics
Volume 2012 (2012), Article ID 340415, 12 pages
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.
- S. J. Haberman, “Log linear models for frequency tables with ordered classifications,” Biometrics, vol. 30, no. 4, pp. 589–600, 1974.
- L. A. Goodman, “Simple models of the analysis of association in cross-classifications having ordered categories,” Journal of the American Statistical Association, vol. 74, pp. 537–552, 1979.
- L. A. Goodman, “The analysis of cross-classified data having ordered and/or unordered categories: association models, correlation models, and asymmetry models for contingency tables with or without missing entries,” The Annals of Statistics, vol. 13, pp. 10–69, 1985.
- A. Agresti, Analysis of Ordinal Categorical Data, Wiley, New York, NY, USA, 1984.
- Z. Gilula and S. J. Haberman, “Canonical analysis of contingency tables by maximum likelihood,” Journal of the American Statistical Association, vol. 81, pp. 780–788, 1986.
- F. Galindo-Garre and J. K. Vermunt, “The order-restricted association model: two estimation algorithms and issues in testing,” Psychometrika, vol. 69, no. 4, pp. 641–654, 2004.
- M. L. Aït-Sidi-Allal, A. Baccini, and A. M. Mondot, “A new algorithm for estimating the parameters and their asymptotic covariance in correlation and association models,” Computational Statistics and Data Analysis, vol. 45, no. 3, pp. 389–421, 2004.
- E. J. Beh and P. J. Davy, “A non-iterative alternative to ordinal log-linear models,” Journal of Applied Mathematics and Decision Sciences, vol. 8, no. 2, pp. 67–86, 2004.
- E. J. Beh and T. B. Farver, “An evaluation of non-iterative methods for estimating the linear-by-linear parameter of ordinal log-linear models,” The Australian and New Zealand Journal of Statistics, vol. 51, no. 3, pp. 335–352, 2009.
- J. A. Nelder and R. W. M. Wedderburn, “Generalized linear models,” Journal of the Royal Statistical Society A, vol. 135, pp. 370–384, 1972.
- A. Agresti, Categorical Data Analysis, Wiley, Hoboken, NJ, USA, 2nd edition, 2002.
- V. N. Nair, “Testing in industrial experiments with ordered categorical data,” Technometrics, vol. 28, no. 4, pp. 283–291, 1986.
- S. Nishisato and P. S. Arri, “Nonlinear programming approach to optimal scaling of partially ordered categories,” Psychometrika, vol. 40, no. 4, pp. 525–548, 1975.