Strong Collapsibility of Association Measures in Linear Models

SUMMARY A measure of association in linear models is strongly collapsible over a discrete background variable if it remains unchanged no matter how the background variable is partially pooled and if it also coincides with the corresponding marginal measure of association. Strong collapsibility implies that the measure of association can be studied no matter how the background variable is categorized and no matter whether or not it is recorded. In this paper, necessary and sufficient conditions are given for strong collapsibility of the measure of association in linear models.