Beyond Multiple Linear Regression

Höfundar: Paul Roback; Julie Legler (Útgáfa: 1)
Beyond Multiple Linear Regression

Kaup valmöguleikar

Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner.

The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling.

Nánar um bókina

Útgefandi
Taylor & Francis
ISBN
9780429527333
Print ISBN
9780367680442
Format
ePub
Útgáfa
1
Höfundar
Paul Roback; Julie Legler
Tungumál
English
Útgefið
2021-01-14
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Cover
  • Half Title
  • Series
  • Title
  • Copyright
  • Dedication
  • Contents
  • Preface
  • 1 Review of Multiple Linear Regression
  • 1.1 Learning Objectives
  • 1.2 Introduction to Beyond Multiple Linear Regression
  • 1.3 Assumptions for Linear Least Squares Regression
  • 1.3.1 Cases Without Assumption Violations
  • 1.3.2 Cases With Assumption Violations
  • 1.4 Review of Multiple Linear Regression
  • 1.4.1 Case Study: Kentucky Derby
  • 1.5 Initial Exploratory Analyses
  • 1.5.1 Data Organization
  • 1.5.2 Univariate Summaries
  • 1.5.3 Bivariate Summaries
  • 1.6 Multiple Linear Regression Modeling
  • 1.6.1 Simple Linear Regression with a Continuous Predictor
  • 1.6.2 Linear Regression with a Binary Predictor
  • 1.6.3 Multiple Linear Regression with Two Predictors
  • 1.6.4 Inference in Multiple Linear Regression: Normal Theory
  • 1.6.5 Inference in Multiple Linear Regression: Bootstrapping
  • 1.6.6 Multiple Linear Regression with an Interaction Term
  • 1.6.7 Building a Multiple Linear Regression Model
  • 1.7 Preview of Remaining Chapters
  • 1.7.1 Soccer
  • 1.7.2 Elephant Mating
  • 1.7.3 Parenting and Gang Activity
  • 1.7.4 Crime
  • 1.8 Exercises
  • 1.8.1 Conceptual Exercises
  • 1.8.2 Guided Exercises
  • 1.8.3 Open-Ended Exercises
  • 2 Beyond Least Squares: Using Likelihoods
  • 2.1 Learning Objectives
  • 2.2 Case Study: Does Sex Run in Families?
  • 2.2.1 Research Questions
  • 2.3 Model 0: Sex Unconditional, Equal Probabilities
  • 2.4 Model 1: Sex Unconditional, Unequal Probabilities
  • 2.4.1 What Is a Likelihood?
  • 2.4.2 Finding MLEs
  • 2.4.2.1 Graphically approximating an MLE
  • 2.4.2.2 Numerically approximating an MLE
  • 2.4.2.3 MLEs using calculus (optional)
  • 2.4.2.4 How does sample size affect the likelihood?
  • 2.4.3 Summary
  • 2.4.4 Is a Likelihood a Probability Function? (optional)
  • 2.5 Model 2: Sex Conditional
  • 2.5.1 Model Specification
  • 2.5.2 Application to Hypothetical Data
  • 2.6 Case Study: Analysis of the NLSY Data
  • 2.6.1 Model Building Plan
  • 2.6.2 Exploratory Data Analysis
  • 2.6.3 Likelihood for the Sex Unconditional Model
  • 2.6.4 Likelihood for the Sex Conditional Model
  • 2.6.5 Model Comparisons
  • 2.6.5.1 Nested models
  • 2.7 Model 3: Stopping Rule Model (waiting for a boy)
  • 2.7.1 Non-nested Models
  • 2.8 Summary of Model Building
  • 2.9 Likelihood-Based Methods
  • 2.10 Likelihoods and This Course
  • 2.11 Exercises
  • 2.11.1 Conceptual Exercises
  • 2.11.2 Guided Exercises
  • 2.11.3 Open-Ended Exercises
  • 3 Distribution Theory
  • 3.1 Learning Objectives
  • 3.2 Introduction
  • 3.3 Discrete Random Variables
  • 3.3.1 Binary Random Variable
  • 3.3.2 Binomial Random Variable
  • 3.3.3 Geometric Random Variable
  • 3.3.4 Negative Binomial Random Variable
  • 3.3.5 Hypergeometric Random Variable
  • 3.3.6 Poisson Random Variable
  • 3.4 Continuous Random Variables
  • 3.4.1 Exponential Random Variable
  • 3.4.2 Gamma Random Variable
  • 3.4.3 Normal (Gaussian) Random Variable
  • 3.4.4 Beta Random Variable
  • 3.5 Distributions Used in Testing
  • 3.5.1 χ2 Distribution
  • 3.5.2 Student's t-Distribution
  • 3.5.3 F-Distribution
  • 3.6 Additional Resources
  • 3.7 Exercises
  • 3.7.1 Conceptual Exercises
  • 3.7.2 Guided Exercises
  • 4 Poisson Regression
  • 4.1 Learning Objectives
  • 4.2 Introduction to Poisson Regression
  • 4.2.1 Poisson Regression Assumptions
  • 4.2.2 A Graphical Look at Poisson Regression
  • 4.3 Case Studies Overview
  • 4.4 Case Study: Household Size in the Philippines
  • 4.4.1 Data Organization
  • 4.4.2 Exploratory Data Analyses
  • 4.4.3 Estimation and Inference
  • 4.4.4 Using Deviances to Compare Models
  • 4.4.5 Using Likelihoods to Fit Models (optional)
  • 4.4.6 Second Order Model
  • 4.4.7 Adding a Covariate
  • 4.4.8 Residuals for Poisson Models (optional)
  • 4.4.9 Goodness-of-Fit
  • 4.5 Linear Least Squares vs. Poisson Regression
  • 4.6 Case Study: Campus Crime
  • 4.6.1 Data Organization
  • 4.6.2 Exploratory Data Analysis
  • 4.6.3 Accounting for Enrollment
  • 4.7 Modeling Assumptions
  • 4.8 Initial Models
  • 4.8.1 Tukey's Honestly Significant Differences
  • 4.9 Overdispersion
  • 4.9.1 Dispersion Parameter Adjustment
  • 4.9.2 No Dispersion vs. Overdispersion
  • 4.9.3 Negative Binomial Modeling
  • 4.10 Case Study: Weekend Drinking
  • 4.10.1 Research Question
  • 4.10.2 Data Organization
  • 4.10.3 Exploratory Data Analysis
  • 4.10.4 Modeling
  • 4.10.5 Fitting a ZIP Model
  • 4.10.6 The Vuong Test (optional)
  • 4.10.7 Residual Plot
  • 4.10.8 Limitations
  • 4.11 Exercises
  • 4.11.1 Conceptual Exercises
  • 4.11.2 Guided Exercises
  • 4.11.3 Open-Ended Exercises
  • 5 Generalized Linear Models: A Unifying Theory
  • 5.1 Learning Objectives
  • 5.2 One-Parameter Exponential Families
  • 5.2.1 One-Parameter Exponential Family: Poisson
  • 5.2.2 One-Parameter Exponential Family: Normal
  • 5.3 Generalized Linear Modeling
  • 5.4 Exercises
  • 6 Logistic Regression
  • 6.1 Learning Objectives
  • 6.2 Introduction to Logistic Regression
  • 6.2.1 Logistic Regression Assumptions
  • 6.2.2 A Graphical Look at Logistic Regression
  • 6.3 Case Studies Overview
  • 6.4 Case Study: Soccer Goalkeepers
  • 6.4.1 Modeling Odds
  • 6.4.2 Logistic Regression Models for Binomial Responses
  • 6.4.3 Theoretical Rationale (optional)
  • 6.5 Case Study: Reconstructing Alabama
  • 6.5.1 Data Organization
  • 6.5.2 Exploratory Analyses
  • 6.5.3 Initial Models
  • 6.5.4 Tests for Significance of Model Coefficients
  • 6.5.5 Confidence Intervals for Model Coefficients
  • 6.5.6 Testing for Goodness-of-Fit
  • 6.5.7 Residuals for Binomial Regression
  • 6.5.8 Overdispersion
  • 6.5.9 Summary
  • 6.6 Linear Least Squares vs. Binomial Regression
  • 6.7 Case Study: Trying to Lose Weight
  • 6.7.1 Data Organization
  • 6.7.2 Exploratory Data Analysis
  • 6.7.3 Initial Models
  • 6.7.4 Drop-in-Deviance Tests
  • 6.7.5 Model Discussion and Summary
  • 6.8 Exercises
  • 6.8.1 Conceptual Exercises
  • 6.8.2 Guided Exercises
  • 6.8.3 Open-Ended Exercises
  • 7 Correlated Data
  • 7.1 Learning Objectives
  • 7.2 Introduction
  • 7.3 Recognizing Correlation
  • 7.4 Case Study: Dams and Pups
  • 7.5 Sources of Variability
  • 7.6 Scenario 1: No Covariates
  • 7.7 Scenario 2: Dose Effect
  • 7.8 Case Study: Tree Growth
  • 7.8.1 Format of the Data Set
  • 7.8.2 Sources of Variability
  • 7.8.3 Analysis Preview: Accounting for Correlation
  • 7.9 Summary
  • 7.10 Exercises
  • 7.10.1 Conceptual Exercises
  • 7.10.2 Guided Exercises
  • 7.10.3 Note on Correlated Binary Outcomes
  • 8 Introduction to Multilevel Models
  • 8.1 Learning Objectives
  • 8.2 Case Study: Music Performance Anxiety
  • 8.3 Initial Exploratory Analyses
  • 8.3.1 Data Organization
  • 8.3.2 Exploratory Analyses: Univariate Summaries
  • 8.3.3 Exploratory Analyses: Bivariate Summaries
  • 8.4 Two-Level Modeling: Preliminary Considerations
  • 8.4.1 Ignoring the Two-Level Structure (not recommended)
  • 8.4.2 A Two-Stage Modeling Approach (better but imperfect)
  • 8.5 Two-Level Modeling: A Unified Approach
  • 8.5.1 Our Framework
  • 8.5.2 Random vs. Fixed Effects
  • 8.5.3 Distribution of Errors: Multivariate Normal
  • 8.5.4 Technical Issues when Testing Parameters (optional)
  • 8.5.5 An Initial Model with Parameter Interpretations
  • 8.6 Building a Multilevel Model
  • 8.6.1 Model Building Strategy
  • 8.6.2 An Initial Model: Random Intercepts
  • 8.7 Binary Covariates at Level One and Level Two
  • 8.7.1 Random Slopes and Intercepts Model
  • 8.7.2 Pseudo R-squared Values
  • 8.7.3 Adding a Covariate at Level Two
  • 8.8 Adding Further Covariates
  • 8.8.1 Interpretation of Parameter Estimates
  • 8.8.2 Model Comparisons
  • 8.9 Centering Covariates
  • 8.10 A Final Model for Music Performance Anxiety
  • 8.11 Modeling Multilevel Structure: Is It Necessary?
  • 8.12 Notes on Using R (optional)
  • 8.13 Exercises
  • 8.13.1 Conceptual Exercises
  • 8.13.2 Guided Exercises
  • 8.13.3 Open-Ended Exercises
  • 9 Two-Level Longitudinal Data
  • 9.1 Learning Objectives
  • 9.2 Case Study: Charter Schools
  • 9.3 Initial Exploratory Analyses
  • 9.3.1 Data Organization
  • 9.3.2 Missing Data
  • 9.3.3 Exploratory Analyses for General Multilevel Models
  • 9.3.4 Exploratory Analyses for Longitudinal Data
  • 9.4 Preliminary Two-Stage Modeling
  • 9.4.1 Linear Trends Within Schools
  • 9.4.2 Effects of Level Two Covariates on Linear Time Trends
  • 9.4.3 Error Structure Within Schools
  • 9.5 Initial Models
  • 9.5.1 Unconditional Means Model
  • 9.5.2 Unconditional Growth Model
  • 9.5.3 Modeling Other Trends over Time
  • 9.6 Building to a Final Model
  • 9.6.1 Uncontrolled Effects of School Type
  • 9.6.2 Add Percent Free and Reduced Lunch as a Covariate
  • 9.6.3 A Final Model with Three Level Two Covariates
  • 9.6.4 Parametric Bootstrap Testing
  • 9.7 Covariance Structure among Observations
  • 9.7.1 Standard Covariance Structure
  • 9.7.2 Alternative Covariance Structures
  • 9.7.3 Non-longitudinal Multilevel Models
  • 9.7.4 Final Thoughts Regarding Covariance Structures
  • 9.7.5 Details of Covariance Structures (optional)
  • 9.8 Notes on Using R (optional)
  • 9.9 Exercises
  • 9.9.1 Conceptual Exercises
  • 9.9.2 Guided Exercises
  • 9.9.3 Open-Ended Exercises
  • 10 Multilevel Data With More Than Two Levels
  • 10.1 Learning Objectives
  • 10.2 Case Studies: Seed Germination
  • 10.3 Initial Exploratory Analyses
  • 10.3.1 Data Organization
  • 10.3.2 Exploratory Analyses
  • 10.4 Initial Models
  • 10.4.1 Unconditional Means
  • 10.4.2 Unconditional Growth
  • 10.5 Encountering Boundary Constraints
  • 10.6 Parametric Bootstrap Testing
  • 10.7 Exploding Variance Components
  • 10.8 Building to a Final Model
  • 10.9 Covariance Structure (optional)
  • 10.9.1 Details of Covariance Structures
  • 10.10 Notes on Using R (optional)
  • 10.11 Exercises
  • 10.11.1 Conceptual Exercises
  • 10.11.2 Guided Exercises
  • 10.11.3 Open-Ended Exercises
  • 11 Multilevel Generalized Linear Models
  • 11.1 Learning Objectives
  • 11.2 Case Study: College Basketball Referees
  • 11.3 Initial Exploratory Analyses
  • 11.3.1 Data Organization
  • 11.3.2 Exploratory Analyses
  • 11.4 Two-Level Modeling with a Generalized Response
  • 11.4.1 A GLM Approach
  • 11.4.2 A Two-Stage Modeling Approach
  • 11.4.3 A Unified Multilevel Approach
  • 11.5 Crossed Random Effects
  • 11.6 Parametric Bootstrap for Model Comparisons
  • 11.7 A Final Model for Examining Referee Bias
  • 11.8 Estimated Random Effects
  • 11.9 Notes on Using R (optional)
  • 11.10 Exercises
  • 11.10.1 Conceptual Exercises
  • 11.10.2 Open-Ended Exercises
  • Bibliography
  • Index