Inference on Collapsibility in Generalized Linear Models

• Published in: Biometrical Journal
• Main Authors: Greenland, S., Maldonado, George
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 1994
• Subjects: Greenland
• Online Access: http://dx.doi.org/10.1002/bimj.4710360702; https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fbimj.4710360702; https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.4710360702

Abstract GREENLAND and MICKEY (1988) derived a closed‐form collapsibility test and confidence interval for IxJxK contingency tables with qualitative factors, and presented a small simulation study of its performance. We show how their method can be extended to regression models linear in the natural parameter of a one‐parameter exponential family, in which the parameter of interest is the difference of “crude” and “adjusted” regression coefficients. A simplification of the method yields a generalization of the test for omitted covariates given by HAUSMAN (1978) for ordinary linear regression. We present an application to a study of coffee use and myocardial infarction, and a simulation study which indicates that the simplified test performs adequately in typical epidemiologic settings.