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Regression & Linear Modeling

Regression & Linear Modeling
Best Practices and Modern Methods

June 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?



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.

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Saint Louis University

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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.”

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University of Pennsylvania

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