Variance estimation for measures of trends with rotated repeated surveys

Abstract

Measuring trend or 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 trends rather than cross sectional estimates. Samples at different waves are not necessarily completely overlapping sets of units, because repeated surveys often use rotating samples which consist in selecting for each wave new units to replace old units that have been in the sample for a specified number of waves (Tam, 1984; Nordberg, 2000; Kalton, 2009). Moreover, surveys are usually stratified and units can be selected with unequal probabilities. In this paper, we propose a novel approach to estimate trends and its variance taking into account of rotations, stratification and unequal probabilities. The variance depends on covariances between estimates calculated from different waves. In a series of simulation based on the Swedish Labour Force Survey, Andersson et al. (2011) showed that the approach proposed by Berger & Priam (2010) can give more accurate estimates of covariance than standard estimators of covariance (Tam, 1984; Qualité & Tillé, 2008). In this paper, we show how the approach proposed by Berger & Priam (2010) can be used to estimate the variance of a trend parameter. The proposed method is a semi-parametric design-based approach which is based upon a multivariate linear regression (or general linear) model (Berger & Priam, 2011). This multivariate regression model captures the effect of rotations, unequal probabilities, stratification and unequal probabilities.

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ORCID for Y.G. Berger: orcid.org/0000-0002-9128-5384

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