In the November 2016 U.S. presidential election, many state level public opinion polls, particularly in the Upper Midwest, incorrectly predicted the winning candidate. One leading explanation for this polling miss is that the precipitous decline in traditional polling response rates led to greater reliance on statistical methods to adjust for the corresponding bias -- and that these methods failed to adjust for important interactions between key variables like education, race, and geographic region. Finding calibration weights that account for important interactions remains challenging with traditional survey methods: raking typically balances the margins alone, while post-stratification, which exactly balances all interactions, is only feasible for a small number of variables. In this paper, we propose multilevel calibration weighting, which enforces tight balance constraints for marginal balance and looser constraints for higher-order interactions. This incorporates some of the benefits of post-stratification while retaining the guarantees of raking. We then correct for the bias due to the relaxed constraints via a flexible outcome model; we call this approach Double Regression with Post-stratification (DRP). We characterize the asymptotic properties of these estimators and show that the proposed calibration approach has a dual representation as a multilevel model for survey response. We then use these tools to to re-assess a large-scale survey of voter intention in the 2016 U.S. presidential election, finding meaningful gains from the proposed methods. The approach is available in the multical R package.
We consider regression analysis in the context of data integration. To combine partial information from external sources, we employ the idea of model calibration which introduces a "working" reduced model based on the observed covariates. The working reduced model is not necessarily correctly specified but can be a useful device to incorporate the partial information from the external data. The actual implementation is based on a novel application of the information projection and model calibration weighting. The proposed method is particularly attractive for combining information from several…
Statistical matching aims to integrate two statistical sources. These sources can be two samples or a sample and the entire population. If two samples have been selected from the same population and information has been collected on different variables of interest, then it is interesting to match the two surveys to analyse, for example, contingency tables or covariances. In this paper, we propose an efficient method for matching two samples that may each contain a weighting scheme. The method matches the records of the two sources. Several variants are proposed in order to create a directly us…
Many data sets contain an inherent multilevel structure, for example, because of repeated measurements of the same observational units. Taking this structure into account is critical for the accuracy and calibration of any statistical analysis performed on such data. However, the large number of possible model configurations hinders the use of multilevel models in practice. In this work, we propose a flexible framework for efficiently assessing differences between the levels of given grouping variables in the data. The assessed group heterogeneity is valuable in choosing the relevant group coe…
We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate the weighting variables under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and implemented …
Complementary features of randomized controlled trials (RCTs) and observational studies (OSs) can be used jointly to estimate the average treatment effect of a target population. We propose a calibration weighting estimator that enforces the covariate balance between the RCT and OS, therefore improving the trial-based estimator's generalizability. Exploiting semiparametric efficiency theory, we propose a doubly robust augmented calibration weighting estimator that achieves the efficiency bound derived under the identification assumptions. A nonparametric sieve method is provided as an alternat…
The comparison of subnational areas is ubiquitous but survey samples of these areas are often biased or prohibitively small. Researchers turn to methods such as multilevel regression and poststratification (MRP) to improve the efficiency of estimates by partially pooling data across areas via random effects. However, the random effect approach can pool observations only through area-level aggregates. We instead propose a weighting estimator, the synthetic area estimator, which weights on variables measured only in the survey to partially pool observations individually. The proposed method cons…
Causal Inference with Multiple Misclassified Exposures: A Control Variate-Adjusted Calibration Weighting Approach
Colorado School of Public Health（科罗拉多公共卫生学院）；Johns Hopkins Bloomberg School of Public Health（约翰斯·霍普金斯大学彭博公共卫生学院）；University of Colorado School of Medicine（科罗拉多大学医学院）；Colorado State University（科罗拉多州立大学）
Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of volunteers. One method of weighting, introduced here, is to assign a unit in the nonprobability sample the weight from its matched case in the probability sample. The properties of resulting estimators depend on whether the probability sample weights are inverses of selection probabilities or are calibrated. In addition, imperfect matching can cause estimates…
Finite population inference is a central goal in survey sampling. Probability sampling is the main statistical approach to finite population inference. Challenges arise due to high cost and increasing non-response rates. Data integration provides a timely solution by leveraging multiple data sources to provide more robust and efficient inference than using any single data source alone. The technique for data integration varies depending on types of samples and available information to be combined. This article provides a systematic review of data integration techniques for combining probabilit…
Dealing with biased data samples is a common task across many statistical fields. In survey sampling, bias often occurs due to unrepresentative samples. In causal studies with observational data, the treated versus untreated group assignment is often correlated with covariates, i.e., not random. Empirical calibration is a generic weighting method that presents a unified view on correcting or reducing the data biases for the tasks mentioned above. We provide a Python library EC to compute the empirical calibration weights. The problem is formulated as convex optimization and solved efficiently …
Calibration Strategies for Robust Causal Estimation: Theoretical and Empirical Insights on Propensity Score-Based Estimators
Economic AI, Nürnberger Str. 262 A, 93059 Regensburg, Bayern, Germany（经济人工智能，德国雷根施塔特）；Chair of Statistics with Application in Business Analytics, University of Hamburg Business School, Moorweidenstr. 18, 20148 Hamburg, Hamburg, Germany（商务分析统计学系，汉堡大学商业学院）；Chair of Mathematics and Statistics in Economics, University of Hamburg Business School, Von-Melle-Park 5, 20146 Hamburg, Hamburg, Germany（经济学数学与统计学系，汉堡大学商业学院）；Düsseldorf Institute for Competition Economics, Heinrich Heine University Düsseldorf, Universitätstr. 1, 20225 Düsseldorf, Nordrhein-Westphalen, Germany（多特蒙德竞争经济学研究所，杜伊斯堡-艾森大学）
