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To model or not to model? Competing modes of inference for finite population sampling

Finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution, rather than on statistical models for the measured variables. This article reviews the debate between design-based and model-based inference. The basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples. Strengths and weakness of design-based and model-based inference for surveys are discussed. It is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings. These ideas are illustrated using the problem of inference from unequal probability samples. A model-based regression analysis that leads to a combination of design-based and model-based weighting is described. KEY WORDS: Bayesian methods; Design-based inference; Regression; Robustness; Sampling weights; Survey sampling.