FOR MODEL PARAMETERS FROM COMPLEX SURVEY DATA

In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, and (ii) validity under a conditional repeated sampling framework. Demnati and Rao (2004) proposed a new approach to deriving Taylor linearization variance estimators that leads directly to a unique variance estimator that satisfies the above considerations for general designs. Afterwards, Demnati and Rao (2002) considered the case of missing responses when adjustment for complete nonresponse and imputation for item nonresponse based on smooth functions of observed values, in particular ratio imputation, are used. When analyzing survey data, finite populations are often assumed to be generated from superpopulation models, and analytical inferences on model parameters are of interest. If the sampling fractions are small, then the sampling variance captures almost the entire variation generated by the design and model random processes. However, when the sampling fractions are not negligible, the model variance should be taken into account in order to construct valid inferences on model parameters under bot