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Regression Diagnostics
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Regression Diagnostics
An Introduction

Second Edition


April 2020 | 168 pages | SAGE Publications, Inc

Regression diagnostics are methods for determining whether a regression model that has been fit to data adequately represents the structure of the data. For example, if the model assumes a linear (straight-line) relationship between the response and an explanatory variable, is the assumption of linearity warranted? Regression diagnostics not only reveal deficiencies in a regression model that has been fit to data but in many instances may suggest how the model can be improved. The Second Edition of this bestselling volume by John Fox considers two important classes of regression models: the normal linear regression model (LM), in which the response variable is quantitative and assumed to have a normal distribution conditional on the values of the explanatory variables; and generalized linear models (GLMs) in which the conditional distribution of the response variable is a member of an exponential family. R code and data sets for examples within the text can be found on an accompanying website at https://tinyurl.com/RegDiag.

 
Series Editors Introduction
 
About the Author
 
Acknowledgements
 
Chapter 1. Introduction
 
Chapter 2. The Linear Regression Model: Review
The Normal Linear Regression Models

 
Least-Squares Estimation

 
Statistical Inference for Regression Coefficients

 
The Linear Regression Model in Matrix Forms

 
 
Chapter 3. Examining and Transforming Regression Data
Univariate Displays

 
Transformations for Symmetry

 
Transformations for Linearity

 
Transforming Nonconstant Variation

 
Interpreting Results When Variables are Transformed

 
 
Chapter 4. Unusual data
Measuring Leverage: Hatvalues

 
Detecting Outliers: Studentized Residuals

 
Measuring Influence: Cook’s Distance and Other Case-Deletion Diagnostics

 
Numerical Cutoffs for Noteworthy Case Diagnostics

 
Jointly Influential Cases: Added-Variable Plots

 
Should Unusual Data Be Discarded?

 
Unusual Data: Details

 
 
Chapter 5. Non-Normality and Nonconstant Error Variance
Detecting and Correcting Non-Normality

 
Detecting and Dealing With Nonconstant Error Variance

 
Robust Coefficient Standard Errors

 
Bootstrapping

 
Weighted Least Squares

 
Robust Standard Errors and Weighted Least Squares: Details

 
 
Chapter 6. Nonlinearity
Component-Plus-Residual Plots

 
Marginal Model Plots

 
Testing for Nonlinearity

 
Modeling Nonlinear Relationships with Regression Splines

 
 
Chapter 7. Collinearity
Collinearity and Variance Inflation

 
Visualizing Collinearity

 
Generalized Variance Inflation

 
Dealing With Collinearity

 
*Collinearity: Some Details

 
 
Chapter 8. Diagnostics for Generalized Linear Models
Generalized Linear Models: Review

 
Detecting Unusual Data in GLMs

 
Nonlinearity Diagnostics for GLMs

 
Diagnosing Collinearity in GLMs

 
Quasi-Likelihood Estimation of GLMs

 
*GLMs: Further Background

 
 
Chapter 9. Concluding Remarks
Complementary Reading

 
 
References
 
Index

The work of a master who knows how to make regression come alive with engaging language and catchy graphics.

Helmut Norpoth
Stony Brook University
Review

This monograph provides very clear and quite comprehensive treatment of many tools and strategies for dealing with the various issues and situations that might arise to compromise the extent to which a regression model accurately represents the structure that exists within a dataset. As such, I would recommend this work to both beginners and experienced researchers in the social sciences. 

William G. Jacoby
Professor Emeritus, Michigan State University
Reviewer

John Fox has substantially updated his authoritative, compact, and accessible presentation on diagnosing and correcting problems in regression models. New sections on graphical inspection and transformation prior to analysis, and on diagnostics for generalized linear models enhance its utility. I recommend it strongly to instructors and practitioners alike.

Peter Marsden
Harvard University
Review

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Chapter 1. Introduction


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