Quasi-Least Squares Regression

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 MATLAB code.

Introduction Introduction When QLS Might Be Considered as an Alternative to GEE Motivating Studies Summary Review of Generalized Linear Models Background 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 alpha Stage-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 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 Summary Appendix 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 Summary Appendix 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 Summary 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 Bibliography Index Exercises appear at the end of each chapter.