GENERALIZED LEAST-SQUARES F-TEST IN REGRESSION-ANALYSIS WITH 2-STAGE CLUSTER SAMPLES

When data are obtained by two-stage cluster sampling, serious problems can arise if conventional methods that ignore the intracluster correl ations are used. Wu, Holt, and Holmes showed that the standard F stati stic in regression analysis leads to inflated type I error rate (or si ze) due to correlated errors in the regression model appropriate for c lustered data. They proposed a simple correction to the standard F sta tistic that takes into account common intracluster correlation, rho, a nd slowed, through simulation, that the corrected F test performs much better than the standard F test in controlling the size for a scalar hypothesis. It also performed almost as well as an iterative generaliz ed least squares (IGLS) F statistic for large values of rho and better than the IGLS for small rho in controlling the size. This article con siders a two-step generalized least squares (GLS) F statistic by first estimating rho, using the well-known method of fitting constants due to Henderson, and then substituting the estimate into the GLS test sta tistic when rho is known. It is shown, through simulation, that the GL S F statistic performs as well as the corrected F statistic in control ling the size even for small rho, and at the same time leads to signif icant power gains over the corrected F for larger values of rho.