Tests for misspecification in binary regression using the generalized estimating equations approach

Includes bibliographical references (pages [134]-140).The generalized estimating equations (GEE) method introduced by Liang and Zeger and extended by Prentice has been the subject of vigorous research activity over the past fifteen years. In particular, it has become a very popular tool for analyzing longitudinal data where correlations exist among the repeated observations on a subject but measurements on different subjects are presumed independent. Through the use of a “working” correlation structure to approximate the unknown dependence structure, the GEE yield consistent estimators of the regression parameters and of their variances. It is well known that this consistency depends crucially on the correct specification of the model for the marginal mean but is robust to misspecifications involving the working correlation matrix. A necessary but not sufficient condition for the mean function to be correct is to have a correct link function. Misspecification of the link function destroys consistency and can lead to substantial bias in the regression parameter estimates. On the other hand, misspecification of the working correlation does not invalidate consistency but can decrease the efficiency of the estimates. In either case, misspecification can lead to invalid statistical inferences. Thus, a crucial step in GEE regression is checking the validity of these assumptions. In this thesis, we propose two tests: (1) a test for misspecification of the link function and (2) a test for misspecification of the working correlation structure under the assumption that the mean model is correctly specified. We derive the asymptotic distribution of the proposed tests and study their finite-sample performance through simulation studies.Ph.D. (Doctor of Philosophy