#### Abstract

Quasi-least squares (QLS) is a two-stage computational approach for estimation of the correlation parameters in the framework of generalized estimating equations (GEE). We prove two general results for the class of mixed linear correlation structures: namely, that the stage one QLS estimate of the correlation parameter always exists and is feasible (yields a positive definite estimated correlation matrix) for any correlation structure, while the stage two estimator exists and is unique (and therefore consistent) with probability one, for the class of mixed linear correlation structures. Our general results justify the implementation of QLS for particular members of the class of mixed linear correlation structures that are appropriate for the analysis of familial data, with families that vary in size and composition. We describe the familial structures and implement them in an analysis of optical spherical values in the Old Order Amish (OOA). For the OOA analysis, we show that we would suffer a substantial loss in efficiency, if the familial structures were the true structures, but were misspecified as simpler approximate structures. We also provide software for implementation of the familial structures in R. Key-Words: Quasi-least squares; linear correlation structure; mixed correlation structure; familial data.

#### Disciplines

Statistical Methodology | Statistical Theory

#### Suggested Citation

Xie, Jichun; Shults, Justine; Peet, Jon; Stambolian, Dwight; and Cotch, Mary F., "Quasi-Least Squares with Mixed Linear Correlation Structures" (October 2009). *UPenn Biostatistics Working Papers.* Working Paper 33.

http://biostats.bepress.com/upennbiostat/art33