Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach

Abstract

<p>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 due to unequal selection probabilities, clustering, and other design features. In particular, the actual type I error rates of tests of hypotheses based on standard tests can be much bigger than the nominal significance level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests that involve the estimated covariance matrices of parameter estimates. Bootstrap methods designed for survey data are often applied 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. 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 and establish the asymptotic validity of the proposed bootstrap tests. In addition, we also consider hypothesis testing from categorical data and present a bootstrap procedure for testing simple goodness of fit and independence in a two-way table. In the simulation studies, the type I error rates of the proposed approach are much closer to their nominal level compared with the naive likelihood ratio test and quasi-score test. An application to data from an educational survey under a logistic regression model is also presented.</p>