by Design-based vs model-based inferences Following the introduction of the model-based inferential framework by Fisher and the introduction of the design-based inferential framework by Neyman [and Pearson], survey sampling statisticians began to identify their respective weaknesses. With regard to the model-based framework, sampling statisticians found that conditioning on all stratification and selection/recruitment variables, and allowing for their potential interactions with independent variables, complicated model specification (Pfeffermann, 1996). Such conditioning also complicated interpretation of substantively interesting model parameters and swallowed needed degrees of freedom (Pfeffermann, Krieger, & Rinott, 1998). Additionally, such conditioning
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Design-based vs model-based inferences
Following the introduction of the model-based inferential framework by Fisher and the introduction of the design-based inferential framework by Neyman [and Pearson], survey sampling statisticians began to identify their respective weaknesses.
With regard to the model-based framework, sampling statisticians found that conditioning on all stratification and selection/recruitment variables, and allowing for their potential interactions with independent variables, complicated model specification (Pfeffermann, 1996). Such conditioning also complicated interpretation of substantively interesting model parameters and swallowed needed degrees of freedom (Pfeffermann, Krieger, & Rinott, 1998). Additionally, such conditioning was found to be error prone; particularly if little was known about the sample selection mechanism, relevant selection/recruitment variables could easily be unknowingly omitted …
With regard to the pure design-based framework, sampling statisticians felt limited by restrictions on the type of parameters that could be estimated (simple statistics such as means, totals, and ratios) and the type of inference that could be obtained (descriptive, finite population inference; Graubard & Korn, 2002; Smith, 1993). Additionally, statisticians increasingly realized that the design-based framework’s arguably greatest purported advantage (according to Neyman, 1923, 1934) is not entirely true: it does not provide inference free of all modeling assumptions. True, the design-based framework does not
involve explicit attempts to write out a model for the substantive process that generated yvalues in an infinite population. However, the sampling weight itself entails an implicit (or hidden) model relating probabilities of selection and the outcome (Little, 2004, p. 550). Adjustments to the weight for nonsampling errors such as under-coverage and nonresponse require further implicit modeling assumptions …