Reducing Variance with Sample Allocation Based on Expected Response Rates

TL;DR

This paper shows that allocating samples based on expected response rates can reduce variance in survey estimates, outperforming traditional proportional-to-size allocation especially when response rates are accurately or approximately known.

Contribution

It introduces and evaluates a novel sample allocation method based on expected response rates, demonstrating its advantages over classical methods through theoretical analysis and simulations.

Findings

ERR allocation reduces variance compared to PS allocation.

Performance holds even with mis-specified response rates.

Theoretical and simulation results support ERR's effectiveness.

Abstract

Several techniques exist to assess and reduce nonresponse bias, including propensity models, calibration methods, or post-stratification. These approaches can only be applied after the data collection, and assume reliable information regarding unit nonresponse patterns for the entire population. In this paper, we demonstrate that sample allocation taking into account the expected response rates (ERR) have advantages in this context. The performance of ERR allocation is assessed by comparing the variances of estimates obtained those arising from a classical allocation proportional to size (PS) and then applying post-stratification. The main theoretical tool is asymptotic calculations using the delta-method, and these are complemented with extensive simulations. The main finding is that the ERR allocation leads to lower variances than the PS allocation, when the response rates are correctly specified, and also under a wide range of conditions when the response rates can not be correctly specified in advance.