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R.J. Little 42337.3.4 The design-model compromiseEmerging from the debate over design-based and model-based inference isthe current consensus, which I have called the Design-Model Compromise(DMC); see Little (2012). Inference is design-based for aspects of surveys thatare amenable to that approach, mainly inferences about descriptive statisticsin large probability samples. These design-based approaches are often modelassisted, using methods such as regression calibration to protect against modelmisspecification; see, e.g., Särndal et al. (1992). For problems where the designbasedapproach is infeasible or yields estimates with insufficient precision,such as small area estimation or survey nonresponse, a model-based approachis adopted. The DMC approach is pragmatic, and attempts to exploit thestrengths of both inferential philosophies. However, it lacks a cohesive overarchingphilosophy, involving a degree of “inferential schizophrenia” (Little,2012).I give two examples of “inferential schizophrenia.” More discussion andother examples are given in Little (2012). Statistical agencies like the USCensus Bureau have statistical standards that are generally written from adesign-based viewpoint, but researchers from social science disciplines likeeconomics are trained to build models. This dichotomy leads to friction whensocial scientists are asked to conform to a philosophy they view as alien. Socialscience models need to incorporate aspects like clustering and stratification toyield robust inferences, and addressing this seems more likely to be successfulfrom a shared modeling perspective.Another example is that the current paradigm generally employs directdesign-based estimates in large samples, and model-based estimates in smallsamples. Presumably there is some threshold sample size where one is designbased for larger samples and model based for smaller samples. This leads toinconsistency, and ad-hoc methods are needed to match direct and modelestimates at different levels of aggregation. Estimates of precision are lesseasily reconciled, since confidence intervals from the model tend to be smallerthan direct estimates because the estimates “borrow strength.” Thus, it isquite possible for a confidence interval for a direct estimate to be wider thana confidence interval for a model estimate based on a smaller sample size,contradicting the notion that uncertainty decreases as information increases.37.4 A unified framework: Calibrated BayesSince a comprehensive approach to survey inference requires models, a unifiedtheory has to be model-based. I have argued (Little, 2012) that the appropriateframework is calibrated Bayes inference (Box, 1980; Rubin, 1984; Little, 2006),where inferences are Bayesian, but under models that yield inferences with