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E-raamat: Beyond Multiple Linear Regression: Applied Generalized Linear Models And Multilevel Models in R

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Beyond Multiple Linear Regression: Applied Generalized Linear Models And Multilevel Models in RSuurem pilt
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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 books 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)

Arvustused

"Overall, this is an excellent text that is highly appropriate for undergraduate students. I am a really big fan of Chapter 2. The authors introduce the concepts of likelihood and model comparisons via likelihood in a very gentle and intuitive way. It will be very useful for the wide audience anticipated for the course we are designing. In Chapter 4, the authors do an excellent job discussing some of the common extensions of Poisson regression that are likely to be observed in practice (overdispersion and ZIP). In particular, they do an excellent job describing situations that might lead to zero-inflate Poissons. The use of case studies across all chapters is a major strength of the textbook." -Jessica Chapman, St. Lawrence University

"This text would be ideal for statistics undergrad majors & minors as a 2nd or 3rd course in statisticsIn particular, this book intuitively covers many topics without delving into technical proofs and details which are not needed for successful application of the methods described. It is a strength that it uses the software R. Use of R is a skill welcomed in any industry, and is not a burden for students to obtain. The book emphasizes methods as well as numerical literacy. For example, it guides the student in how to assess the appropriateness of methods (e.g. assumptions of linear model), not just the use and interpretation of the results. There is a strong focus on understanding and checking assumptions, as well as the effect violations of those assumptions will have on the result. I think this may be an effective way to train the reader to think like a statistician, without overwhelming the reader with technical details." ---Kirsten Eilertson, Colorado State University "Overall, this is an excellent text that is highly appropriate for undergraduate students. I am a really big fan of Chapter 2. The authors introduce the concepts of likelihood and model comparisons via likelihood in a very gentle and intuitive way. It will be very useful for the wide audience anticipated for the course we are designing. In Chapter 4, the authors do an excellent job discussing some of the common extensions of Poisson regression that are likely to be observed in practice (overdispersion and ZIP). In particular, they do an excellent job describing situations that might lead to zero-inflate Poissons.

The use of case studies across all chapters is a major strength of the textbook." (Jessica Chapman, St. Lawrence University)

"This text would be ideal for statistics undergrad majors & minors as a 2nd or 3rd course in statisticsIn particular, this book intuitively covers many topics without delving into technical proofs and details which are not needed for successful application of the methods described. It is a strength that it uses the software R. Use of R is a skill welcomed in any industry, and is not a burden for students to obtain. The book emphasizes methods as well as numerical literacy. For example, it guides the student in how to assess the appropriateness of methods (e.g. assumptions of linear model), not just the use and interpretation of the results. There is a strong focus on understanding and checking assumptions, as well as the effect violations of those assumptions will have on the result. I think this may be an effective way to train the reader to think like a statistician, without overwhelming the reader with technical details." (Kirsten Eilertson, Colorado State University)

Kirsten.Eilertson@colostate.edu

"There are a lot of books about linear models, but it is not that common to find a really good book about this interesting and complex subject. The book Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R can for sure be included in this category of good books about linear models"

- David Manteigas, International Society for Clinical Biostatistics, 72, 2021

Preface xv
1 Review of Multiple Linear Regression 1(38)
1.1 Learning Objectives
1(2)
1.2 Introduction to Beyond Multiple Linear Regression
1(2)
1.3 Assumptions for Linear Least Squares Regression
3(5)
1.3.1 Cases Without Assumption Violations
4(2)
1.3.2 Cases With Assumption Violations
6(2)
1.4 Review of Multiple Linear Regression
8(1)
1.4.1 Case Study: Kentucky Derby
8(1)
1.5 Initial Exploratory Analyses
8(4)
1.5.1 Data Organization
8(1)
1.5.2 Univariate Summaries
9(1)
1.5.3 Bivariate Summaries
9(3)
1.6 Multiple Linear Regression Modeling
12(14)
1.6.1 Simple Linear Regression with a Continuous Predictor
12(5)
1.6.2 Linear Regression with a Binary Predictor
17(1)
1.6.3 Multiple Linear Regression with Two Predictors
18(1)
1.6.4 Inference in Multiple Linear Regression: Normal Theory
19(1)
1.6.5 Inference in Multiple Linear Regression: Bootstrapping
20(2)
1.6.6 Multiple Linear Regression with an Interaction Term
22(2)
1.6.7 Building a Multiple Linear Regression Model
24(2)
1.7 Preview of Remaining
Chapters
26(3)
1.7.1 Soccer
26(1)
1.7.2 Elephant Mating
27(1)
1.7.3 Parenting and Gang Activity
28(1)
1.7.4 Crime
28(1)
1.8 Exercises
29(10)
1.8.1 Conceptual Exercises
29(3)
1.8.2 Guided Exercises
32(4)
1.8.3 Open-Ended Exercises
36(3)
2 Beyond Least Squares: Using Likelihoods 39(32)
2.1 Learning Objectives
39(1)
2.2 Case Study: Does Sex Run in Families?
40(2)
2.2.1 Research Questions
41(1)
2.3 Model 0: Sex Unconditional, Equal Probabilities
42(1)
2.4 Model 1: Sex Unconditional, Unequal Probabilities
43(7)
2.4.1 What Is a Likelihood?
43(3)
2.4.2 Finding MLEs
46(3)
2.4.3 Summary
49(1)
2.4.4 Is a Likelihood a Probability Function? (optional)
50(1)
2.5 Model 2: Sex Conditional
50(3)
2.5.1 Model Specification
50(1)
2.5.2 Application to Hypothetical Data
51(2)
2.6 Case Study: Analysis of the NLSY Data
53(8)
2.6.1 Model Building Plan
53(1)
2.6.2 Exploratory Data Analysis
54(1)
2.6.3 Likelihood for the Sex Unconditional Model
55(1)
2.6.4 Likelihood for the Sex Conditional Model
56(2)
2.6.5 Model Comparisons
58(3)
2.7 Model 3: Stopping Rule Model (waiting for a boy)
61(3)
2.7.1 Non-nested Models
63(1)
2.8 Summary of Model Building
64(1)
2.9 Likelihood-Based Methods
65(1)
2.10 Likelihoods and This Course
66(1)
2.11 Exercises
67(4)
2.11.1 Conceptual Exercises
67(1)
2.11.2 Guided Exercises
67(1)
2.11.3 Open-Ended Exercises
68(3)
3 Distribution Theory 71(22)
3.1 Learning Objectives
71(1)
3.2 Introduction
71(1)
3.3 Discrete Random Variables
72(8)
3.3.1 Binary Random Variable
72(1)
3.3.2 Binomial Random Variable
73(1)
3.3.3 Geometric Random Variable
74(1)
3.3.4 Negative Binomial Random Variable
75(2)
3.3.5 Hypergeometric Random Variable
77(2)
3.3.6 Poisson Random Variable
79(1)
3.4 Continuous Random Variables
80(5)
3.4.1 Exponential Random Variable
80(1)
3.4.2 Gamma Random Variable
81(2)
3.4.3 Normal (Gaussian) Random Variable
83(1)
3.4.4 Beta Random Variable
84(1)
3.5 Distributions Used in Testing
85(3)
3.5.1 X2 Distribution
86(1)
3.5.2 Student's t-Distribution
87(1)
3.5.3 F-Distribution
87(1)
3.6 Additional Resources
88(1)
3.7 Exercises
88(5)
3.7.1 Conceptual Exercises
88(2)
3.7.2 Guided Exercises
90(3)
4 Poisson Regression 93(52)
4.1 Learning Objectives
93(1)
4.2 Introduction to Poisson Regression
94(2)
4.2.1 Poisson Regression Assumptions
95(1)
4.2.2 A Graphical Look at Poisson Regression
95(1)
4.3 Case Studies Overview
96(1)
4.4 Case Study: Household Size in the Philippines
97(16)
4.4.1 Data Organization
98(1)
4.4.2 Exploratory Data Analyses
98(4)
4.4.3 Estimation and Inference
102(2)
4.4.4 Using Deviances to Compare Models
104(2)
4.4.5 Using Likelihoods to Fit Models (optional)
106(1)
4.4.6 Second Order Model
107(2)
4.4.7 Adding a Covariate
109(1)
4.4.8 Residuals for Poisson Models (optional)
110(2)
4.4.9 Goodness-of-Fit
112(1)
4.5 Linear Least Squares vs. Poisson Regression
113(1)
4.6 Case Study: Campus Crime
114(4)
4.6.1 Data Organization
114(1)
4.6.2 Exploratory Data Analysis
115(2)
4.6.3 Accounting for Enrollment
117(1)
4.7 Modeling Assumptions
118(1)
4.8 Initial Models
118(3)
4.8.1 Tukey's Honestly Significant Differences
119(2)
4.9 Overdispersion
121(4)
4.9.1 Dispersion Parameter Adjustment
121(2)
4.9.2 No Dispersion vs. Overdispersion
123(1)
4.9.3 Negative Binomial Modeling
123(2)
4.10 Case Study: Weekend Drinking
125(8)
4.10.1 Research Question
125(1)
4.10.2 Data Organization
126(1)
4.10.3 Exploratory Data Analysis
126(1)
4.10.4 Modeling
127(2)
4.10.5 Fitting a ZIP Model
129(2)
4.10.6 The Vuong Test (optional)
131(1)
4.10.7 Residual Plot
132(1)
4.10.8 Limitations
132(1)
4.11 Exercises
133(12)
4.11.1 Conceptual Exercises
133(3)
4.11.2 Guided Exercises
136(6)
4.11.3 Open-Ended Exercises
142(3)
5 Generalized Linear Models: A Unifying Theory 145(6)
5.1 Learning Objectives
145(1)
5.2 One-Parameter Exponential Families
145(3)
5.2.1 One-Parameter Exponential Family: Poisson
146(1)
5.2.2 One-Parameter Exponential Family: Normal
147(1)
5.3 Generalized Linear Modeling
148(1)
5.4 Exercises
149(2)
6 Logistic Regression 151(42)
6.1 Learning Objectives
151(1)
6.2 Introduction to Logistic Regression
151(2)
6.2.1 Logistic Regression Assumptions
152(1)
6.2.2 A Graphical Look at Logistic Regression
153(1)
6.3 Case Studies Overview
153(1)
6.4 Case Study: Soccer Goalkeepers
154(5)
6.4.1 Modeling Odds
155(1)
6.4.2 Logistic Regression Models for Binomial Responses
155(3)
6.4.3 Theoretical Rationale (optional)
158(1)
6.5 Case Study: Reconstructing Alabama
159(11)
6.5.1 Data Organization
159(1)
6.5.2 Exploratory Analyses
160(1)
6.5.3 Initial Models
161(1)
6.5.4 Tests for Significance of Model Coefficients
162(1)
6.5.5 Confidence Intervals for Model Coefficients
163(1)
6.5.6 Testing for Goodness-of-Fit
164(2)
6.5.7 Residuals for Binomial Regression
166(1)
6.5.8 Overdispersion
167(3)
6.5.9 Summary
170(1)
6.6 Linear Least Squares vs. Binomial Regression
170(1)
6.7 Case Study: Trying to Lose Weight
171(10)
6.7.1 Data Organization
172(1)
6.7.2 Exploratory Data Analysis
173(3)
6.7.3 Initial Models
176(3)
6.7.4 Drop-in-Deviance Tests
179(1)
6.7.5 Model Discussion and Summary
180(1)
6.8 Exercises
181(12)
6.8.1 Conceptual Exercises
181(1)
6.8.2 Guided Exercises
182(7)
6.8.3 Open-Ended Exercises
189(4)
7 Correlated Data 193(18)
7.1 Learning Objectives
193(1)
7.2 Introduction
193(1)
7.3 Recognizing Correlation
194(1)
7.4 Case Study: Dams and Pups
195(1)
7.5 Sources of Variability
195(1)
7.6 Scenario 1: No Covariates
196(3)
7.7 Scenario 2: Dose Effect
199(4)
7.8 Case Study: Tree Growth
203(4)
7.8.1 Format of the Data Set
204(1)
7.8.2 Sources of Variability
205(1)
7.8.3 Analysis Preview: Accounting for Correlation
206(1)
7.9 Summary
207(1)
7.10 Exercises
207(4)
7.10.1 Conceptual Exercises
207(2)
7.10.2 Guided Exercises
209(1)
7.10.3 Note on Correlated Binary Outcomes
210(1)
8 Introduction to Multilevel Models 211(52)
8.1 Learning Objectives
211(1)
8.2 Case Study: Music Performance Anxiety
212(1)
8.3 Initial Exploratory Analyses
213(7)
8.3.1 Data Organization
213(1)
8.3.2 Exploratory Analyses: Univariate Summaries
214(2)
8.3.3 Exploratory Analyses: Bivariate Summaries
216(4)
8.4 Two-Level Modeling: Preliminary Considerations
220(5)
8.4.1 Ignoring the Two-Level Structure (not recommended)
220(1)
8.4.2 A Two-Stage Modeling Approach (better but imperfect)
221(4)
8.5 Two-Level Modeling: A Unified Approach
225(9)
8.5.1 Our Framework
225(2)
8.5.2 Random vs. Fixed Effects
227(1)
8.5.3 Distribution of Errors: Multivariate Normal
227(2)
8.5.4 Technical Issues when Testing Parameters (optional)
229(2)
8.5.5 An Initial Model with Parameter Interpretations
231(3)
8.6 Building a Multilevel Model
234(2)
8.6.1 Model Building Strategy
234(1)
8.6.2 An Initial Model: Random Intercepts
234(2)
8.7 Binary Covariates at Level One and Level Two
236(6)
8.7.1 Random Slopes and Intercepts Model
236(3)
8.7.2 Pseudo R-squared Values
239(1)
8.7.3 Adding a Covariate at Level Two
240(2)
8.8 Adding Further Covariates
242(4)
8.8.1 Interpretation of Parameter Estimates
243(2)
8.8.2 Model Comparisons
245(1)
8.9 Centering Covariates
246(2)
8.10 A Final Model for Music Performance Anxiety
248(3)
8.11 Modeling Multilevel Structure: Is It Necessary?
251(3)
8.12 Notes on Using R (optional)
254(1)
8.13 Exercises
255(8)
8.13.1 Conceptual Exercises
255(1)
8.13.2 Guided Exercises
256(2)
8.13.3 Open-Ended Exercises
258(5)
9 Two-Level Longitudinal Data 263(58)
9.1 Learning Objectives
263(1)
9.2 Case Study: Charter Schools
264(1)
9.3 Initial Exploratory Analyses
265(8)
9.3.1 Data Organization
265(1)
9.3.2 Missing Data
266(2)
9.3.3 Exploratory Analyses for General Multilevel Models
268(1)
9.3.4 Exploratory Analyses for Longitudinal Data
269(4)
9.4 Preliminary Two-Stage Modeling
273(6)
9.4.1 Linear Trends Within Schools
273(1)
9.4.2 Effects of Level Two Covariates on Linear Time Trends
274(5)
9.4.3 Error Structure Within Schools
279(1)
9.5 Initial Models
279(7)
9.5.1 Unconditional Means Model
280(1)
9.5.2 Unconditional Growth Model
281(3)
9.5.3 Modeling Other Trends over Time
284(2)
9.6 Building to a Final Model
286(15)
9.6.1 Uncontrolled Effects of School Type
286(3)
9.6.2 Add Percent Free and Reduced Lunch as a Covariate
289(2)
9.6.3 A Final Model with Three Level Two Covariates
291(3)
9.6.4 Parametric Bootstrap Testing
294(7)
9.7 Covariance Structure among Observations
301(7)
9.7.1 Standard Covariance Structure
302(3)
9.7.2 Alternative Covariance Structures
305(1)
9.7.3 Non-longitudinal Multilevel Models
306(1)
9.7.4 Final Thoughts Regarding Covariance Structures
306(1)
9.7.5 Details of Covariance Structures (optional)
307(1)
9.8 Notes on Using R (optional)
308(1)
9.9 Exercises
309(12)
9.9.1 Conceptual Exercises
309(3)
9.9.2 Guided Exercises
312(4)
9.9.3 Open-Ended Exercises
316(5)
10 Multilevel Data With More Than Two Levels 321(52)
10.1 Learning Objectives
321(1)
10.2 Case Studies: Seed Germination
322(1)
10.3 Initial Exploratory Analyses
323(9)
10.3.1 Data Organization
323(2)
10.3.2 Exploratory Analyses
325(7)
10.4 Initial Models
332(5)
10.4.1 Unconditional Means
333(2)
10.4.2 Unconditional Growth
335(2)
10.5 Encountering Boundary Constraints
337(6)
10.6 Parametric Bootstrap Testing
343(6)
10.7 Exploding Variance Components
349(3)
10.8 Building to a Final Model
352(6)
10.9 Covariance Structure (optional)
358(5)
10.9.1 Details of Covariance Structures
361(2)
10.10 Notes on Using R (optional)
363(1)
10.11 Exercises
364(9)
10.11.1 Conceptual Exercises
364(4)
10.11.2 Guided Exercises
368(2)
10.11.3 Open-Ended Exercises
370(3)
11 Multilevel Generalized Linear Models 373(36)
11.1 Learning Objectives
373(1)
11.2 Case Study: College Basketball Referees
374(1)
11.3 Initial Exploratory Analyses
374(6)
11.3.1 Data Organization
374(2)
11.3.2 Exploratory Analyses
376(4)
11.4 Two-Level Modeling with a Generalized Response
380(6)
11.4.1 A GLM Approach
380(1)
11.4.2 A Two-Stage Modeling Approach
381(3)
11.4.3 A Unified Multilevel Approach
384(2)
11.5 Crossed Random Effects
386(4)
11.6 Parametric Bootstrap for Model Comparisons
390(4)
11.7 A Final Model for Examining Referee Bias
394(4)
11.8 Estimated Random Effects
398(1)
11.9 Notes on Using R (optional)
399(2)
11.10 Exercises
401(8)
11.10.1 Conceptual Exercises
401(4)
11.10.2 Open-Ended Exercises
405(4)
Bibliography 409(8)
Index 417
Authors

Paul Roback is the Kenneth O. Bjork Distinguished Professor of Statistics and Data Science and Julie Legler is Professor Emeritus of Statistics at St. Olaf College in Northfield, MN. Both are Fellows of the American Statistical Association and are founders of the Center for Interdisciplinary Research at St. Olaf. Dr. Roback is the past Chair of the ASA Section on Statistics and Data Science Education, conducts applied research using multilevel modeling, text analysis, and Bayesian methods, and has been a statistical consultant in the pharmaceutical, health care, and food processing industries. Dr. Legler is past Chair of the ASA/MAA Joint Committee on Undergraduate Statistics, is a co-author of Stat2: Modelling with Regression and ANOVA, and was a biostatistician at the National Cancer Institute.
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