Model-based methods for estimating the population mean in stratified clustered sampling are described. The importance of adjusting the weights is assessed by an approach considering the sampling variation of the adjusted weights and its (variance) components. The resulting estimators are more efficient than the jackknife estimators for a variety of datasets obtained from the 1990 Mathematics Trial State Assessment of the National Assessment of Educational Progress (NAEP). The methods can be extended to two-stage clustering. A general method for estimation of more complex population summaries, such as regression coefficients, is outlined. There are no distributional assumptions in model-based methods, apart from the normality of the sample means. Model-based methods use only the final adjusted weights; the replicate weights can be disposed of, thus radically reducing the size of the dataset and simplifying data handling procedures. The principal advantage of the model-based methods is in efficiency and small bias of the estimators of standard errors for the population mean. Contrary to theoretical claims, the NAEP operationally implemented jackknife estimator of the sampling variance is not unbiased. Eleven tables and 7 figures are included. (Contains 13 references.) (Author/SLD)
