Beyond Multiple Linear Regression

Name: Beyond Multiple Linear Regression
Price: 5690 ISK
Availability: InStock
Author: Paul Roback; Julie Legler
ISBN: 9780429527333

Höfundar: Paul Roback; Julie Legler (Útgáfa: 1)

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.

A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR)

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

Flokkar: Stærðfræði og tölfræði Tölvunarfræði

Efnisflokkar: Stærðfræði › Afturvirk greining Tölvur › Stærðfræðileg og tölfræðileg forrit

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