Standard Error Estimation for Measures of Population Change over Time from Repeated Surveys

Lead Research Organisation: University of Southampton
Department Name: Statistical Sciences Research institute

Abstract

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Description 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 JRSS-D) 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 estimators of change. Sampling variances require the estimation of correlations between waves. Estimation of correlations 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. We propose to use a multivariate linear regression approach to estimate correlations and variances of changes. The proposed method is flexible and can handles complex sampling designs, non-response and complex measure of change. We analysed the accuracy of the proposed method theoretically and via simulation.

The multivariate regression approach proposed consists in fitting a multivariate regression with the variables of interests (weighted by inclusion probabilities) as dependent variables and design variables as independent variables. This model needs to incorporate interactions to account for the rotation in the sampling design. The residual covariance matrix gives estimates of correlations. For example, if we are interested in change in totals, the dependent variables are the values of the variables at the first and second wave divided by inclusion probabilities. The design variables are stratification variables. Although a model is used, this approach is robust as it gives consistent estimator for the correlation whether or not the model fits the data.

We have compared the proposed method (the multivariate regression approach) with alternative estimators. We compare the estimators theoretically and via simulations. We found out that the proposed method is equivalent to alternative methods in simple situation: basic sampling design, and the simple measure of change. However, our proposed method is more general and can handle situation which are not considered with those alternative methods. The advantage of the proposed method is not its accuracy, but its generality and flexibility. The proposed method can handles complex sampling designs, stratification, non-response and complex measure of change (involving weighting).

The multivariate regression approach is simple to implement as it can be easily implemented in most statistical software. It is only necessary to create the design variables which characterise the sampling design. For example, with the statistical software R, the multivariate linear regression approach can be implemented in a couple of lines of codes. The simplicity of the proposed estimator was not something that we could have anticipated before starting the project. We thought that it would be necessary to create a new library in R. However, we find out that it is possible to use existing libraries (developed for different problems) to implement the proposed method. This is explained in a paper we published in the Journal of the Royal Statistical Society (Series A). In the applied paper, we propose to show how the proposed method can be implemented with standard statistical software.
Exploitation Route The techniques developed is used by the European Statistical agency (Eurostat) for estimation of variance of change of social surveys, such as EU-SILC. It is essentially used to assess the change in poverty over time.
Sectors Digital/Communication/Information Technologies (including Software)
URL https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssa.12116
 
Description The techniques developed is used by the European Statistical agency (Eurostat) for estimation of variance of change of social surveys, such as EU-SILC.
First Year Of Impact 2012
Sector Digital/Communication/Information Technologies (including Software)
Impact Types Policy & public services
 
Description Standard error estimation for measures of population change over time from repeated surveys 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Primary Audience
Results and Impact Invited Departmental Seminar
Year(s) Of Engagement Activity