Abstract
Summary A distinction is made between the uses of models in sample design and in survey analysis. Sampling practitioners regularly employ models to guide their choice of sample design, but seldom place complete reliance in a model (which would eliminate the need for probability sampling). With the large samples typical of most surveys, they are reluctant to use model-based estimators of descriptive parameters because of the bias resulting from any misspecifications of the model. With small samples, however, they may prefer a model-based estimator, accepting its unknown bias where its variance is much smaller than the design-based estimator; synthetic estimation for small areas illustrates this point. Models are essential for handling nonresponse and with the technique of statistical matching. The use of models for predicting sampling errors is noted. Causal analysis of survey data necessarily involves models; even so, in some circumstances design-based analysis may provide greater protection against model misspecifications than model-based analysis.
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