Comparing Regression Coefficients Between Nested Linear Models for Clustered Data With Generalized Estimating Equations

Comparing regression coefficients between models when one model is nested within another is of great practical interest when two explanations of a given phenomenon are specified as linear models. The statistical problem is whether the coefficients associated with a given set of covariates change significantly when other covariates are added into the model as controls. Methods for such comparison exist for independent data but do not apply when data are clustered such as longitudinal or familial data. Under the framework of generalized estimating equations, the authors develop statistical methods for such comparison. The properties of the proposed estimator of the difference in regression coefficients between two models are studied asymptotically and for finite samples through simulation. Application of the method to data on changes in depression mood from adolescence through young adulthood reveals that the effect of age after controlling for work status and marital status, although still significant, is largely reduced.