Quasi-Least Squares Regression

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Quasi Least Squares (QLS) regression is a computational approach for estimation of the correlation parameters in the framework of generalized estimating equations (GEE). The methodology ameliorates some of the difficulties that some statisticians and analysts have had with GEE. For example, it yields consistent estimators of the correlation parameters that for some patterns of association are also gauranteed to yield positive definite estimated working correlation structures. As a result, QLS can sometimes be implemented as an alternative approach should convergence be an issue for GEE. In addition, the method allows for application of correlation structures that are not currently available in the major software packages that allow for implementation of GEE. As a result, QLS can be used to extend the application of GEE for analysis of data with unequal temporal spacing on patients; data that arise within families; or, data with multiple sources of correlation. This monograph explains the theoretical underpinnings of QLS and will also describe how to implement QLS in a variety of settings, primarily using software in Stata, but with code also provided for some examples in SAS, Matlab, and R.


This book summarizes new and prior research on quasi-least squares regression, including results from an NIH funded R01 project (for J. Shults) that developed improved approaches for longitudinal analysis of data from diverse populations (LADP). As described in its abstract, the aims of this project involved developing practical exensions of GEE that included applying QLS for a wide range of correlation models not currently implemented for GEE and providing approaches for sample size and power calculations for these structures. This book would therefore appeal to statisticians who are interested in extensions of GEE, either for their own methodological research, or for application in a particular data analysis.

Prior to its official publication (and with the approval of our editor Rob Calver) this monograph was also used as the text for an Advanced Elective that was offered by J. Shults for graduate students in the http://www.cceb.med.upenn.edu/education/bio-degree/" target="_blank"> Ph.D. program in Biostatistics at the University of Pennsylvania. This course was designed for students who have completed most of their coursework for a Ph.D. program in Biostatistics. This monograph would therefore be suitable as the text for advanced graduate students who are enrolled in a Ph.D. program in Biostatistics, or in Statistics. Prerequisites for the course would include Linear Models, with some knowledge of longitudinal data analysis (and in particular GEE) being helpful.


Justine Shults in an Associate Professor of Biostatistics in the Department of Biostatistics and Epidemiology at the University of Pennsylvania School of Medicine, the Co-director of the Pediatrics Biostatistics Section within the Division of Biostatistics in the Department of Biostatistics and Epidemiology in the CCEB, the Statistical Editor of the Journal of the Pediatric Infectious Diseases Society, the Statistics Section Editor of Springer Plus, and is currently the principal investigator of the NIH funded Renal and urologic biostatistics training grant (T32DK060455). She was funded by the National Science Foundation and was the principal investigator of the NIH funded LADP project, on whose findings this monograph is largely based. She was one of the developers of QLS (with N. Rao Chaganty) and participated in the development of software for QLS in Stata, SAS, Matlab, and R.

Joseph M. Hilbe is an emeritus professor at the University of Hawaii, an adjunct professor of statistics at Arizona State University, and Solar System Ambassador at NASA's Jet Propulsion Laboratory. An elected Fellow of the American Statistical Association and elected member (Fellow) of the International Statistical Institute, Professor Hilbe is chair of the International Astrostatistics Network, is currently on the editorial boards of six statistics journals and is author of several popular texts in statistical modeling, including two editions of Negative Binomial Regression (Cambridge Univ. Press), Logistic Regression Models (Chapman & Hall/CRC), and with James Hardin, Generalized estimating Equations, (C&H/CRC) and three editions of Generalized Linear Models and Extensions (Stata Press). He is also the author (with Robert Muenchen) of R for Stata Users (Springer).