Kpop: A kernel balancing approach for reducing specification assumptions in survey weighting
Abstract
With the precipitous decline in response rates, researchers and pollsters have been left with highly non-representative samples, relying on constructed weights to make these samples representative of the desired target population. Though practitioners employ valuable expert knowledge to choose what variables, X must be adjusted for, they rarely defend particular functional forms relating these variables to the response process or the outcome. Unfortunately, commonly-used calibration weights -- which make the weighted mean X in the sample equal that of the population -- only ensure correct adjustment when the portion of the outcome and the response process left unexplained by linear functions of X are independent. To alleviate this functional form dependency, we describe kernel balancing for population weighting (kpop). This approach replaces the design matrix X with a kernel matrix, K encoding high-order information about X. Weights are then found to make the weighted average row of K among sampled units approximately equal that of the target population. This produces good calibration on a wide range of smooth functions of X, without relying on the user to decide which X or what functions of them to include. We describe the method and illustrate it by application to polling data from the 2016 U.S. presidential election.