Improved generalized estimating equation analysis via xtqls for implementation of quasi-least squares in Stata

Quasi-least squares (QLS) is a method based on the popular generalized estimating equation (GEE) approach that is widely used for analysis of correlated cross-sectional and longitudinal data.This article summarizes the development of QLS that occurred in several manuscripts and describes its implementation with the user-written program xtqls in Stata.In addition, it demonstrates the following advantages of QLS: (i) QLS allows for implementation of some correlation structures that have not yet been implemented in the framework of GEE; (ii) QLS can be applied as an alternative to GEE if the GEE estimate is infeasible; and (iii) QLS is a method in the framework of GEE that uses the same estimating equation for estimation of β as GEE; as a result, implementation of QLS can involve programs already available for GEE.In particular, xtqls calls up the Stata program xtgee within an iterative approach that alternatives between updating estimates of the correlation parameter α and then using xtgee to solve the GEE estimating equation for β at the current estimate of α.The benefit of this approach is that following implementation of xtqls, all the usual post-regression estimation commands are readily available to the user.The xtqls program is available on the website for the Longitudinal Analysis for Diverse Populations project: http://www.cceb.upenn.edu/~sratclif/QLSproject.html.