# Double symmetry model and its decompositions in square contingency tables having ordered categories

## Author

Listed:
• Bayo Lawal

()

• Richard Sundheim

()

## Abstract

In this paper, we have employed the non-standard log-linear models to fit the double symmetry models and some of its decompositions to square contingency tables having ordered categories. SAS PROC GENMOD was employed to fit these models although we could similarly have used GENLOG in SPSS or GLM in STATA. A SAS macro generates the factor or scalar variables required to fit these models. Two sets of $$4 \times 4$$ 4 × 4 unaided distance vision data that have been previously analyzed in (Tahata and Tomizawa, Journal of the Japan Statistical Society 36:91–106, 2006 ) were employed for verification of results. We also extend the approach to the Danish $$5 \times 5$$ 5 × 5 Mobility data as well as to the $$3 \times 3$$ 3 × 3 Danish longitudinal study data of subjective health, firstly reported in (Andersen, The Statistical Analysis of Categorical Data, Springer:Berlin, 1994 ) and analyzed in (Tahata and Tomizawa, Statistical Methods and Applications 19:307–318, 2010 ). Results obtained agree with those published in previous literature on the subject. The approaches suggest here eliminate any programming that might be required in order to apply these class of models to square contingency tables. Copyright Springer Science+Business Media Dordrecht 2014

## Suggested Citation

• Bayo Lawal & Richard Sundheim, 2014. "Double symmetry model and its decompositions in square contingency tables having ordered categories," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1995-2005, July.
• Handle: RePEc:spr:qualqt:v:48:y:2014:i:4:p:1995-2005
DOI: 10.1007/s11135-013-9876-7
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File URL: http://hdl.handle.net/10.1007/s11135-013-9876-7

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## References listed on IDEAS

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1. H. Lawal, 2000. "Implementing point-symmetry models for square contingency tables having ordered categories in SAS," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 9(1), pages 1-22, January.
2. Lawal, H. Bayo & Sundheim, Richard A., 2002. "Generating Factor Variables for Asymmetry, Non-independence and Skew-symmetry Models in Square Contingency Tables using SAS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i08).
3. Kouji Tahata & Sadao Tomizawa, 2010. "Double linear diagonals-parameter symmetry and decomposition of double symmetry for square tables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 307-318, August.
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### Keywords

Double symmetry; Local odds ratios; Point symmetry ; Square contingency table; Symmetry; Quasi double symmetry;

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