Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories
Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories
复制标题
有序类别交叉分类分析中的关联模型和典型相关
DOI：
10.1080/01621459.1981.10477651
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发表时间：
1981
影响因子：
3.7
通讯作者：
L. A. Goodman
中科院分区：
文献类型：
--
作者：
L. A. Goodman
Goodman（1979a）中所考虑的用于分析具有有序类别的交叉分类的关联模型，在本文中以稍有不同的形式提出，以便于将用这些模型得到的结果与用早期的典型相关方法得到的结果进行比较。关联模型和典型相关方法都可以为行和列类别提供有意义的分数，并且这些分数可以用于将通常的卡方统计量划分为相关分量，用于测试行分类和列分类之间的统计独立性的零假设。然而，当卡方分量基于典型相关时，通常用于检验卡方分量的统计显著性的程序是无效的，当这些分量是用关联模型获得时，相应的程序是有效的。用缔合模型求出的缔合成分与实验结果吻合较好。
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 mo...