Doubly robust integration of nonprobability and probability survey data

TL;DR

This paper reviews and advances methods for integrating nonprobability and probability survey data using doubly robust estimators, providing variance formulas and a framework for efficient combination of estimates.

Contribution

It introduces a new framework for combining doubly robust estimates with probability survey estimates, including variance and covariance formulas.

Findings

Derived variance formulas for doubly robust estimators.

Developed a framework for efficient combination of survey estimates.

Provided covariance estimates between different survey estimators.

Abstract

Doubly robust estimators combine an inverse probability weighting estimator and a mass imputation estimator. Several doubly robust estimators for estimating the population mean (or prevalence) of an outcome have been proposed for integrating outcome and covariate data from a nonprobability survey with covariate data from an auxiliary probability survey. However, the question of how to combine a doubly robust estimate with a corresponding estimate based on outcome data from the auxiliary probability survey alone has only received limited attention. In this paper, we (i) review previously proposed doubly robust estimators, (ii) provide formulae for the variance of doubly robust estimators and the covariance between doubly robust and probability survey estimates, (iii) propose a framework for how to combine efficiently a doubly robust estimate from a nonprobability sample with an estimate based on the auxiliary probability sample alone, and (iv) provide formulae for the variance of such combined estimates.