Accounting for dependent informative sampling in model-based finite population inference

The paper considers model-based inference for finite population parameters under informative sampling, when the draws of the different units are not independent and the joint selection probability is modeled using a copula. We extend the “sample likelihood” approach to the case of dependent draws and provide the expression of the likelihood given the selected sample, called here “selection likelihood”. We show how to derive maximum likelihood estimators of the model parameters based on the resulting selection likelihood. Further, we find optimal predictors of individual values and of finite population parameters under the proposed informative selection models. In an experiment based on the 1988 U.S. National Maternal and Infant Health Survey, results indicate that, for small sample size, the proposed selection likelihood method reduces systematically the bias and standard errors of the estimators obtained from the sample likelihood based on independent draws and become the same for large sample size. It reduces considerably the bias due to informativeness and gives more efficient estimators than the pseudo likelihood (or quasi-likelihood) approach based on weighting the sample estimating equations by the survey weights.