#### Date of Award

1986

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### Abstract

The correlated logistic regression model, a new model for correlated binary observations in the presence of covariates, is introduced and its relationship with other logistic models established. Comparisons are made with other models for correlated binary outcomes, particularly those that allow unit-specific covariates. A conditional model is derived and shown to be equivalent to a well-known model used in case-control studies.;Properties of several estimators of the regression parameter are investigated. Consistency of the unconditional and conditional maximum likelihood estimators is established and expressions derived for the asymptotic variance of the two estimators under the full model and also under a simpler model. Two other estimators, namely, the estimator obtained by using the usual logistic model and an estimator obtained by using dummy variables in the usual logistic model, are investigated. These two estimators are shown to be, in general, asymptotically biased. Some conditions are given for consistency of the two estimators. Expressions for the asymptotic variances of the two estimators, and the misspecification factors for their estimated variance, are obtained.;In the case of a single binary covariate, it is shown that the bias of the usual estimator is large even for moderate sample size, whereas the bias of the dummy variables estimator becomes small for moderate sample size. It is shown that, although in special cases the usual and dummy variables estimators may have higher asymptotic relative efficiency than the maximum likelihood estimator, unless both the intraclass correlation of the covariate and the residual intraclass correlation are close to zero, the usual, dummy variables and conditional estimators are, in general, not highly efficient. In particular, the asymptotic relative efficiency of the conditional estimator may be quite low.;Examples are given with simulated and real data showing how the usual, dummy variables and conditional estimators produce falsely significant test statistics.

#### Recommended Citation

Koval, John Joseph, "Properties Of Logistic Regression Models With Correlated Observations" (1986). *Digitized Theses*. 1504.

https://ir.lib.uwo.ca/digitizedtheses/1504