SOME ASSOCIATION MEASURES AND THEIR COLLAPSIBILITY

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.