The Analysis of Survey Data Using the Bootstrap

• Activity Number: 504
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Jean-Francois Beaumont*+
• Companies: Statistics Canada
• Keywords: bootstrap tests; bootstrap weights; design variance; model variance

Abstract

The bootstrap is a convenient tool for estimating design variances of finite population parameters or model parameters. It is typically implemented by producing design bootstrap weights that are made available to survey analysts. When analysts are interested in making inferences about model parameters, two sources of variability are normally taken into account: the model that generates data of the finite population and the sampling design. When the overall sampling fraction is negligible, the model variability can be ignored and standard bootstrap techniques that account for the sampling design variability can be used. However, there are many practical cases where the model variability cannot be ignored. We show how to modify design bootstrap weights in a simple way to account for the model variability. The analyst may also be interested in testing hypotheses about model parameters. This can be achieved by replicating a simple weighted model-based test statistic using the bootstrap weights. Our approach is related to the Rao-Scott test (Rao-Scott, 1981). We illustrate through a simulation study that both methods perform better than the standard Wald or Bonferroni test.