Variance Estimation for Survey Data with Composite Imputation and Nonnegligible Sampling Fractions

Abstract

This article considers variance estimation for Horvitz–Thompson–type estimated totals based on survey data with imputed non-respondents and with nonnegligible sampling fractions. A method based on a variance decomposition is proposed. Our method can be applied to complicated situations where a composite of some deterministic and/or random imputation methods is used, including using imputed data in subsequent imputations. Although here linearization or Taylor expansion–type techniques are adopted, replication methods such as the jackknife, balanced repeated replication, and random groups can also be used in applying our method to derive variance estimators. Using our method, variance estimators can be derived under either the customary design-based approach or the model-assisted approach, and are asymptotically unbiased and consistent. The Transportation Annual Survey conducted at the U.S. Census Bureau, in which nonrespondents are imputed using a composite of cold deck and ratio type imputation methods, is used as an example as well as the motivation for our study.

Key Words:

• Complex survey
• Design-based
• Model-assisted
• Nonrespondents
• Unconfounded response
• Variance decomposition