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

该研究项目将开发一个统一的框架，通过多层次回归和后分层（MRP）的新修改，将设计为基础的信息纳入建模调查加权。 现实生活中的调查数据往往是不具有代表性的，由于选择偏见和无响应。 现有的调整样本和样本所来自的总体之间的已知差异的方法有一些优点，但也有实际的局限性。 经典权重受大的可变性的影响，并且可能导致不稳定的估计，而回归方法提出了计算和建模的挑战。 这些研究人员开发的新框架将允许调整选择偏差和无反应，以及改进设计尊重推理。 使用这种方法，调查分析师将能够在回归框架中正确地解释不可解释的设计问题，在政府，学术，商业和非营利部门进行调查的从业人员将能够以常规方式构建统计上有效的调查权重。 这一新框架可能适用于新出现的“大数据”爆炸所产生的问题，如整合来自多个来源的调查，分析流数据和受访者驱动的抽样。 该项目将开发可供一般研究界使用的软件。本研究将在MRP框架下，将调查加权与后分层相结合。 在MRP中，数据在建模过程中被部分合并，然后通过后分层将局部估计组合以获得总体推断。 这种平滑的估计借用信息从相邻的poststratification细胞，并允许灵活的多层次建模策略，有可能是强大的模型误指定。 该项目将MRP推广到处理回归的加权调整，深度交互，非人口普查变量的校准，复杂的调查设计，多级抽样，多个调查框架以及现实世界调查分析中出现的其他复杂问题。 新方法将应用于两项正在进行的调查，即纽约纵向贫困衡量研究和脆弱家庭与儿童福利研究。 计算将使用开源贝叶斯程序Stan进行，并将免费传播。 该项目得到了方法、测量和统计方案以及联邦统计机构联合会的支持，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.