Comments: The Big Picture for Small Areas Alan M. Zaslavsky Harvard Medical School

Thanks to presenters 3 interesting talks Raise significant policy issues

Voting rights tabulation Generic approach for beta-binomial modeling – Shrinkage calculations (R. Little) – Approach to quasi-Bayesian estimation for clustered survey data (D. Malec) Why jurisdictional classes rather than prior centered on prediction? – Use of classes predictably biases up or down just above or below class boundary. – Problem of discreteness/thresholds

Voting rights tabulation How ‘general purpose’ is the product? – Inference for point estimate of % – vs inference for P(>5%). Presentation of results – Bayes methods → posterior distributions  – Present results for multiple inferences? – SAE of aggregates ≠ aggregate of SAEs – Perils of thresholds/discreteness

“Context specificity” What does it add beyond predictive variance? – Model error worse than a sampling error – why? – Might be better understood as a measure of model- robustness. Might not have unambiguous definition – In lead example, should precision of NHIS or BRFSS data define ‘specificity’? (NHIS-BRFSS association is a model estimate.) – Depends on which inference: Estimate of absolute levels sensitive to calibration Estimate of differences/ranking among areas unaffected by calibration

“Context specificity” Highlights value of transparency of methodology – Develop heuristic explanations of components contributing to estimation and their ‘weights’ – “For estimation of XXX … – “Total (predictive) SE is … – “XX% from sampling in BRFSS … – “YY% from estimation of NHIS calibration model… – “ZZ% from model error of covariate model…”

Outcome screening Prioritizing more global SAE program Technical concerns – Do methods properly account for sampling variance of domain proportions? In this 2-level model, why use ad hoc methods for level-2 variance estimation? Strategic concerns – Consider costs & benefits as well as variances Posterior ranking Є {overkill} ? – Consider families of outcomes, not just individual outcomes e.g. 12 binomial variables, likely related, for same Asian population

Current state of SAE Typically one variable or a few closely related – Relationships only as explicitly selected for models – Not higher-order interactions Each major SAE a major project – High-level statistical expertise involved – Takes a long time Lack of fully generic methods – (… although principles fairly well established) – Depends on amount & structure of available data, distributions & relationships, etc. – Often new methods required for each project

Path that extends current methods More estimation projects Elaborate more generic methods – Adapt to various data structures – More use of multilevel structure – Still univariate or low-dimensional OK for many… – single-purpose surveys – health care applications (“profiling”)

Some goals for general-purpose surveys Generate SAE for all current products – Detailed cross-tabulations – Microdata Plausible (not “correct”) for all relationships Valid presentation of uncertainty Consistency of all products – Margins and aggregation of estimates

What might this look like? Almost certainly requires some form of microdata synthesis – Yields consistency Units that look ‘enough’ like real units Two approaches – “Bottom up” synthesis of units (persons, households) – “Top down” imposition of constraints on synthetic samples of real units

Advantages of ‘top-down’ approach Building from observed units makes high-order interactions realistic – Otherwise most difficult to model Impose constraints via weighting or constrained resampling – Weighting is like predictive mean estimation; properties more readily controllable properties – Constraints may be from direct estimates, SAE, purely predictive estimates – Uncertainty via stochastic prediction of constraints and MI

Previous applications Reweighting/Imputation of households for census undercount (Zaslavsky 1988, 1989) Reweighting for food stamp microsimulations – “Large numbers of estimates for small areas” (Schirm & Zaslavsky ) – High-order interactions crucial to simulation of program provisions – Reweight national CPS data to simulate each state in turn (direct and SAE controls)

Synthesis Work will proceed on many fronts – Develop and integrate new data sources – Targeted SAE projects responsive to needs – Advances in dissemination & explication Integrate improvements in SAE for marginal (single-variable) estimates into overall synthetic framework.

Thank you!