Lipsitz S R, Fitzmaurice G
Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115.
Biometrics. 1994 Sep;50(3):847-52.
In this note we describe a summary measure of pairwise association for multivariate binary data based on the conditional odds ratio. The proposed measure is an extension of Yule's Q to more than two binary random variables. Unlike marginal measures of association, this measure is not constrained by the marginal probabilities of success. For example, when each binary variable has a different probability of success, the upper limit of the pairwise marginal correlation coefficient is constrained to be less than 1. If one prefers a measure of association that is unconstrained, then with only two binary variables, Bishop, Feinberg, and Holland (1975, Discrete Multivariate Analysis: Theory and Practice, Cambridge, Massachusetts: MIT Press) suggest the use of the odds ratio or, equivalently, Yule's Q. Yule's Q transforms the odds ratio between the two binary variables from [0, infinity) to [-1, 1]. We propose an extension of Yule's Q to more than two binary random variables. This measure of pairwise association is based on the conditional odds ratio from a log-linear model.
在本笔记中，我们描述了一种基于条件优势比的多变量二元数据成对关联的汇总度量。所提出的度量是尤尔Q向两个以上二元随机变量的扩展。与边际关联度量不同，该度量不受成功的边际概率的约束。例如，当每个二元变量具有不同的成功概率时，成对边际相关系数的上限被限制为小于1。如果有人更喜欢不受约束的关联度量，那么对于只有两个二元变量的情况，毕晓普、费恩伯格和霍兰德（1975年，《离散多变量分析：理论与实践》，马萨诸塞州剑桥：麻省理工学院出版社）建议使用优势比，或者等效地，尤尔Q。尤尔Q将两个二元变量之间的优势比从[0, ∞) 转换为[-1, 1]。我们提出了尤尔Q向两个以上二元随机变量的扩展。这种成对关联度量基于对数线性模型的条件优势比。
