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

Quasi-least squares (QLS) is an alternative method for estimating the correlation parameters within the framework of the generalized estimating equation (GEE) approach for analyzing correlated cross-sectional and longitudinal data. This article summarizes the development of QLS that occurred in several reports and describes its use with the user-written program xtqls in Stata. Also, it demonstrates the following advantages of QLS: (1) QLS allows some correlation structures that have not yet been implemented in the framework of GEE, (2) QLS can be applied as an alternative to GEE if the GEE estimate is infeasible, and (3) QLS uses the same estimating equation for estimation of beta as GEE; as a result, QLS can involve programs already available for GEE. In particular, xtqls calls the Stata program xtgee within an iterative approach that alternates between updating estimates of the correlation parameter a and then using xtgee to solve the GEE for beta at the current estimate of a. The benefit of this approach is that after xtqls, all the usual postregression estimation commands are readily available to the user.