Improving Small-Area Estimates of Public Opinion by Calibrating to Known Population Quantities

Multilevel regression and poststratification (MRP) is widely used to estimate opinion in small sub- groups and to adjust unrepresentative surveys. Yet, even flexible MRP models contain errors generated by non-response and model misspecification. We propose a principled, data-driven method to leverage observable errors on auxiliary quantities with known marginal distributions — e.g., election outcomes — to improve estimates of policy attitudes. Our method leverages the correlation between auxiliary variables and outcomes of interest to calibrate MRP estimates to these known marginal distributions. We illustrate our approach using a pre-election poll measuring support for an abortion referendum. We find that the method reduces county-level error by two-thirds relative to traditional MRP. We also show how our calibration approach can be used to generate estimates for smaller nested geographies, such as precincts, even in the absence of poststratification data at this level. Our approach provides a framework for fully incorporating known population data to improve estimates of public opinion in small subgroups, providing scholars another tool to study representation.