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Modern Methods for Robust Regression offers a brief but in-depth treatment of various methods for detecting and properly handling influential cases in regression analysis. This volume, geared toward both future and practicing social scientists, is unique in that it takes an applied approach and offers readers empirical examples to illustrate key concepts. It is ideal for readers who are interested in the issues related to outliers and influential cases.
Key Features
- Defines key terms necessary to understanding the robustness of an estimator: Because they form the basis of robust regression techniques, the book also deals with various measures of location and scale.
- Addresses the robustness of validity and efficiency: After having described the robustness of validity for an estimator, the author discusses its efficiency.
- Focuses on the impact of outliers: The book compares the robustness of a wide variety of estimators that attempt to limit the influence of unusual observations.
- Gives an overview of some traditional techniques: Both formal statistical tests and graphical methods detect influential cases in the general linear model.
- Offers a Web appendix: This volume provides readers with the data and the R code for the examples used in the book.
Intended Audience
This is an excellent text for intermediate and advanced Quantitative Methods and Statistics courses offered at the graduate level across the social sciences.
List of Figures
List of Tables
Series Editor's Introduction
Acknowledgments
1. Introduction
Defining Robustness
Defining Robust Regression
A Real-World Example: Coital Frequency of Married Couples in the 1970s
2. Important Background
Bias and Consistency
Breakdown Point
Influence Function
Relative Efficiency
Measures of Location
Measures of Scale
M-Estimation
Comparing Various Estimates
Notes
3. Robustness, Resistance, and Ordinary Least Squares Regression
Ordinary Least Squares Regression
Implications of Unusual Cases for OLS Estimates and Standard Errors
Detecting Problematic Observations in OLS Regression
Notes
4. Robust Regression for the Linear Model
L-Estimators
R-Estimators
M-Estimators
GM-Estimators
S-Estimators
Generalized S-Estimators
MM-Estimators
Comparing the Various Estimators
Diagnostics Revisited: Robust Regression-Related Methods for Detecting Outliers
Notes
5. Standard Errors for Robust Regression
Asymptotic Standard Errors for Robust Regression Estimators
Bootstrapped Standard Errors
Notes
6. Influential Cases in Generalized Linear Models
The Generalized Linear Model
Detecting Unusual Cases in Generalized Linear Models
Robust Generalized Linear Models
Notes
7. Conclusions
Appendix: Software Considerations for Robust Regression
References
Index
About the Author
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