Quasi-Least Squares Regression

Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.

Introduction Introduction When QLS Might Be Considered as an Alternative to GEE Motivating StudiesSummary Review of Generalized Linear Models BackgroundGeneralized Linear ModelsGeneralized Estimating EquationsApplication for Obesity Study Provided in Chapter One Quasi-Least Squares Theory and Applications History and Theory of QLS Regression Why QLS Is a "Quasi" Least Squares Approach The Least-Squares Approach Employed in Stage One of QLS for Estimation of aStage-Two QLS Estimates of the Correlation Parameter for the AR(1) Structure Algorithm for QLS Other Approaches That Are Based on GEE Example Summary Mixed Linear Structures and Familial Data Notation for Data from Nuclear Families Familial Correlation Structures for Analysis of Data from Nuclear FamiliesOther Work on Assessment of Familial Correlations with QLS Justification of Implementation of QLS for Familial Structures via Consideration of the Class of Mixed Linear Correlation StructuresDemonstration of QLS for Analysis of Balanced Familial Data Using Stata Software Demonstration of QLS for Analysis of Unbalanced Familial Data Using R Software Simulations to Compare Implementation of QLS with Correct Specification of the Trio Structure versus Correct Specification with GEE and Incorrect Specification of the Exchangeable WorkingStructure with GEE Summary and Future Research Directions Correlation Structures for Clustered and Longitudinal Data Characteristics of Clustered and Longitudinal Data The Exchangeable Correlation Structure for Clustered DataThe Tri-Diagonal Correlation StructureThe AR(1) Structure for Analysis of (Planned) Equally Spaced Longitudinal DataThe Markov Structure for Analysis of Unequally Spaced Longitudinal DataThe Unstructured Matrix for Analysis of Balanced DataOther Structures Implementation of QLS for Patterned Correlation StructuresSummaryAppendix Analysis of Data with Multiple Sources of Correlation Characteristics of Data with Multiple Sources of Correlation Multi-Source Correlated Data That Are Totally BalancedMulti-Source Correlated Data That Are Balanced within ClustersMulti-Source Correlated Data That Are UnbalancedAsymptotic Relative Efficiency Calculations Summary Appendix Correlated Binary DataAdditional Constraints for Binary DataWhen Violation of the Prentice Constraints for Binary Data Is Likely to OccurImplications of Violation of Constraints for Binary Data Comparison between GEE, QLS, and MARK1MLPrentice-Corrected QLS and GEESummary Assessing Goodness of Fit and Choice of Correlation Structure for QLS and GEE Simulation ScenariosSimulation ResultsSummary and Recommendations Sample Size and Demonstration Two-Group ComparisonsMore Complex Situations Worked ExampleDiscussion and Summary Bibliography Index Exercises appear at the end of each chapter.

Justine Shults is an associate professor and co-director of the Pediatrics Section in the Division of Biostatistics in the Perelman School of Medicine at the University of Pennsylvania, where she is the principal investigator of the biostatistics training grant in renal and urologic diseases. She is the Statistical Editor of the Journal of the Pediatric Infectious Disease Society and the Statistical Section Editor of Springer Plus. Professor Shults (with N. Rao Chaganty) developed Quasi-Least Squares (QLS) and was funded by the National Science Foundation and the National Institutes of Health to extend QLS and develop user-friendly software for implementing her new methodology. She has authored or co-authored over 100 peer-reviewed publications, including the initial papers on QLS for unbalanced and unequally spaced longitudinal data and on MARK1ML and the choice of working correlation structure for GEE. Joseph M. Hilbe is a Solar System Ambassador with the Jet Propulsion Laboratory, an adjunct professor of statistics at Arizona State University, and an Emeritus Professor at the University of Hawaii. An elected fellow of the American Statistical Association and an elected member of the International Statistical Institute (ISI), Professor Hilbe is president of the International Astrostatistics Association as well as chair of the ISI Sports Statistics and Astrostatistics committees. He has authored two editions of the bestseller Negative Binomial Regression, Logistic Regression Models, and Astrostatistical Challenges for the New Astronomy. He also co-authored Methods of Statistical Model Estimation (with A. Robinson), Generalized Estimating Equations, Second Edition (with J. Hardin), and R for Stata Users (with R. Muenchen), as well as 17 encyclopedia articles and book chapters in the past five years.