A Comparison Of Five Robust Regression Methods With Ordinary Least Squares

Offering an in-depth treatment of robust and resistant regression, this volume takes an applied approach and offers readers empirical examples to illustrate key concepts.

The second edition features: a CD with all of the book's Amos, EQS, and LISREL programs and data sets; new chapters on importing data issues related to data editing and on how to report research; an updated introduction to matrix notation and programs that illustrate how to compute these calculations; many more computer program examples and chapter exercises; and increased coverage of factors that affect correlation, the 4-step approach to SEM and hypothesis testing, significance, power, and sample size issues. The new edition's expanded use of applications make this book ideal for advanced students and researchers in psychology, education, business, health care, political science, sociology, and biology. A basic understanding of correlation is assumed and an understanding of the matrices used in SEM models is encouraged.

A Beginner’s Guide to Structural Equation Modeling, fifth edition, has been redesigned with consideration of a true beginner in structural equation modeling (SEM) in mind. The book covers introductory through intermediate topics in SEM in more detail than in any previous edition. All of the chapters that introduce models in SEM have been expanded to include easy-to-follow, step-by-step guidelines that readers can use when conducting their own SEM analyses. These chapters also include examples of tables to include in results sections that readers may use as templates when writing up the findings from their SEM analyses. The models that are illustrated in the text will allow SEM beginners to conduct, interpret, and write up analyses for observed variable path models to full structural models, up to testing higher order models as well as multiple group modeling techniques. Updated information about methodological research in relevant areas will help students and researchers be more informed readers of SEM research. The checklist of SEM considerations when conducting and reporting SEM analyses is a collective set of requirements that will help improve the rigor of SEM analyses. This book is intended for true beginners in SEM and is designed for introductory graduate courses in SEM taught in psychology, education, business, and the social and healthcare sciences. This book also appeals to researchers and faculty in various disciplines. Prerequisites include correlation and regression methods.

An introduction to the theory and methods of robust statistics, providing students with practical methods for carrying out robust procedures in a variety of statistical contexts and explaining the advantages of these procedures. In addition, the text develops techniques and concepts likely to be useful in the future analysis of new statistical models and procedures. Emphasizing the concepts of breakdown point and influence functon of an estimator, it demonstrates the technique of expressing an estimator as a descriptive measure from which its influence function can be derived and then used to explore the efficiency and robustness properties of the estimator. Mathematical techniques are complemented by computational algorithms and Minitab macros for finding bootstrap and influence function estimates of standard errors of the estimators, robust confidence intervals, robust regression estimates and their standard errors. Includes examples and problems.

Ideal for experienced students and researchers in the social sciences who wish to refresh or extend their understanding of statistics, and to apply advanced statistical procedures using SPSS or R. Key theory is reviewed and illustrated with examples of how to apply these concepts using real data.

At the present time there is no well accepted test for comparing least squares and robust linear regression coefficient estimates. To fill this gap we propose and demonstrate the efficacy of two Wald-like statistical tests for the above purposes, using for robust regression the class of MM-estimators. The tests are designed to detect significant differences between least squares and robust estimates due to both inefficiency of least squares under fat-tailed non-normality and significantly larger biases of least squares relative to robust regression coefficient estimators under bias inducing distributions. The asymptotic normality of the test statistics is established and the finite sample level and power of the tests are evaluated by Monte Carlo, with the latter yielding promising results. The first part of our research focuses on the LS and robust regression slope estimators, both of which are consistent under skewed error distributions. A second part of the research focuses on intercept estimation, in which case there is a need to adjust for some bias in the robust MM-intercept estimator under skewed error distributions. An interesting by-product of our research is that use of the slowly re-descending Tukey bisquare loss function leads to better test performance than the rapidly re-descending min-max bias optimal loss function.