Logistic regression under complex survey designs

Estimation procedures for obtaining consistent estimators of the parameters of a generalized logistic function and of its asymptotic covariance matrix under complex survey designs are presented. A correction in the Taylor estimator of the covariance matrix is made to produce a positive definite covariance matrix. The correction also reduces the small sample bias. The estimation procedure is first presented for cluster sampling and then extended to more complex situations. A Monte Carlo study is conducted to examine the small sample properties of F-tests constructed from alternative covariance matrices. The maximum likelihood estimation method where the survey design is completely ignored is compared with the usual Taylor’s series expansion method and with the modified Taylor procedure.