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Regression & Linear Modeling
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Regression & Linear Modeling
Best Practices and Modern Methods

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March 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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Summary

 
Enrichment

 
 
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

 
Summary

 
Enrichment

 
 
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

 
Summary

 
Enrichment

 
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

 
Enrichment

 
 
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

 
Summary

 
Enrichment

 
 
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

 
Exercises

 
 
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

 
Summary

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Enrichment

 
 
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

 
Summary

 
 
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

 
Summary

 
Enrichment

 

Supplements

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

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Jason W. Osborne

Jason W. Osborne is Associate Provost and Dean of the Graduate School at Clemson University in Clemson, South Carolina.  He is also Professor of Applied Statistics in the Department of Mathematical Sciences, with a secondary appointment in Public Health Science.  He teaches and publishes on "best practices" in quantitative and applied research methods. He has served as evaluator or consultant on projects in public education (K-12), instructional technology, higher education, nursing and health care, medicine and medical training, epidemiology, business and marketing, and jury selection in death penalty cases. He served as... More About Author

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ISBN: 9781506302768
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