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Regression & Linear Modeling

Regression & Linear Modeling
Best Practices and Modern Methods

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April 2016 | 488 pages | SAGE Publications, Inc
In a conversational tone, Regression & Linear Modeling provides conceptual, user-friendly coverage of the generalized linear model (GLM). Readers will become familiar with applications of ordinary least squares (OLS) regression, binary and multinomial logistic regression, ordinal regression, Poisson regression, and loglinear models. The author returns to certain themes throughout the text, such as testing assumptions, examining data quality, and, where appropriate, nonlinear and non-additive effects modeled within different types of linear models.

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Chapter 1: A Nerdly Manifesto
The Variables Lead the Way  
Different Classifications of Measurement  
It’s All About Relationships!  
A Brief Review of Basic Algebra and Linear Equations  
The GLM in One Paragragh  
A Brief Consideration of Prediction  
A Brief Primer on Null Hypothesis Statistical Testing  
A Tale of Two Errors  
What Conclusions Can We Draw Based on NHST Results?  
So What Does Failure to Reject the Null Hypothesis Mean?  
Moving Beyond NHST  
The Importance of Replication and Generalizability  
Where We Go From Here  
Chapter 2: Basic Estimation and Assumptions
Estimation and the GLM  
What Is OLS Estimation?  
ML Estimation—A Gentle but Deeper Look  
Assumptions for OLS and ML Estimation  
Simple Univariate Data Cleaning and Data Transformations  
What If We Cannot Meet the Assumptions?  
Where We Go From Here  
Chapter 3: Simple Linear Models With Continuous Dependent Variables: Simple Regression Analyses
Advance Organizer  
It’s All About Relationships!  
Basics of the Pearson Product-Moment Correlation Coefficient  
Calculating r  
Effect Sizes and r  
A Real Data Example  
The Basics of Simple Regression  
Basic Calculations for Simple Regression  
Standardized Versus Unstandardized Regression Coefficients  
Hypothesis Testing in Simple Regression  
A Real Data Example  
Does Centering or z-Scoring Make a Difference?  
Some Simple Multivariate Data Cleaning  
Chapter 4: Simple Linear Models With Continuous Dependent Variables: Simple ANOVA Analyses
Advance Organizer  
It’s All About Relationships! (Part 2)  
Analyzing These Data via t-Test  
Analyzing These Data via ANOVA  
ANOVA Within an OLS Regression Framework  
When Your IV Has More Than Two Groups: Dummy Coding Your Unordered Polytomous Variable  
Smoking and Diabetes Analyzed via ANOVA  
Smoking and Diabetes Analyzed via Regression  
What If the Dummy Variables Are Coded Differently?  
Unweighted Effects Coding  
Weighted Effects Coding  
Common Alternatives to Dummy or Effects Coding  
Chapter 5: Simple Linear Models With Categorical Dependent Variables: Binary Logistic Regression
Advance Organizer  
It’s All About Relationships! (Part 3)  
The Linear Probability Model  
How Logistic Regression Solves This Issue: The Logit Link Function  
A Brief Digression Into Probabilities, Conditional Probabilities, and Odds  
Simple Logistic Regression Using Statistical Software  
The Logistic Regression Equation  
Interpreting the Constant  
What If You Want CIs for the Constant?  
Summary So Far  
Logistic Regression With a Continuous IV  
Some Best Practices When Using a Continuous Variable in Logistic Regression  
Testing Assumptions and Data Cleaning in Logistic Regression  
Hosmer and Lemeshow Test for Model Fit  
Appendix 5A: A Brief Primer in Probit Regression  
Chapter 6: Simple Linear Models With Polytomous Categorical Dependent Variables: Multinomial and Ordinal Logistic Regression
Advance Organizer  
Understanding Marijuana Use  
Dummy-Coded DVs and Our Hypotheses to Be Tested  
Basics and Calculations  
Multinomial Logistic Regression (Unordered) With Statistical Software  
Multinomial Logistic Regression With a Continuous Predictor  
Multinomial Logistic Regression as a Series of Binary Logistic Regressions  
Data Cleaning and Multinomial Logistic Regression  
Testing Whether Groups Can Be Combined  
Ordered Logit (Proportional Odds) Model  
Assumptions of the Ordinal Logistic Model  
Interpreting the Results of the Ordinal Regression  
Interpreting the Intercepts/Thresholds  
Interpreting the Parameter Estimates  
Data Cleaning and More Advanced Models in Ordinal Logistic Regression  
The Measured Variable is Continous, Why Not Just Use OLS Regression for This Type of Analysis?  
A Brief Note on Log-Linear Analyses  
Summary and Conclusions  
Chapter 7: Simple Curvilinear Models
Advance Organizer  
Zeno’s Paradox, a Nerdy Science Joke, and Inherent Curvilinearity in the Universe…  
A Brief Review of Simple Algebra  
Hypotheses to Be Tested  
Illegitimate Causes of Curvilinearity  
Detection of Nonlinear Effects  
Basic Principles of Curvilinear Regression  
Curvilinear OLS Regression Example: Size of the University and Faculty Salary  
Data Cleaning  
Interpreting Curvilinear Effects Effectively  
Reality Testing This Effect  
Summary of Curvilinear Effects in OLS Regression  
Curvilinear Logistic Regression Example: Diabetes and Age  
Curvilinear Effects in Multinomial Logistic Regression  
Replication Becomes Important  
More Fun With Curves: Estimating Minima and Maxima as Well as Slope at Any Point on the Curve  
Chapter 8: Multiple Independent Variables
Advance Organizer  
The Basics of Multiple Predictors  
What Are the Implications of This Act?  
Hypotheses to Be Tested in Multiple Regression  
Assumptions of Multiple Regression and Data Cleaning  
Predicting Student Achievement From Real Data  
Testing Assumptions and Data Cleaning in the NELS88 Data  
Methods of Entering Variables  
Using Multiple Regression for Theory Testing  
Logistic Regression With Multiple IVs  
Assessing the Overall Logistic Regression Model: Why There Is No R2 for Logistic Regression  
Summary and conclusions  
Chapter 9: Interactions Between Independent Variables: Simple moderation
Advance Organizer  
What is an Interaction?  
Procedural and Conceptual Issues in Testing for Interactions Between Continuous Variables  
Procedural and Conceptual Issues in Testing for Interactions Containing Categorical Variables  
Hypotheses to Be Tested in Multiple Regression With Interactions Present  
An OLS Regression Example: Predicting Student Achievement From Real Data  
Interpreting the Results From a Significant Interaction  
Graphing Interaction Effects  
An Interaction Between a Continuous and a Categorical Variable in OLS Regression  
Interactions With Logistic Regression  
Example Summary of Interaction Analysis  
Interactions and Multinomial Logistic Regression  
Example Summary of Findings  
Can These Effects Replicate?  
Post Hoc Probing of Interactions  
Chapter 10: Curvilinear Interactions Between Independent Variables
Advance Organizer  
What is a Curvilinear Interaction?  
A Quadratic Interaction Between X and Z  
A Cubic Interaction Between X and Z  
A Real-Data Example and Exploration of Procedural Details  
Curvilinear Interactions Between Continuous and Categorical Variables  
Curvilinear Interactions With Categorical DVs (Multinomial Logistic)  
Curvilinear Interaction Effects in Ordinal Regression  
Chapter Summary  
Chapter 11: Poisson Models: Low-Frequency Count Data as Dependent Variables
Advance Organizer  
The Basics and Assumptions of Poisson Regression  
Why Can’t We Just Analyze Count Data via OLS, Multinomial, or Ordinal Regression?  
Hypotheses Tested in Poisson Regression  
Poisson Regression With Real Data  
Interactions in Poisson regression  
Data Cleaning in Poisson Regression  
Refining the Model by Eliminating Excess (Inappropriate) Zeros  
A Refined Analysis With Excess Zeros Removed  
Curvilinear Effects in Poisson Regression  
Dealing With Overdispersion or Underdispersion  
Negative Binomial Model  
Summary and Conclusions  
Chapter 12: Log-Linear Models: General Linear Models When All of Your Variables Are Unordered Categorical
Advance Organizer  
The Basics of Loglinear Analysis  
Hypotheses Being Tested  
Assumptions of Loglinear Models  
A Slightly More Complex Loglinear Model  
Can We Replicate These Results in Logistic Regression?  
Data Cleaning in Loglinear Models  
Summary and Conclusions  
Chapter 13: A Brief Introduction to Hierarchical Linear Modeling
Advance Organizer  
Why HLM models Are Necessary  
How Do Hierarchical Models Work? A Brief Primer  
Generalizing the Basic HLM Model  
Residuals in HLM  
Results of DROPOUT Analysis in HLM  
Summary and Conclusions  
Chapter 14: Missing Data in Linear Modeling
Advance Organizer  
Not All Missing Data Are the Same  
Categories of Missingness: Why Do We Care If Data Are MCAR or Not?  
How Do You Know If Your Data Are MCAR, MAR, or MNAR?  
What Do We Do With Randomly Missing Data?  
Data MCAR  
Data MNAR  
How Missingness Can Be an Interesting Variable in and of Itself  
Summing Up: Benefits of Appropriately Handling Missing Data  
Chapter 15: Trustworthy Science: Improving Statistical Reporting
Advance Organizer  
What Is Power, and Why Is It Important?  
Power in Linear Models  
Summary of Points Thus Far  
Who Cares as Long as p < .05? Volatility in Linear Models  
A Brief Introduction to Bootstrap Resampling  
Summary and Conclusions  
Chapter 16: Reliable Measurement Matters
Advance Organizer  
A More Modern View of Reliability  
What is Cronbach’s Alpha (and What Is It Not)?  
Factors That Influence Alpha  
What Is “Good Enough” for Alpha?  
Reliability and Simple Correlation or Regression  
Reliability and Multiple IVs  
Reliability and Interactions in Multiple Regression  
Protecting Against Overcorrecting During Disattenuation  
Other (Better) Solutions to the Issue of Measurement Error  
Does Reliability Influence Other Analyses, Such as Analysis of Variance?  
Reliability in Logistic Models  
But Other Authors Have Argued That Poor Reliability Isn’t That Important. Who Is Right?  
Sample Size and the Precision/Stability of Alpha-Empirical CIs  
Summary and Conclusions  
Chapter 17: Prediction in the Generalized Linear Model
Advance Organizer  
Prediction vs. Explanation  
How is a Prediction Equation Created?  
Shrinkage and Evaluating the Quality of Prediction Equations  
An Example Using Real Data  
Improving on Prediction Models  
Calculating a Predicted Score, and CIs Around That Score  
Prediction (Prognostication) in Logistic Regression (and Other) Models  
An Example of External Validation of a Prognostic Equation Using Real Data  
External Validation of a Prediction Equation  
Using Bootstrap Analysis to Estimate a More Robust Prognostic Equation  
Chapter 18: Modeling in Large, Complex Samples: The Importance of Using Appropriate Weights and Design Effect Compensation
Advance Organizer  
What Types of Studies Use Complex Sampling?  
Why Does Complex Sampling Matter?  
What Are Best Practices in Accounting for Complex Sampling?  
Does It Really Make a Difference in the Results?  
Conditions Used  
Comparison of Unweighted Versus Weighted Analyses  


Companion Website
Data sets for the exercises and additional resources are available on the free open-access site.

“I really enjoyed reading this, which is rare to say about a statistics textbook. The style of writing is very approachable, and the material is presented in a way that is informative even to someone who thinks about these topics often.”

Cort W. Rudolph
Saint Louis University

“The author has taught this subject matter for years. . . . He speaks to me as I face similar situations in the classroom. He writes in an accessible way for those who are not methodologists.”

Bruce McCollaum
The University of North Carolina at Greensboro

“The conversational language is a strength of the text. I can see it helping to put some otherwise anxious readers at ease. The author’s sharing of their experience in data analysis is a nice touch, too. The manner in which the material is presented is not at all threatening or intimidating.”

Timothy W. Victor
University of Pennsylvania
Key features

  • An applied, non-mathematical perspective helps readers understand complex topics in a straightforward and practical manner.
  • User-friendly tutorials cover basic multilevel models (MLM/HLM), missing data, replication and bootstrap resampling applications, reliability, prediction, and weighting.
  • Use of real, publicly available data from a variety of disciplines makes the content more relevant and valuable to students.
  • Chapter-ending enrichment exercises reinforce basic learning objectives, requiring students to use real data as they replicate findings from the chapter and then attempt similar analyses on new data sets.
  • Chapters containing guides for how to perform the analyses in SPSS allow students to apply concepts learned (although the text is written so that it can be used with any common statistical package).

Sample Materials & Chapters

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