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E-raamat: Practical Multilevel Modeling Using R

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Practical Multilevel Modeling Using R provides students with a step-by-step guide for running their own multilevel analyses. Detailed examples illustrate the conceptual and statistical issues that multilevel modeling addresses in a way that is clear and relevant to students in applied disciplines. Clearly annotated R syntax illustrates how multilevel modeling (MLM) can be used, and real-world examples show why and how modeling decisions can affect results. The book covers all the basics but also important advanced topics such as diagnostics, detecting and handling heteroscedasticity, power analysis, and missing data handling methods. Unlike other detailed texts on MLM which are written at a very high level, this text with its applied focus and use of R software to run the analyses is much more suitable for students who have substantive research areas but are not training to be methodologists or statisticians. Each chapter concludes with a "Test Yourself" section, and solutions are available on the instructor website for the book. A companion R package is available for use with this text.

Arvustused

A major strength of this book is its accessibility. Huang effortlessly bridges the divide between the sometimes-abstruse literature on advanced statistics and the needs of applied researchers who lack extensive quantitative training. The result is an approachable text that covers all the basics, but also does not shy away from important advanced topics such as diagnostics, detecting and handling heteroscedasticity, and missing data handling methods. This book would make not only a useful guide to the application of multilevel modeling, but could also serve as an excellent companion text for a course on multilevel modeling. -- Kristopher J. Preacher This book is an excellent book for a graduate level multilevel modeling course that utilizes R; it perfectly combines the depth and breadth on this topic. -- Wei Wang

Acknowledgments xv
Preface xvii
About the Author xix
1 Introduction
1(10)
1.1 Why Bother With Multilevel Modeling?
1(4)
1.2 Why Another MLM Book?
5(1)
1.3 Using R for MLM
6(5)
2 The Unconditional Means Model
11(12)
Learning Objectives
11(1)
2.1 Understanding MLM Notation
11(4)
2.2 Fitting an Unconditional/Null Model
15(6)
2.2.1 Computing the Intraclass Correlation Coefficient
19(1)
2.2.2 Understanding the ICC Further
20(1)
2.3 Summary
21(2)
Test Yourself
22(1)
3 Adding Predictors to a Random Intercept Model
23(20)
Learning Objectives
23(1)
3.1 Adding a Level-1 Predictor
24(5)
3.1.1 How Much Variance Is Explained at Level One?
28(1)
3.2 Creating and Adding Level-2 Predictors
29(1)
3.2.1 How Much Variance Is Explained at Level Two?
30(4)
3.2.2 What About an Overall R2?
34(1)
3.2.3 Adding Categorical Predictors at Level Two
35(1)
3.2.3.1 Changing the Reference Group of a Factor
36(1)
3.3 Revisiting the Need for Multilevel Models
37(3)
3.3.1 Comparing MLM and OLS Regression Results
37(1)
3.3.2 Can We Really Ignore Clustering If the ICC Is Low?
38(1)
3.3.2.1 Design Effects
39(1)
3.4 Summary
40(3)
Test Yourself
41(2)
4 Investigating Cross-Level Interactions and Random Slope Models
43(20)
Learning Objectives
43(1)
4.1 Testing for Cross-Level Interactions
43(5)
4.1.1 Using a Likelihood Ratio Test (LRT) for Fixed Effects
45(3)
4.2 Investigating the Presence of Random Slopes
48(7)
4.2.1 Using a Modified LRT for Random Effects
52(3)
4.3 Revisiting the Random Intercept
55(2)
4.4 When Should Random Slopes Be Included?
57(1)
4.5 Dealing With Modeling Issues
58(2)
4.6 Summary
60(3)
Test Yourself
61(2)
5 Understanding Growth Models
63(20)
Learning Objectives
63(1)
5.1 Introduction
63(2)
5.2 Exploring and Reshaping the Data
65(6)
5.2.1 Plotting Using the lattice Package
67(3)
5.2.1.1 Computing Means by Groups
70(1)
5.3 Specifying the Multilevel Growth Model
71(9)
5.3.1 The Unconditional Growth Model
71(2)
5.3.2 Adding a Random Slope
73(2)
5.3.3 Adding a Person-Level Predictor
75(3)
5.3.4 An Alternative Approach: Using Robust Standard Errors
78(2)
5.4 Summary
80(3)
Test Yourself
81(2)
6 Centering in Multilevel Models
83(20)
Learning Objectives
83(1)
6.1 What Is Centering?
83(1)
6.2 Types of Centering
84(1)
6.3 Understanding Different Effects Related to Centering
85(9)
6.3.1 The Total Effect
85(2)
6.3.2 The Wlthin-Group Effect
87(2)
6.3.2.1 The Fixed Effects Approach
89(1)
6.3.2.2 Including the Group Mean Approach
90(2)
6.3.3 The Between-Group Effect
92(1)
6.3.4 The Compositional/Contextual Effect
93(1)
6.4 Respecifying the Models Using MLM
94(1)
6.5 Centering Binary Variables
95(5)
6.6 Which Type of Centering to Use?
100(1)
6.7 Summary
100(3)
Test Yourself
101(2)
7 Multilevel Modeling Diagnostics
103(30)
Learning Objectives
103(1)
7.1 Why Conduct Regression Diagnostics?
103(3)
7.2 Residual Diagnostics
106(23)
7.2.1 Spotting Nonlinear Relationships
106(6)
7.2.2 Detecting Outliers
112(3)
7.2.3 Assessing Normality
115(3)
7.2.4 Understanding Influential Data
118(5)
7.2.5 Assessing Issues Related to Homoskedasticity
123(2)
7.2.5.1 Using the H Statistic
125(1)
7.2.5.2 Using Robust Standard Errors
126(3)
7.3 Multicollinearity
129(1)
7.4 Summary
130(3)
Test Yourself
131(2)
8 Multilevel Logistic Regression Models
133(18)
Learning Objectives
133(1)
8.1 Introduction
133(1)
8.2 Fitting a Multilevel Logistic Regression Model
134(11)
8.2.1 Understanding Our Data
135(2)
8.2.2 Getting the ICC
137(3)
8.2.3 Adding Predictors of Interest
140(3)
8.2.4 Obtaining an R2 Measure
143(2)
8.3 Dealing With Nonconvergence Issues
145(3)
8.4 Beyond Binary Outcomes
148(1)
8.5 Summary
148(3)
Test Yourself
149(2)
9 Modeling Data Structures With Three (or More) Levels
151(14)
Learning Objectives
151(1)
9.1 Specifying a Three-Level Model
151(5)
9.1.1 Estimating the ICC
153(1)
9.1.2 Specifying the Model of Interest
154(2)
9.1.3 Alternative Model Syntax for Multiple Levels
156(1)
9.2 What If a Level Is Ignored?
156(3)
9.2.1 What Happens If the Intermediate Level Is Ignored?
156(1)
9.2.2 What Happens If the Higher Level Is Ignored?
157(1)
9.2.3 Comparison of Output If a Level Is Ignored
157(2)
9.3 Including Random Slopes in a Three-Level Model
159(3)
9.4 Do You Really Need a Three-Level Model?
162(1)
9.5 Summary
163(2)
Test Yourself
164(1)
10 Missing Data in Multilevel Models
165(20)
Learning Objectives
165(1)
10.1 Introduction
165(4)
10.1.1 Types of Missing Data
167(1)
10.1.2 How Much and Which Data Are Missing?
168(1)
10.2 Inspecting Our Data
169(4)
10.3 From Imputation to Pooling Results
173(9)
10.3.1 Getting Ready to Impute
173(1)
10.3.2 Imputing the Data
174(3)
10.3.3 Analyzing the Imputed Datasets
177(1)
10.3.6 Pooling Results
178(1)
10.3.5 Checking for Convergence
179(3)
10.4 Other Options for Dealing With Missing Data
182(1)
10.5 Summary
183(2)
Test Yourself
184(1)
11 Basic Power Analyses for Multilevel Models
185(20)
Learning Objectives
185(1)
11.1 Why Conduct a Power Analysis?
185(2)
11.1.1 Approaches to Power Analyses
186(1)
11.2 Elements Needed for a Power Analysis
187(4)
11.2.1 The Significance Level
187(1)
11.2.2 The Level of Power
188(1)
11.2.3 Specifying an Effect Size
188(2)
11.2.4 The Sample Size
190(1)
11.3 Example of a Single-Level Power Analysis
191(3)
11.3.1 Using Base R
191(1)
11.3.2 Using PowerUpl
192(2)
11.4 Accounting for Clustering in a Power Analysis
194(7)
11.6.1 The Role of the Intraclass Correlation Coefficient and Design Effect
194(2)
11.6.2 Conducting a Multilevel Power Analysis Using PowerUp!
196(1)
11.6.3 Conducting a Multilevel Power Analysis Using PowerUpR
197(3)
11.6.6 Writing Up a Power Analysis
200(1)
11.5 Other Software/Websites for Power Analysis
201(1)
11.6 Summary
201(4)
Test Yourself
203(2)
12 Alternatives to Multilevel Models
205(14)
Learning Objectives
205(1)
12.1 Introduction
205(1)
12.2 Level-1 Variables of Interest: Estimating Fixed Effect (FE) Models
206(5)
12.2.1 Computing Cluster Robust Standard Errors
208(2)
12.2.2 Using Im_robust
210(1)
12.3 Adding Level-2 Predictors: Beyond FE Models
211(2)
12.4 Using the Generalized Estimating Equations (GEE) Approach
213(4)
12.4.1 The Working Correlation Matrix
214(1)
12.4.2 Using geeglm
215(2)
12.5 Some Limitations
217(1)
12.6 Summary
217(2)
Test Yourself
218(1)
Glossary 219(4)
References 223(8)
Index 231
Francis Huang, Ph.D. is an Associate Professor at the University of Missouri (MU) in the Statistics, Measurement, and Evaluation in Education program in the Department of Educational, School, and Counseling Psychology of the College of Education. He teaches courses on multilevel modeling, program evaluation, and data management and is the co-director of the methodology branch of the Missouri Prevention Science Institute. Dr. Huangs research has been funded by federal agencies such as the U.S. Department of Education and the National Institute of Justice. His research focuses on both methodological (e.g., analysis of clustered data) and substantive (e.g., school climate, bullying, disparities in disciplinary sanctions) areas of interest. His work has been cited in outlets such as the New York Times, the Washington Post, and National Public Radio (among others). He has published in journals such as the Journal of Educational and Behavioral Statistics, Behavior Research Methods, and Educational Researcher. Prior to joining MU, he was a Senior Scientist at the University of Virginia and has worked at the American Institutes for Research, providing technical expertise on survey methods and the analysis of large-scale secondary datasets. He has worked as a management consultant and a high school teacher. He has an MA from Teachers College, Columbia University and a PhD from the University of Virginia. He is a father of two and married to his best friend. Francis does not take himself too seriously, plays the guitar, and dreams of being in a jazz trio in his retirement.
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