A simple variance estimator of change for rotating repeated surveys: an application to the EU-SILC household surveys

Abstract

A common problem is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions, and to judge whether the change observed is statistically significant. This involves the estimation of the sampling variance of the estimator of change. The estimation of this variance would be relatively straightforward if cross-sectional estimates were based on the same sample. Unfortunately, samples are not completely overlapping, because of rotations used in repeated surveys. We propose a simple approach based on a multivariate (general) linear regression model. The variance estimator proposed is not a model-based estimator. We show that the estimator proposed is design consistent when the sampling fractions are negligible. It can accommodate stratified and two-stage sampling designs. The main advantage of the approach proposed is its simplicity and flexibility. It can be applied to a wide class of sampling designs and can be implemented with standard statistical regression techniques. Because of its flexibility, the approach proposed is well suited for the estimation of variance for the European Union Statistics on Income and Living Conditions surveys. It allows us to use a common approach for variance estimation for the different types of design. The approach proposed is a useful tool, because it involves only modelling skills and requires limited knowledge of survey sampling theory.

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