A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multilevel Regression and Poststratification (MRP), a model-based approach, is gaining traction against the traditional weighted approach for survey estimates. MRP estimates are susceptible to bias if there is an underlying structure that the methodology does not capture. This work aims to provide a new framework for specifying structured prior distributions that lead to bias reduction in MRP estimates. We use simulation studies to explore the benefit of these prior distributions and demonstrate their efficacy on non-representative US survey data. We show that structured prior distributions offer absolute bias reduction and variance reduction for posterior MRP estimates in a large variety of data regimes.
Multilevel regression and poststratification (MRP) is a popular method for addressing selection bias in subgroup estimation, with broad applications across fields from social sciences to public health. In this paper, we examine the inferential validity of MRP in finite populations, exploring the impact of poststratification and model specification. The success of MRP relies heavily on the availability of auxiliary information that is strongly related to the outcome. To enhance the fitting performance of the outcome model, we recommend modeling the inclusion probabilities conditionally on auxil…
Real-time small area estimation of food security in Zimbabwe: integrating mobile-phone and face-to-face surveys using joint multilevel regression and poststratification
Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studies have been focused on non-causal settings, where estimating a single population value using a nonrepresentative sample was of primary interest. In this manuscript, MRP-style estimators will be evaluated in an experimental causal inference setting. We simulate a large-scale randomized control trial with a stratified cluster sampling design, and compare traditional and nonparametric treatment effect estimation methods…
In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on validation. We explore how leave-one-out cross-validation (LOO) can be used to compare Bayesian models for MRP. We investigate two approximate calculations of LOO, the Pareto smoothed importance sampling (PSIS-LOO) and a survey-weighted alternative (WTD-PSIS-LOO). Using two simulation designs, we examine how accurately these two criteria recover the correct or…
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 tr…
Uladzimir Karatkevich National University of Belarus（白俄罗斯乌拉济米尔·卡拉特克维奇国立大学）
Independent sociological polls are forbidden in Belarus. Online polls performed without sound scientific rigour do not yield representative results. Yet, both inside and outside Belarus it is of great importance to obtain precise estimates of the ratings of all candidates. These ratings could function as reliable proxies for the election's outcomes. We conduct an independent poll based on the combination of the data collected via Viber and on the streets of Belarus. The Viber and the street data samples consist of almost 45000 and 1150 unique observations respectively. Bayesian regressions wit…
Multilevel Regression Modeling of Covariance Matrix Outcomes
Indiana University School of Medicine（印第安纳大学医学院）；The University of Texas Health Science Center at Houston（德克萨斯大学健康科学中心休斯顿分校）；Johns Hopkins Bloomberg School of Public Health（约翰霍普金斯大学布隆伯格公共卫生学院）
Multilevel models (mixed-effect models or hierarchical linear models) are now a standard approach to analysing clustered and longitudinal data in the social, behavioural and medical sciences. This review article focuses on multilevel linear regression models for continuous responses (outcomes or dependent variables). These models can be viewed as an extension of conventional linear regression models to account for and learn from the clustering in the data. Common clustered applications include studies of school effects on student achievement, hospital effects on patient health, and neighbourho…
Multilevel network meta-regression for multistate models: Population-adjusted joint synthesis of progression and survival data from individual and aggregate evidence
University of California, San Francisco（旧金山加利福尼亚大学）；UCSF Helen Diller Family Comprehensive Cancer Center（UCSF海伦·迪勒家族综合癌症中心）；The Philip R. Lee Institute for Health Policy Studies（菲利普·李健康政策研究所）；Precision AQ
The classical multilevel model fails to capture the proximity effect in epidemiological studies, where subjects are nested within geographical units. Multilevel Conditional Autoregressive models are alternatives to help explain the spatial effect better. They have been developed for cross-sectional studies but not for longitudinal studies so far. This paper has two goals. Firstly, it further develops the multilevel (growth) models for longitudinal data by adding existing area level random effect terms with CAR prior specification, whose structure is changing over time. We name these models MLM…
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…
This is an overview of the R package iprior, which implements a unified methodology for fitting parametric and nonparametric regression models, including additive models, multilevel models, and models with one or more functional covariates. Based on the principle of maximum entropy, an I-prior is an objective Gaussian process prior for the regression function with covariance kernel equal to its Fisher information. The regression function is estimated by its posterior mean under the I-prior, and hyperparameters are estimated via maximum marginal likelihood. Estimation of I-prior models is simpl…
Calibrating hierarchical Bayesian domain inference for a proportion
Continuing Academic Specialist Center for Statistical Training and Consulting, Michigan State University（密歇根州立大学统计培训与咨询中心继续教育学术专员）；Institute for Social Research, University of Michigan（密歇根大学社会研究所）
Georgia State University（佐治亚州立大学）；University of Toronto（多伦多大学）
Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to a…
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional regression. This enables us to model effects on all distributional parameters for arbitrary parametric distributions, and to consider various effect types such as non-linear or spatial effects as well as hierarchical regression structures. Our spike and slab prior relies on a parameter expansion that separates blocks of regression coefficients into overall scal…
We present a general approach to synthesizing evidence of time-to-event endpoints in meta-analyses of aggregate data (AD). Our work goes beyond most previous meta-analytic research by using reconstructed survival data as a source of information. A Bayesian multilevel regression model, called the "meta-analysis of reconstructed survival data" (MARS), is introduced, by modeling and integrating reconstructed survival information with other types of summary data, to estimate the hazard ratio function and survival probabilities. The method attempts to reduce selection bias, and relaxes the presumpt…
