Generalized Least Squares F Test in Regression Analysis With Two-Stage Cluster Samples

Abstract

When data are obtained by two-stage cluster sampling, serious problems can arise if conventional methods that ignore the intracluster correlations are used. Wu, Holt, and Holmes showed that the standard F statistic in regression analysis leads to inflated type I error rate (or size) due to correlated errors in the regression model appropriate for clustered data. They proposed a simple correction to the standard F statistic that takes into account common intracluster correlation, p, and showed, 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 generalized least squares (IGLS) F statistic for large values of ρ and better than the IGLS for small ρ in controlling the size. This article considers a two-step generalized least squares (GLS) F statistic by first estimating ρ, using the well-known method of fitting constants due to Henderson, and then substituting the estimate into the GLS test statistic when ρ is known. It is shown, through simulation, that the GLS F statistic performs as well as the corrected F statistic in controlling the size even for small ρ, and at the same time leads to significant power gains over the corrected F for larger values of ρ.

Key Words:

• Corrected F
• Generalized least squares
• Intra-cluster correlation
• Size and power
• Two-stage cluster sampling