We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked, or different sampling methods used, in different strata or clusters. Our method involves multiply-imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights were based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed to nonimputed data. We illustrate with the example that motivated this project --- a ...

Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It's well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly-sampled areas. Unfortunately, adjusting the observed rates to account for the effects of small-sample noise can introduce an opposite effect, in which the highest adjusted rates tend to be found disproportionately in wellsampled areas. In either case, the maps can be difficult to interpret because the display of spatial variation in the underlying parameters of interest is confounded with spatial variation in sample sizes. As a result, spatial patterns occur in adjusted rates even if there is no spatial structure in the underlying parameters of interest, and adjusted rates tend to look too uniform in areas with little data. We introduce two models (normal...

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Introduction Raftery's paper addresses two important problems in the statistical analysis of social science data: (1) choosing an appropriate model when so much data are available that standard P-values reject all parsimonious models; and (2) making estimates and predictions when there are not enough data available to fit the desired model using standard techniques. For both problems, we agree with Raftery that classical frequentist methods fail and that Raftery's suggested methods based on BIC can point in better directions. Nevertheless, we disagree with his solutions because, in principle, they are still directed off-target and only by serendipity manage to hit the target in special circumstances. Our primary criticisms of Raftery's proposals are that (1) he promises the impossible: the selection of a model that is adequate for specific purposes without consideration of those purposes; and (2) he uses the same limited tool for model averaging as for model selection, thereby

In this report we focus on the use of propensity score methodology in multisite studies of the effects of educational programs and practices in which both treatment and control conditions are enacted within each of the schools in a sample, and the assignment to treatment is not random. A key challenge in applying propensity score methodology in such settings is that the process by which students wind up in treatment or control conditions may differ substantially from school to school. To help capture differences in selection processes across schools, and achieve balance on key covariates between treatment and control students in each school, we propose the use of multilevel logistic regression models for propensity score estimation in which intercepts and slopes are treated as varying across schools. Through analyses of the data from the Early Academic Outreach Program (EAOP), we compare the performance of this approach with other possible strategies for estimating propensity scores (e.g., single-level logistic regression models; multilevel logistic regression models with intercepts treated as random and slopes treated as fixed). Furthermore, we draw attention to how the failure to achieve balance within each school can result in misleading inferences concerning

It frequently arises in statistics – especially in Bayesian statistics – that we encounter some complicated, high-dimensional density function π: X → [0, ∞), for some high-dimensional subspace X ⊆ R d. We then want to