Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories
- 1 June 1981
- journal article
- theory and-method
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 76 (374) , 320-334
- https://doi.org/10.1080/01621459.1981.10477651
Abstract
The association models considered in Goodman (1979a) for the analysis of cross-classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach. Both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories, and these scores can be used to partition into relevant components the usual chi-squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification. However, while the usual procedure for testing the statistical significance of chi-squared components is invalid when these components are based on the canonical correlations, a corresponding procedure is valid when these components are obtained with the association models. The components of association obtained with the association models can be tested in a straightforward manner.Keywords
This publication has 27 references indexed in Scilit:
- Simple Models for the Analysis of Association in Cross-Classifications Having Ordered CategoriesJournal of the American Statistical Association, 1979
- ASYMPTOTIC DISTRIBUTIONS OF THE CANONICAL CORRELATIONS FROM CONTINGENCY TABLESAustralian Journal of Statistics, 1978
- Alternative Analyses for the Singly-Ordered Contingency TableJournal of the American Statistical Association, 1974
- An Analysis of a Two-Way Model with Interaction and No ReplicationJournal of the American Statistical Association, 1972
- Partitioning of Chi-Square, Analysis of Marginal Contingency Tables, and Estimation of Expected Frequencies in Multidimensional Contingency TablesJournal of the American Statistical Association, 1971
- A New Analysis of Variance Model for Non-additive DataTechnometrics, 1971
- The Multivariate Analysis of Qualitative Data: Interactions among Multiple ClassificationsJournal of the American Statistical Association, 1970
- A Class of Bivariate DistributionsJournal of the American Statistical Association, 1965
- The Structure of Bivariate DistributionsThe Annals of Mathematical Statistics, 1958
- On a property which holds good for all groupings of a normal distribution of frequency for two variables, with applications to the study of contingency-tables for the inheritance of unmeasured qualitiesProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1906