Quasi-Least Squares Regression

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Drawing on the authors' substantial expertise in modeling longitudinal and clustered data, this book presents a comprehensive treatment of quasi-least squares (QLS) regression — a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEE). The authors present an overview and detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. A fully worked out example is provided that leads readers from the planning stages of a study, including sample size considerations, through model construction and interpretation. Special focus is given to goodness-of-fit analysis and strategies on selecting the appropriate working correlation structure. The text includes additional examples throughout to demonstrate each topic of discussion and uses Stata for the majority of examples, along with corresponding R, SAS, and MATLABr code.

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Product Details

Meet the Author

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.

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Table of Contents

When QLS Might Be Considered as an Alternative to GEE
Motivating Studies

Review of Generalized Linear Models
Generalized Linear Models
Generalized Estimating Equations
Application 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 α
Stage-Two QLS Estimates of the Correlation Parameter for the AR(1) Structure
Algorithm for QLS
Other Approaches That Are Based on GEE

Mixed Linear Structures and Familial Data
Notation for Data from Nuclear Families
Familial Correlation Structures for Analysis of Data from Nuclear Families
Other 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 Structures
Demonstration 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 Working
Structure 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 Data
The Tri-Diagonal Correlation Structure
The AR(1) Structure for Analysis of (Planned) Equally Spaced Longitudinal Data
The Markov Structure for Analysis of Unequally Spaced Longitudinal Data
The Unstructured Matrix for Analysis of Balanced Data
Other Structures
Implementation of QLS for Patterned Correlation Structures

Analysis of Data with Multiple Sources of Correlation
Characteristics of Data with Multiple Sources of Correlation
Multi-Source Correlated Data That Are Totally Balanced
Multi-Source Correlated Data That Are Balanced within Clusters
Multi-Source Correlated Data That Are Unbalanced
Asymptotic Relative Efficiency Calculations

Correlated Binary Data
Additional Constraints for Binary Data
When Violation of the Prentice Constraints for Binary Data Is Likely to Occur
Implications of Violation of Constraints for Binary Data
Comparison between GEE, QLS, and MARK1ML
Prentice-Corrected QLS and GEE

Assessing Goodness of Fit and Choice of Correlation Structure for QLS and GEE
Simulation Scenarios
Simulation Results
Summary and Recommendations

Sample Size and Demonstration
Two-Group Comparisons
More Complex Situations
Worked Example
Discussion and Summary



Exercises appear at the end of each chapter.

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