Locally Equivalent Weights for Bayesian Multilevel Regression and Poststratification

Multilevel Regression with Post-stratification (MrP) has become a workhorse method for estimating population quantities using non-probability surveys, and is the primary alternative to traditional survey calibration weights, e.g.~ as computed by raking. For simple linear regression models, MrP methods admit “equivalent weights”, allowing for direct comparisons between MrP and traditional calibration weights (Gelman 2006). In the present paper, we develop a more general framework for computing and interpreting “MrP approximate weights” (MrPaw), which admit direct comparison with calibration weights in terms of important diagnostic quantities such as covariate balance, frequentist sampling variability, and partial pooling. MrPaw is based on a local equivalent weighting approximation, which we show in theory and practice to be accurate. Importantly, MrPaw can be easily computed based on existing MCMC samples and conveniently wraps standard MrP software implementations. We illustrate our approach for several canonical studies that use MrP, including for the binary outcome of vote choice, showing a high degree of variability in the performance of MrP models in terms of frequentist diagnostics relative to raking.

To join this seminar virtually, please request Zoom connection details from ea@stat.ubc.ca.