title: An extension of Yule's Q to multivariate binary data.
abstract: 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.
authors.affiliation: Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115.
authors.forename: S R
authors.initials: SR
authors.lastname: Lipsitz
authors.forename: G
authors.initials: G
authors.lastname: Fitzmaurice
mesh_terms: D000818:Animals; D001699:Biometry; D016014:Linear Models; D051379:Mice; D015233:Models, Statistical; D015999:Multivariate Analysis; D009152:Mutagenicity Tests / Q000379:methods*; D016017:Odds Ratio; D011897:Random Allocation; D014116:Toxicology / Q000379:methods*