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Statistica Sinica 18(2008), 1165-1183





SOME ASSOCIATION MEASURES AND THEIR

COLLAPSIBILITY


Xianchao Xie$^1$, Zongming Ma$^2$ and Zhi Geng$^1$


$^1$Peking University and $^2$Stanford University


Abstract: For two variables $X$ and $Y$ with arbitrary distributions, we consider three general association measures, the mixed derivative of interaction, the partial derivative of the conditional distribution function and the partial derivative of the conditional expectation. The sign of an association measure between $X$ and $Y$ may sometimes be reversed after marginalization over a third variable $W$. In this paper, we first compare the stringency of these measures for evaluating a positive association. Then we present the condition for avoiding the effect reversal after marginalization over $W$. Further we show that a modification of the condition can be used for collapsibility of the association measures over $W$.



Key words and phrases: Association measure, collapsibility, Yule-Simpson paradox.

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