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Inference on Collapsibility in Generalized Linear Models
Author(s) -
Greenland S.,
Maldonado George
Publication year - 1994
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710360702
Subject(s) - statistics , mathematics , contingency table , linear regression , confidence interval , covariate , generalized linear model , generalization , proper linear model , inference , regression analysis , linear model , regression , statistical inference , econometrics , computer science , bayesian multivariate linear regression , artificial intelligence , mathematical analysis
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.