Linear Regression Models: Applications in R
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| Author(s): John P. Hoffmann
Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences Publisher: Chapman and Hall/CRC, Year: 2021 ISBN: 0367753685,9780367753689 Description:
Research in social and behavioral sciences has benefited from linear regression models (LRMs) for decades to identify and understand the associations among a set of explanatory variables and an outcome variable. Linear Regression Models: Applications in R provides you with a comprehensive treatment of these models and indispensable guidance about how to estimate them using the R software environment.
After furnishing some background material, the author explains how to estimate simple and multiple LRMs in R, including how to interpret their coefficients and understand their assumptions. Several chapters thoroughly describe these assumptions and explain how to determine whether they are satisfied and how to modify the regression model if they are not. The book also includes chapters on specifying the correct model, adjusting for measurement error, understanding the effects of influential observations, and using the model with multilevel data. The concluding chapter presents an alternative model―logistic regression―designed for binary or two-category outcome variables. The book includes appendices that discuss data management and missing data and provides simulations in R to test model assumptions.
Features
The book is aimed primarily at advanced undergraduate and graduate students in social, behavioral, health sciences, and related disciplines, taking a first course in linear regression. It could also be used for self-study and would make an excellent reference for any researcher in these fields. The R code and detailed examples provided throughout the book equip the reader with an excellent set of tools for conducting research on numerous social and behavioral phenomena.
John P. Hoffmann is a professor of sociology at Brigham Young University where he teaches research methods and applied statistics courses and conducts research on substance use and criminal behavior. |
| Table of contents : Cover Half Title Series Page Title Page Copyright Page Table of Contents Preface Acknowledgments Author Biography Chapter 1 Introduction Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win Best Statistical Practices Statistical Software Chapter 2 Review of Elementary Statistical Concepts Measures of Central Tendency Measures of Dispersion Samples and Populations Sampling Error and Standard Errors Significance Tests Unbiasedness and Efficiency The Standard Normal Distribution and Z-Scores Covariance and Correlation Comparing Means from Two Groups Examples Using R Chapter Summary Chapter Exercises Chapter 3 Simple Linear Regression Models Assumptions of Simple LRMs An Example of an LRM Using R Formulas for the Slope Coefficient and Intercept Hypothesis Tests for the Slope Coefficient Chapter Summary Chapter Exercises Chapter 4 Multiple Linear Regression Models An Example of a Multiple LRM Comparing Slope Coefficients Assumptions of Multiple LRMs Some Important Characteristics of Multiple LRMs Chapter Summary Chapter Exercises Chapter 5 The ANOVA Table and Goodness-of-Fit Statistics Another Example of a Multiple LRM Chapter Summary Chapter Exercises Chapter 6 Comparing Linear Regression Models The Partial F-Test and Multiple Partial F-Test Evaluating Model Fit with Information Criterion Measures Confounding Variables Chapter Summary Chapter Exercises Chapter 7 Indicator Variables in Linear Regression Models Indicator Variables in Multiple LRMs LRMs with Indicator and Continuous Explanatory Variables Chapter Summary Chapter Exercises Chapter 8 Independence Determining Dependence Example of Adjustment for Clustering LRM with No Adjustment for Clustering LRM That Adjusts for Clustering Serial Correlation Linear Regression Model Solutions for Serial Correlation Linear Regression Model (OLS) Prais–Winsten Regression Model Generalized Estimating Equations for Longitudinal Data Linear Regression Model (OLS) General Estimating Equation (GEE) Model with AR(1) Pattern General Estimating Equation (GEE) Model with Unstructured Pattern Spatial Autocorrelation Chapter Summary Chapter Exercises Chapter 9 Homoscedasticity Assessing Homoscedasticity in Multiple LRMs What to Do About Heteroscedasticity Chapter Summary Chapter Exercises Chapter 10 Collinearity and Multicollinearity Multicollinearity How to Detect Collinearity and Multicollinearity What to Do About Collinearity and Multicollinearity Chapter Summary Chapter Exercises Chapter 11 Normality, Linearity, and Interaction Effects Are the Errors of Prediction Normally Distributed? Nonlinearities Testing for Nonlinearities in LRMs Incorporating Nonlinear Associations in LRMs Interaction Effects Interaction Effects with Continuous Explanatory Variables Classification and Regression Trees (CART) A Cautionary Note about Interaction Effects Chapter Summary Chapter Exercises Chapter 12 Model Specification Variable Selection Overfitting—or the Case of Irrelevant Variables Underfitting—or the Case of the Absent Variables Endogeneity Bias Selection Bias How Do We Assess Specification Error and What Do We Do about It? What to Do about Selection Bias? Cross-Validation Variable Selection Procedures Chapter Summary Chapter Exercises Chapter 13 Measurement Errors The Outcome Variable Is Measured with Error The Explanatory Variables Are Measured with Error What Should We Do about Measurement Error? Latent Variables as a Solution to Measurement Error Chapter Summary Chapter Exercises Chapter 14 Influential Observations: Leverage Points and Outliers Detecting Influential Observations An Example of Using Diagnostic Methods to Identify Influential Observations What to Do about Influential Observations Chapter Summary Chapter Exercises Chapter 15 Multilevel Linear Regression Models The Basics of Multilevel Regression Models The Multilevel LRM Examining Assumptions of the Model Group-Level Variables and Cross-Level Interactions Chapter Summary Chapter Exercises Chapter 16 A Brief Introduction to Logistic Regression An Alternative to the LRM: Logistic Regression Extending the Logistic Regression Model Chapter Summary Chapter Exercises Chapter 17 Conclusions Sampling Weights Establishing Causal Associations Final Words Linear Regression Modeling: A Summary Appendix A: Data Management Appendix B: Using Simulations to Examine Assumptions of Linear Regression Models Appendix C: Selected Formulas Appendix D: User-Written R Packages Employed in the Examples References Index |
