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

Double symmetry model and its decompositions in square contingency tables having ordered categories 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

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

, Volume 48 (4) – Jun 11, 2013
11 pages

/lp/springer_journal/double-symmetry-model-and-its-decompositions-in-square-contingency-cABcE5pdrg
Publisher
Springer Netherlands
Subject
Social Sciences, general; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-013-9876-7
Publisher site
See Article on Publisher Site

### 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.

### Journal

Quality & QuantitySpringer Journals

Published: Jun 11, 2013

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