Hypotheses Testing from Categorical Survey Data Using Bootstrap Weights

Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data. In particular, the actual type I error rates of tests of hypotheses based on standard tests can be much bigger than the nominal level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests (Rao, Scott and Skinner 1998) that involve the estimated covariance matrices of parameter estimates. The bootstrap method of Rao and Wu (1983) is often applied at Statistics Canada to estimate the covariance matrices, using the data file containing columns of bootstrap weights. Standard statistical packages often permit the use of survey weighted test statistics and it is attractive to approximate their distributions under the null hypothesis by their bootstrap analogues computed from the bootstrap weights supplied in the data file. Beaumont and Bocci (2009) applied this bootstrap method to testing hypotheses on regression parameters under a linear regression model, using weighted F statistics. In this paper, we present a unified approach to the above method by constructing bootstrap approximations to weighted likelihood ratio statistics and weighted quasi-score statistics. We report the results of a simulation study on testing independence in a two way table of categorical survey data. We studied the relative performance of the proposed method to alternative methods, including Rao-Scott corrected chi-squared statistic for categorical survey data.