Collaborative Research: Multilevel Regression and Poststratification: A Unified Framework for Survey Weighted Inference

该研究项目将通过对多层次回归和后分层（MRP）的新颖修改，开发一个统一的调查加权框架，将基于设计的信息纳入建模。由于选择偏差和无反应，现实生活中的调查数据往往不具有代表性。现有的调整样本和抽取样本的总体之间已知差异的方法有一些优点，但也有实际的局限性。经典的权重受制于很大的可变性，并且可能导致不稳定的估计，而回归方法则存在计算和建模方面的挑战。这些研究人员开发的新框架将允许对选择偏差和无反应进行调整，并改进尊重设计的推理。使用这种方法，调查分析师将能够适当地解释回归框架中不可忽视的设计问题，而在政府、学术、商业和非营利部门进行调查的从业者将能够以常规方式构建统计上有效的调查权重。这个新框架可能适用于新出现的“大数据”爆炸所带来的问题，例如来自多个来源的调查整合、流数据分析和受访者驱动的抽样。该项目将开发供一般研究界使用的软件。本研究项目将在MRP框架下，将调查加权与后分层联系起来。在MRP中，在建模过程中将部分数据池化，然后通过后分层将局部估计值组合得到总体推断。这种平滑估计从相邻的后分层单元中借鉴信息，并允许灵活的多级建模策略，这些策略有可能对模型错误规范具有鲁棒性。该项目将MRP推广到处理回归的权重调整、深度交互、非普查变量的校准、复杂的调查设计、多阶段抽样、多个调查框架以及实际调查分析中出现的其他复杂性。新方法将应用于两项正在进行的调查，即纽约纵向贫困测量研究和脆弱家庭和儿童福利研究。计算将使用开源贝叶斯程序Stan进行，并将免费传播。该项目由方法、测量和统计项目和联邦统计机构联盟支持，作为支持调查和统计方法研究的联合活动的一部分。

This research project will develop a unified framework for survey weighting through novel modifications of multilevel regression and poststratification (MRP) to incorporate design-based information into modeling. Real-life survey data often are unrepresentative due to selection bias and nonresponse. Existing methods for adjusting for known differences between the sample and population from which the sample is drawn have some advantages but also practical limitations. Classical weights are subject to large variability and can result in unstable estimators, while regression approaches present computational and modeling challenges. The new framework developed by these investigators will allow adjustment for selection bias and nonresponse as well as improvements in design-respecting inference. Using this approach, survey analysts will be able to properly account for non-ignorable design issues in the regression framework, and practitioners who conduct surveys in government, academic, commercial, and non-profit sectors will be able to construct statistically efficient survey weights in a routine manner. This new framework may be applicable to problems resulting from the newly emerging explosion of "big data," such as integration of surveys from multiple sources, analysis of streaming data, and respondent-driven sampling. The project will develop software that can be accessed by the general research community. This research project will connect survey weighting with poststratification under the framework of MRP. In MRP, data are partially pooled during the modeling process and then local estimates are combined via poststratification to obtain the population inference. This smoothed estimation borrows information from neighboring poststratification cells and allows flexible multilevel modeling strategies that have the potential to be robust to model misspecification. The project generalizes MRP to handle weighting adjustments for regression, deep interactions, calibration for non-census variables, complex survey design, multistage sampling, multiple survey frames, and other complications that arise in real-world survey analysis. The new methods will be applied to two ongoing surveys, the New York Longitudinal Poverty Measure study and the Fragile Families and Child Wellbeing study. Computations will be performed using the open source Bayesian program Stan and will be freely disseminated. The project is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.