Collapsibility of regression coefficients and its extensions

Collapsibility with respect to a measure of association implies that the measure of association can be obtained from the marginal model. We first discuss model collapsibility and collapsibility with respect to regression coefficients for linear regression models. For parallel regression models, we give simple and different proofs of some of the known results and obtain also certain new results. For random coefficient regression models, we define (average) A-collapsibility and obtain conditions under which it holds. We consider Poisson regression and logistic regression models also, and derive conditions for collapsibility and A-collapsibility, respectively. These results generalize some of the results available in the literature. Some suitable examples are also discussed.