Having a Cake and Eating it Too – Robust and Efficient Estimation by Benchmarking Web Samples to Probability Survey Samples

• Activity Number: 434 - Robust and Efficient Inferences in Observational Studies and from Nonrandom Samples
• Type: Invited
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Government Statistics Section
• Author(s): Vladislav Beresovsky*
• Companies: National Center for Health Statistics
• Keywords: Web surveys; implicit logistic regression; group Lasso; double robust estimators

Abstract

At the time of increasing nonresponse rates and the cost of traditional (established) probability surveys, web surveys offer attractive alternatives. We propose a family of estimators of population mean that uses outcome and response models for bias reduction to combine information from both web surveys and traditional probability surveys. This is based on the assumption that both surveys share a number of possible predictors. We derive a rigorous method for modeling response to a web survey from a web sample and a traditional probability sample with unknown web response indicator. We use Lasso for variable selection from large number of possible covariates. We show that robustness of estimates may be improved without sacrificing efficiency by allowing estimates of one model to affect estimating parameters of another model. In case of Gaussian outcome, simulations show that dramatic bias reduction can be achieved by using group Lasso for simultaneous regression of outcome and response.