# Improving multilevel regression and poststratification with structured priors

## TL;DR

This paper introduces a new structured prior framework for multilevel regression and poststratification (MRP) that reduces bias and variance in survey estimates, especially with non-representative data.

## Contribution

It proposes a novel approach for specifying structured priors in MRP, demonstrating bias and variance reduction through simulations and real US survey data.

## Key findings

- Structured priors reduce bias in MRP estimates.
- Structured priors decrease variance in posterior estimates.
- Effective across various data regimes.

## 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.