Model‐based Variance Estimation in Surveys With Stratified Clustered Design

Summary A model‐based method for estimating the sampling variances of estimators of (sub‐)population means, proportions, quantiles, and regression parameters in surveys with stratified clustered design is described and applied to a survey of US secondary education. The method is compared with the jackknife by a simulation study. The model‐based estimators of the sampling variances have much smaller mean squared errors than their jackknife counterparts. In addition, they can be improved by incorporating information about the unknown parameters (variances) from external sources. A regression‐based smoothing method for estimating the sampling variances of the estimators for a large number of subpopulation means is proposed. Such smoothing may be invaluable when subpopulations are represented in the sample by only few subjects.