Berger, Y.G. and Priam, Rodolphe
(2010)
Estimation of correlations between cross-sectional estimates from repeated surveys: an application to the variance of change.
At *Symposium of Statistics Canada: Social Statistics: The Interplay among Censuses, Surveys and Administrative Data*
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Symposium of Statistics Canada: Social Statistics: The Interplay among Censuses, Surveys and Administrative Data, Canada.
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*26 - 29 Oct 2010.*

## Abstract

Measuring change over time is a central problem for many users of social, economic and demographic data and is of interest in many areas of economics and social sciences. Smith et al. (2003) recognised that assessing change is one of the most important challenges in survey statistics. The primary interest of many users is often in changes or trends from one time period to another. 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 observed change is statistically significant. This involves the estimation of the sampling variance of the estimator of change. Estimation of variance of change would be relatively straightforward if cross-sectional estimates were based upon the same sample. Unfortunately, samples from different waves are usually not completely overlapping sets of units, because of rotations used in repeated surveys. This implies that crosssectional estimates are not independent. Correlation plays an important role in estimating the variance of a change between the cross-sectional estimates. The unbiasedness of an estimator of a correlation is crucial, because a small bias can significantly over-estimate or under-estimate the variance of change (Berger, 2004). Several methods can be used to estimate correlations, some of which use re-sampling and/or Taylor linearization. We propose to use a multivariate linear regression approach to estimate the correlation. The proposed estimator is not a model-based estimator, as this estimator is valid even if the model does not fit the data. We show that the regression approach gives design-consistent estimator for the correlation when the finite population corrections are negligible. We show how the proposed estimator can accommodate stratified and two-stage sampling designs. We also show how the proposed estimator can be used for estimator of correlation between complex estimators of change.

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