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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$4 \times 4$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>4</mn> <mo>×</mo> <mn>4</mn> </mrow> </math> </EquationSource> </InlineEquation> unaided distance vision data that have been previously analyzed in (Tahata and Tomizawa, Journal of the Japan Statistical Society 36:91–106, <CitationRef CitationID="CR13">2006</CitationRef>) were employed for verification of results. We also extend the approach to the Danish <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$5 \times 5$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>5</mn> <mo>×</mo> <mn>5</mn> </mrow> </math> </EquationSource> </InlineEquation> Mobility data as well as to the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$3 \times 3$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </math> </EquationSource> </InlineEquation> Danish longitudinal study data of subjective health, firstly reported in (Andersen, The Statistical Analysis of Categorical Data, Springer:Berlin, <CitationRef CitationID="CR1">1994</CitationRef>) and analyzed in (Tahata and Tomizawa, Statistical Methods and Applications 19:307–318, <CitationRef CitationID="CR14">2010</CitationRef>). 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
Year of publication: |
2014
|
---|---|
Authors: | Lawal, Bayo ; Sundheim, Richard |
Published in: |
Quality & Quantity: International Journal of Methodology. - Springer. - Vol. 48.2014, 4, p. 1995-2005
|
Publisher: |
Springer |
Subject: | Double symmetry | Local odds ratios | Point symmetry | Square contingency table | Symmetry | Quasi double symmetry |
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