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Generalizing the Regression Model

Generalizing the Regression Model
Techniques for Longitudinal and Contextual Analysis

February 2021 | 688 pages | SAGE Publications, Inc

This comprehensive text introduces regression, the general linear model, structural equation modeling, the hierarchical linear model, growth curve models, panel data, and event history models, and includes discussion of published implementations of each technique showing how it was used to address substantive and interesting research questions. It takes a step-by-step approach in the presentation of each topic, using mathematical derivations where necessary, but primarily emphasizing how the methods involved can be implemented, are used in addressing representative substantive problems than span a number of disciplines, and can be interpreted in words. The book demonstrates the analyses in STATA and SAS. Generalizing the Regression Model provides students with a bridge from the classroom to actual research practice and application.

A website for the book at (coming soon!) includes resources for instructors and students.

Reviewer Acknowledgements
About the Authors
Chapter 1: A Review of Correlation and Regression

1.1 Association in a Bivariate Table

1.2 Correlation as a Measure of Association

1.3 Bivariate Regression Theory

1.4 Partitioning of Variance in Bivariate Regression

1.5 Bivariate Regression Example

1.6 Assumptions of the Regression Model

1.7 Multiple Regression

1.8 A Multiple Regression Example: The Gender Pay Gap

1.9 Dummy Variables

Concluding Words

Practice Questions

Chapter 2: Generalizations of Regression 1: Testing and Interpreting Interactions
2.0.1 Limitations of the Additive Model

2.1 Interactions in Multiple Regression

2.2 A Three-Way Interaction Between Education, Race, and Gender

2.3 Interactions Involving Continuous Variables

2.4 Interactions Between Categorical Variables: The N-Way Analysis of Variance

2.5 Cautions In Studying Interactions

2.6 Published Examples

Concluding Words

Practice Questions

Chapter 3: Generalizations of Regression 2: Nonlinear Regression

3.1 A simple example of a quadratic relationship

3.2 Estimating Higher-Order Relationships

3.3 Basic Math for nonlinear models

3.4 Interpretation of Nonlinear Functions

3.5 An Alternative Approach Using Dummy Variables

3.6 Spline Regression

3.7 Published Examples

Concluding Words

Practice Questions

Chapter 4: Generalizations of Regression 3: Logistic Regression
4.1 A First Take: The Linear Probability Model

4.2 The logistic Regression MODEL

4.3 Interpreting Logistic Models

4.4 Running a Logistic Regression in Statistical Software

4.5 Multinomial Logistic Regression

4.6 The Ordinal Logit Model

4.7 Estimation of Logistic Models

4.8 Tests for Logistic Regression

4.9 Published Examples

Concluding Words

Practice Questions

Chapter 5: Generalizations of Regression 4: The Generalized Linear Model
5.1 The Poisson Regression Model

5.2 The Complementary Log-Mog Model

5.3 Published Examples

Concluding Words

Practice Questions

Chapter 6: From Equations to Models: The Process of Explanation
6.1 What is Wrong With Equations?

6.2 Equations versus Models: Some Examples

6.3 Why Causality?

6.4 Criteria For Causality

6.5 The analytical roles of Variables in causal models

6.6 Interpretating an association using controls and mediators

6.7 Special Cases

6.8 From Recursive to Non-Recursive Models: What to do about reciprocal  Causation

6.9 Published Examples

Concluding Words

Practice Questions

Chapter 7: An Introduction to Structural Equation Models
7.1 Latent Variables

7.2 Identifying the Factor analysis Model

7.3 The Full Sem model

7.4 Published Examples

Concluding Words

Practice Question

Chapter 8: Identification and Testing of Models
8.1 Identification

8.2 Testing And Fitting Models

8.3 Published Examples

Concluding Words

Practice Questions

Chapter 9: Variations and Extensions of SEM
9.1 The Comparative SEM framework

9.2 A Multiple Group Example

9.3 SEM for Nonnormal and Ordinal Data

9.4 Nonlinear Effects in SEM Models

Concluding Words

Chapter 10: An Introduction to Hierarchical Linear Models
10.1 Introduction to the Model

10.2 A Formal Statement of a Two-Level HLM Model

10.3 Sub-Models of the Full HLM Model

10.4 The Three-Level Hierarchical Linear Model

10.5 Implications of Centering Level-1 Variables

10.6 Sample Size Consideations

10.7 Estimating Multilevel Models IN SAS and STATA

10.8 Estimating a Three-Level Model

10.9 Published Examples

Concluding Words

Practice Questions

Chapter 11: The Generalized Hierarchical Linear Model
11.1 Multilevel Logistic Regression

11.2 Running the Generalized HLM in SAS

11.3 Multilevel Poisson Regression

11.4 Published Example

Concluding Words

Chapter 12: Growth Curve Models
12.1 Deriving the Structure of Growth Models

12.2 Running Growth Models in SAS

12.3 Modeling The Trajectory of Net Worth From Early to Mid-Adulthood

12.4 Modeling the Trajectory of Internalizing Problems over Adolescence

12.5 Published Examples

Concluding Words

Practice Questions

Chapter 13: Introduction to Regression for Panel Data
13.1 The Generalized Panel Regression Model

13.2 Examples of Panel Eegression

13.3 Published Examples

Concluding Words

Practice Questions

Chapter 14: Variations and Extensions of Panel Regression
14.1 Models for the Effects of events between Waves

14.2 Dynamic Panel Models

14.3 Fixed Effect Methods For Logistic Regression

14.4 Fixed-Effects Methods For Structural Equation Models

14.5 Published Example

Concluding Words

Chapter 15: Event History Analysis in Discrete Time
15.1 Overview of Concepts and Models

15.2 The Discrete-Time Event History Model

15.3 Basic Concepts

15.4 Creating and Analyzing A Person-Period Data Set

15.5 Studying Women’s Entry into the Work Role After Having a First Child

15.6 The Competing Risks Model

15.7 Repeated Events: The Multiple

15.8 Published Example

Concluding Words

Practice Questions

Chapter 16: The Continuous Time Event History Model
16.1 The Proportional Hazards Model

16.2 The Complementary Log-Log Model

Concluding Words


Quantitative analyses are so often relegated to OLS techniques when they should not be. The authors more than adequately demonstrate the why, what, and how other procedures (GMM, SEM, panel regression, event history analysis to name a few) are far superior to the OLS approaches widely but inappropriately found in published research or used in practice. Kudos to them.

Dane Joseph
George Fox University

Generalizing the Regression Model is a highly accessible textbook that covers a remarkable array of complex material with ease. Its applications and examples make the material intuitive and interesting for students to learn.

Jennifer Hayes Clark
University of Houston