Improving Multilevel Regression and Poststratification with Structured Priors

Abstract

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.

Forecasting sub-national trends in COVID-19 vaccine uptake in the UK

“…Multilevel regression and poststratification (MRP) 15,17 is used to estimate intent to accept a COVID-19 vaccine across the 174 sub-national NUTS across the UK and to identify the socio-econo-demographic barriers to * See https://www.ons.gov.uk/methodology/geography/ukgeographies/eurostat for further details (accessed 25 November 2020) uptake. MRP comprises two stages 18 . In stage one, a multilevel regression model is fit (using response and covariate data described above and in table 1) to determine, for each possible stratum of socio-econodemographic status and sub-national unit, the probability of COVID-19 vaccine acceptance for each of the four ordinal responses (see Outcome variable).…”

“…Multilevel regression and poststratification (MRP) is used to estimate opinions aggregated at subnational regions from survey data collected at the national level, via partial pooling of information between these national and sub-national scales 32 . This pooling of information between the two levels is a compromise between estimates derived via a total aggregation of data (to estimate national trends only) and estimates via complete disaggregation (that is, estimating regional trends only).…”

Modeling public opinion over time and space: Trust in state institutions in Europe, 1989-2019

“…However, recent work (Gao et al, 2020;Bisbee, 2019;Ornstein, 2020) suggests that regularizing models other than a multilevel regression can be used. In particular, Gao et al (2020) suggests that in some cases a smoother regularizing tool (in their work auto-regressive (1), random walk or spatial models) can outperform a simple MRP model. We use these findings in our work when predicting the change in political trust over time by modeling political trust using a spline for the time component.…”

Fast and Accurate Estimation of Non-Nested Binomial Hierarchical Models Using Variational Inference

“…The benefits and challenges of these models can be illustrated by an increasingly popular application for survey research in social science: Multilevel Regression and Post-Stratification (MRP; Gelman and Little 1997;Park et al 2004;Gao et al 2020). Described in more detail in Section 5, the core purpose of this method is to extrapolate outcomes from nationally representative surveys to small geographic areas with limited data (e.g.…”

“…That paper increased the complexity of the model substantially by using eighteen mostly non-nested random effects and thus specifying a model with thousands of parameters. More broadly, the idea of using a more complex model has led to a variety of papers implementing more complex hierarchical models (Gelman et al 2016;Gao et al 2020) or relying on machine learning methods (Bisbee 2019;Ornstein 2020;Goplerud et al 2018). Regardless of whether one relies on a "traditional" MRP or a recent extension, it is clear that comparing multiple specifications in a principled way is fundamental to performing reliable inference.…”