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E-raamat: Categorical Data Analysis and Multilevel Modeling Using R

(Eastern Connecticut State University)
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  • Ilmumisaeg: 25-Feb-2022
  • Kirjastus: SAGE Publications Inc
  • Keel: eng
  • ISBN-13: 9781544324890
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Categorical Data Analysis and Multilevel Modeling Using RSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 25-Feb-2022
  • Kirjastus: SAGE Publications Inc
  • Keel: eng
  • ISBN-13: 9781544324890
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"Categorical Data Analysis and Multilevel Modeling Using R provides a practical guide to regression techniques for analyzing binary, ordinal, nominal, and count response variables using the R software. Author Xing Liu offers a unified framework for both single-level and multilevel modeling of categorical and count response variables with both frequentist and Bayesian approaches. Each chapter demonstrates how to conduct the analysis using R, how to interpret the models, and how to present the results for publication. A companion website for this book contains PowerPoint slides and solutions for the end-of-chapter exercises on the instructor site, and datasets and R commands used in the book on the student site"--

Categorical Data Analysis and Multilevel Modeling Using R provides a practical guide to regression techniques for analyzing binary, ordinal, nominal, and count response variables using the R software. Author Xing Liu offers a unified framework for both single-level and multilevel modeling of categorical and count response variables with both frequentist and Bayesian approaches. Each chapter demonstrates how to conduct the analysis using R, how to interpret the models, and how to present the results for publication. A companion website for this book contains datasets and R commands used in the book for students, and solutions for the end-of-chapter exercises on the instructor site. 

Arvustused

This book provides a highly accessible and practical introduction to some of the most useful regression models in social science research. Most students and applied researchers will find it valuable. -- Yang Cao This is an excellent book that covers many topics that are given just slight attention in many other books. -- Ahmed Ibrahim I would highly recommend this book, especially if readers are beginners. -- Man-Kit Lei This book provides an engaging and intuitive introduction to maximum likelihood estimation through contemporary examples. -- Jennifer Hayes Clark

Acknowledgments xxv
About the Author xxvii
Preface xxix
1 R Basics
1(48)
Objectives of This
Chapter
1(1)
1.1 Introduction to R
1(14)
1.1.1 Installing, Starting, and Exiting R
2(2)
1.1.2 R at First Sight: R Console, Menus, and Toolbar
4(1)
1.1.3 RStudio
5(2)
1.1.6 R Commander
7(1)
1.1.5 R Base Package and Add-on Packages
8(1)
1.1.6 Objects in R
9(1)
1.1.7 Functions and Arguments in R
10(1)
1.1.8 R Script Files
10(1)
1.1.9 How to Open an Existing Dataset via the Command Line or the Menus in RStudio
11(3)
1.1.10 How to Save R Output
14(1)
1.1.11 What If I Have a Question? How Do I Get Help?
14(1)
1.2 R Data Structures: Vectors, Matrices, Data Frames, and Lists
15(7)
1.2.1 Vector
16(2)
1.2.2 Matrix
18(1)
1.2.3 Data Frame
19(2)
1.2.4 List
21(1)
1.3 Data Management
22(10)
1.3.1 Selecting Variables
22(1)
1.3.2 Selecting Observations
23(1)
1.3.3 Selecting Observations and Variables
23(1)
1.3.4 Creating a New Variable
24(1)
1.3.5 Recoding a Variable
25(3)
1.3.6 Creating a Dummy or Binary Variable
28(1)
1.3.7 Reverse Coding with rec ()
29(1)
1.3.8 Labeling Values for Factor Variables
29(1)
1.3.9 Labeling a Variable
30(1)
1.3.10 The row sums () and row means () Functions in the sjmi.sc Package
30(1)
1.3.11 How to Deal With Missing Values When Recoding Variables
31(1)
1.3.12 Other Useful Data Management Functions
31(1)
1.4 Data Management with the tidyverse and sjmisc Packages
32(3)
1.5 Graphs
35(10)
1.5.1 Histograms
36(1)
1.5.2 Bar Charts
37(1)
1.5.3 Box Plots
38(2)
1.5.4 Scatterplots
40(2)
1.5.5 Scatterplots with ggplots2
42(1)
1.5.6 How to Save Graphs
43(2)
1.6 Summary of R Commands in This
Chapter
45(4)
Glossary
48(1)
Exercises
48(1)
2 Review of Basic Statistics
49(46)
Objectives of This
Chapter
49(1)
2.1 Understand Your Data Using Descriptive Statistics
50(1)
2.2 Descriptive Statistics for Continuous Variables Using R
50(7)
2.2.1 The summary () Function
50(2)
2.2.2 The tapplyO Function for Grouped Summaries
52(1)
2.2.3 The group by () Function and the summarize () Function for Grouped Summaries
53(1)
2.3.4 The group by () Function and the descr () Function for Grouped Summaries
54(1)
2.2.5 Descriptive Statistics for Multiple Variables With stat.descO
54(1)
2.2.6 Descriptive Statistics for Multiple Variables With descr ()
55(1)
2.2.7 The group, by () Function and the descr () Function for Grouped Summaries of Multiple Variables
56(1)
2.3 Frequency Distribution for Categorical Variables Using R
57(5)
2.3.1 The table () Function for a Single Categorical Variable
57(1)
2.3.2 The frq() Function in the sjmisc Package for a Single Categorical Variable
58(1)
2.3.3 The table () Function for a Two-Way Table
59(1)
2.3.4 The CrossTable() Function in the gmodels Package
60(2)
2.4 Simple Linear Regression
62(6)
2.4.1 Simple Linear Regression: An Introduction
62(1)
2.4.2 The lm() Function and Extractor Functions
63(1)
2.4.3 Interpreting R Output: The Coefficients Table
64(1)
2.4.4 Interpreting R Output: The Multiple R2 and the F Statistic
65(1)
2.4.5 The ANOVA Table
66(1)
2.4.6 The coef () Function and the confintO Function
67(1)
2.4.7 Effect Size With the eta_sq() Function
67(1)
2.4.8 Reporting the Results
67(1)
2.5 Multiple Linear Regression
68(11)
2.5.1 Multiple Linear Regression: An Introduction
68(1)
2.5.2 The im() Function
68(1)
2.5.3 Interpreting R Output: The Coefficients Table
69(1)
2.5.4 Interpreting R Output: The Multiple R2 and the F Statistic
70(1)
2.5.5 ThecoefO Function and the confint () Function
71(1)
2.5.6 The ANOVA Table
72(1)
2.5.7 Effect Size With the eta_sq() Function
72(1)
2.5.8 Computing the Predicted Values With the ggpredict () Function in ggeffects
73(5)
2.5.9 Reporting the Results
78(1)
2.6 Chi-Square Test
79(6)
2.6.1 The Chi-Square Test: An Introduction
79(1)
2.6.2 The CrossTable () Function in the gmodels Package
79(2)
2.6.3 The chisq. test () Function
81(1)
2.6.4 Cramer's V
81(3)
2.6.5 Follow-Up Chi-Square Test With the chisq. test() Function
84(1)
2.6.6 Reporting the Results
85(1)
2.7 Making Publication-Quality Tables Using R
85(3)
2.8 General Guidelines for Reporting Results
88(1)
2.9 Summary of R Commands in this
Chapter
89(6)
Glossary
93(1)
Exercises
93(2)
3 Logistic Regression for Binary Data
95(48)
Objectives of This
Chapter
95(1)
3.1 Logistic Regression Models: An Introduction
96(14)
3.1.1 Why Do We Need a Logistic Transformation?
96(2)
3.1.2 Probabilities, Odds, and Odds Ratios
98(2)
3.1.3 Transformation Among Probabilities, Odds, and Log Odds in Logistic Regression
100(1)
3.1.4 Bernoulli Distributions, the Likelihood Function, and Maximum Likelihood Estimation
101(3)
3.1.5 Goodness-of-Fit Statistics
104(3)
3.1.6 Testing Significance of Predictors
107(1)
3.1.7 Interpretation of Model Parameter Estimates in Logistic Regression
108(2)
3.2 Research Example and Description of the Data and Sample
110(1)
3.3 Generalized Linear Models and the glm () Function
111(2)
3.3.1 Generalized Linear Models and the glm() Function: An Introduction
111(1)
3.3.2 The glm () Function
112(1)
3.4 Simple Logistic Regression Using R
113(6)
3.4.1 Simple Logistic Regression: R Syntax
113(1)
3.4.2 Interpreting R Output
114(1)
3.4.3 Interpreting the Coefficients
115(1)
3.4.4 Interpreting the Odds Ratio
116(1)
3.4.5 Interpreting the Pseudo R7
116(2)
3.4.6 AIC and BIC Statistics
118(1)
3.4.7 Testing the Overall Model Using the Likelihood Ratio Test
118(1)
3.5 Multiple Logistic Regression Using R
119(14)
3.5.1 Interpretation of Model Parameter Estimates and Odds Ratios in Multiple Logistic Regression
120(1)
3.5.2 Model Fitting Based on the Likelihood Ratio Test and Information Criteria Statistics
120(1)
3.5.3 The glm() Function for Multiple Logistic Regression
121(1)
3.5.4 Interpreting R Output
122(1)
3.5.5 Interpreting the Coefficients
122(1)
3.5.6 Interpreting the Odd Ratios
123(1)
3.5.7 Interpreting the Pseudo R2
124(1)
3.5.8 AIC and BIC Statistics
125(1)
3.5.9 Hosmer-Lemeshow Goodness-of-Fit Statistic
125(1)
3.5.10 Testing the Overall Model Using the Likelihood Ratio Test
126(1)
3.5.11 Model Comparison Using the Likelihood Ratio Test
127(1)
3.5.12 Interpreting the Marginal Effects in Logistic Regression
128(1)
3.5.13 Computing the Predicted Probabilities With the predict () Function
128(1)
3.5.14 Computing the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
129(4)
3.6 Probit Regression Using R
133(2)
3.6.1 Interpretation of Model Parameter Estimates in Probit Regression
133(1)
3.6.2 The glm () Function for Multiple Probit Regression
133(1)
3.6.3 Interpreting Probit Coefficients in R Output
134(1)
3.7 Making Publication-Quality Tables
135(1)
3.7.1 Presenting the Results Using the stargazer Package
135(1)
3.8 Reporting the Results
136(2)
3.9 Summary of R Commands in This
Chapter
138(5)
Glossary
141(1)
Exercises
141(2)
4 Proportional Odds Models for Ordinal Response Variables
143(46)
Objectives of This
Chapter
143(1)
4.1 Proportional Odds Models: An Introduction
144(5)
4.1.1 Odds and Odds Ratios in PO Models
145(3)
4.1.2 The PO Assumption
148(1)
4.1.3 Goodness-of-Fit Statistics
148(1)
4.1.4 Interpretation of Model Parameter Estimates
149(1)
4.2 Research Example and Description of the Data and Sample
149(1)
4.3 Fitting a One-Predictor PO Model Using the elm () Function
150(7)
4.3.1 Packages and Functions for Proportional Odds Models in R
150(1)
4.3.2 The elm () Function in the Ordinal Package
150(1)
4.3.3 The PO Model: One-Predictor Model With the elm () Function
151(1)
4.3.4 Interpreting R Output
151(1)
4.3.5 Interpreting the Coefficients and the Intercepts/Thresholds
152(1)
4.3.6 Odds Ratios
153(1)
4.3.7 Interpreting the Odds Ratio of Being at or Below a Particular Category
153(1)
4.3.8 Interpreting the Odds Ratio of Being Above a Particular Category
154(1)
4.3.9 Model Fit Statistics
154(2)
4.3.10 Using the Likelihood Ratio Test to Test the PO Assumption
156(1)
4.4 Fitting a Multiple-Predictor PO Model Using the elm () Function
157(9)
4.4.1 The PO Model: Multiple-Predictor Model With the clm() Function
157(1)
4.4.2 Interpreting R Output
158(1)
4.4.3 Interpreting the Coefficients and the Intercepts/Thresholds
158(1)
4.4.4 Interpreting the Odds Ratios of Being Above a Particular Category
159(1)
4.4.5 Interpreting the Odds Ratios of Being at or Below a Particular Category
160(1)
4.4.6 Computing the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
161(1)
4.4.7 Model Fit Statistics
162(3)
4.4.8 Using the Likelihood Ratio Test to Test the PO Assumption
165(1)
4.4.9 Model Comparison Using the Likelihood Ratio Test
165(1)
4.5 Fitting a Single-Predictor PO Model Using the vglm() Function
166(4)
4.5.1 The vglm() Function in the vsam Package
166(1)
4.5.2 Using the vglm() Function to Fit a Single-Predictor PO Model
166(2)
4.5.3 Interpreting R Output
168(1)
4.5.4 Odds Ratios
168(1)
4.5.5 AIC Statistic
169(1)
4.5.6 Logit Coefficients of Being at or Above a Category
169(1)
4.5.7 Odds Ratios of Being at or Above a Category
170(1)
4.6 Fitting a Multiple-Predictor PO Model Using the vglmf) Function
170(10)
4.6.1 Using the vglm() Function to Fit a Multiple-Predictor PO Model
170(3)
4.6.2 Logit Coefficients of Being at or Above a Category in the Multiple-Predictor PO Model
173(1)
4.6.3 Computing the Predicted Probabilities With the predict () Function
174(1)
4.6.4 Computing the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
174(2)
4.6.5 Computing the Cumulative Probabilities With the ggpredict() Function
176(2)
4.6.6 Using the lrtest() Function to Test the PO Assumption
178(1)
4.6.7 Model Comparison Using the Likelihood Ratio Test With the lrtest () Function
179(1)
4.7 Making Publication-Quality Tables
180(2)
4.7.1 Presenting the Results of the elm Models Using the stargazer Package
180(1)
4.7.2 Presenting the Results of the vglm Models Using the texreg Package
181(1)
4.8 Reporting the Results
182(2)
4.9 Summary of R Commands in This
Chapter
184(5)
Glossary
188(1)
Exercises
188(1)
5 Generalized Ordinal Logistic Regression Models and Partial Proportional Odds Models
189(40)
Objectives of This
Chapter
189(1)
5.1 Partial Proportional Odds Models and Generalized Ordinal Logistic Regression Models: An Introduction
190(4)
5.1.1 Odds and Odds Ratios
191(2)
5.1.2 Goodness of Fit
193(1)
5.1.3 Interpretation of Model Parameter Estimates
194(1)
5.2 Research Example and Description of the Data and Sample
194(1)
5.3 Generalized Ordinal Logistic Regression Models with R
195(14)
5.3.1 The vglm() Function in the vgam Package
195(1)
5.3.2 The Multiple-Predictor PO Model
195(2)
5.3.3 Using the lrtest() Function to Test the PO Assumption
197(1)
5.3.4 The Multiple-Predictor Generalized Ordinal Logistic Regression Model
197(1)
5.3.5 Interpreting R Output
198(1)
5.3.6 Logit Coefficients of Being at or Below a Category
199(1)
5.3.7 Odds Ratios of Being at or Below a Category
199(1)
5.3.8 Model Fit Statistics
200(3)
5.3.9 Logit Coefficients of Being at or Above a Category
203(1)
5.3.10 Odds Ratios of Being at or Above a Category
204(2)
5.3.11 Computing the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
206(2)
5.3.12 Computing the Predicted Cumulative Probabilities With the ggpredict() Function
208(1)
5.4 Partial Proportional Odds Models With R
209(11)
5.4.1 The Partial Proportional Odds (PPO) Model With the vglm() Function
209(2)
5.4.2 Interpreting R Output
211(2)
5.4.3 Interpreting the Odds Ratios of Being at or Below a Particular Category
213(1)
5.4.4 Model Fit Statistics
213(1)
5.4.5 Logit Coefficients of Being at or Above a Category
214(1)
5.4.6 Interpreting R Output
215(2)
5.4.7 Interpreting the Odds Ratios of Being at or Above a Particular Category
217(1)
5.4.8 Computing the Predicted Probabilities With the ggpredict() Function for the PPO Model
218(2)
5.4.9 Computing the Predicted Cumulative Probabilities With the ggpredict() Function
220(1)
5.5 Making Publication-Quality Tables
220(1)
5.6 Reporting the Results
221(3)
5.7 Summary of R Commands in This
Chapter
224(5)
Glossary
227(1)
Exercises
227(2)
6 Other Ordinal Logistic Regression Models
229(42)
Objectives of This
Chapter
229(1)
6.1 Continuation Ratio Models
230(17)
6.1.1 Continuation Ratio Models: An Introduction
230(1)
6.1.2 Conditional Probabilities, Odds, and Odds Ratios
231(2)
6.1.3 Interpretation of Model Parameter Estimates
233(1)
6.1.4 Research Example and Description of the Data and Sample
233(1)
6.1.5 The vglm() Function With sratio or cratio in the vgam Package
233(1)
6.1.6 The CR Model: Multiple-Predictor Model With the vglm() Function
234(1)
6.1.7 Interpreting R Output
235(1)
6.1.8 Interpreting the Odds Ratio of Stopping in a Particular Category
236(1)
6.1.9 Interpreting Odds Ratios of Being Above a Particular Category
237(2)
6.1.10 Model Fit Statistics
239(1)
6.1.11 Computing the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
240(3)
6.1.12 The CR Model With Non-Proportional Odds
243(4)
6.2 Adjacent Categories Models
247(9)
6.2.1 Adjacent Categories Models: An Introduction
247(1)
6.2.2 Odds and Odds Ratios in AC Models
247(2)
6.2.3 Interpretation of Model Parameter Estimates
249(1)
6.2.4 Research Example and Description of the Data and Sample
249(1)
6.2.5 The vglm() Function With the acat Family in the vgam Package
250(1)
6.2.6 The AC Model: Multiple-Predictor Model
250(1)
6.2.7 Interpreting R Output
251(2)
6.2.8 Interpreting the Odds Ratios of Being in a Higher Category [ j + 1] Versus the Next Lower Category j
253(1)
6.2.9 Interpreting the Odds Ratios of Being in a Lower Category for the AC Model
254(1)
6.2.10 Model Fit Statistics
255(1)
6.3 Stereotype Logistic Regression Models
256(7)
6.3.1 Stereotype Logistic Regression Models: An Introduction
256(1)
6.3.2 Odds and Odds Ratios in Stereotype Logistic Regression Models
257(2)
6.3.3 Interpretation of Model Parameter Estimates
259(1)
6.3.4 Research Example and Description of the Data and Sample
259(1)
6.3.5 The rrvglm() Function With the multinomial Family in the vgam Package
259(1)
6.3.6 The SL Model: Multiple-Predictor Model With R
260(1)
6.3.7 Interpreting the Output
261(1)
6.3.8 Interpreting the Odds Ratios of Being in a Particular Category Versus the Base Category
262(1)
6.3.9 Interpreting the Odds Ratios of Being in the Base Category Versus a Particular Category
262(1)
6.4 Making Publication-Quality Tables
263(1)
6.4.1 Presenting the Results of the vglm Models Using the texreg Package
263(1)
6.5 Reporting the Results
264(3)
6.6 Summary of R Commands in This
Chapter
267(4)
Glossary
270(1)
Exercises
270(1)
7 Multinomial Logistic Regression Models
271(38)
Objectives of This
Chapter
271(1)
7.1 Multinomial Logistic Regression Models: An Introduction
272(3)
7.1.1 The Multinomial Distribution
272(1)
7.1.2 Odds in Multinomial Logistic Models
273(1)
7.1.3 Odds Ratios or Relative Risk Ratios in Multinomial Logistic Regression Models
274(1)
7.1.4 Model Fit Statistics
275(1)
7.1.5 Interpretation of Model Parameter Estimates
275(1)
7.2 Research Example and Description of the Data and Sample
275(1)
7.3 Fitting a One-Predictor Multinomial Logistic Regression Model With R
276(7)
7.3.1 Packages and Functions for Multinomial Logistic Regression Models in R
276(1)
7.3.2 The vglm () Function With the multinomial Family in the vgam Package
276(1)
7.3.3 The Multinomial Logistic Regression Model: One-Predictor Model
277(1)
7.3.4 Interpreting the Output
278(1)
7.3.5 Interpreting the Odds Ratios of Being in a Particular Category Versus the Base Category for the Multinomial Logistic Regression Model
279(1)
7.3.6 Model Fit Statistics
280(3)
7.4 Fitting a Multiple-Predictor Multinomial Logistic Regression Model With R
283(11)
7.4.1 The Multinomial Logistic Regression Model: Multiple-Predictor Model
283(1)
7.4.2 Interpreting R Output
284(2)
7.4.3 Interpreting the Odds Ratios of Being in a Category j Versus the Base Category 1
286(2)
7.4.4 Model Fit Statistics
288(1)
7.4.5 Interpreting the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
289(5)
7.4.6 Model Comparisons Using the Likelihood Ratio Test
294(1)
7.5 Multinomial Logistic Regression With the multinom() Function in the nnet Package
294(3)
7.6 Multinomial Logistic Regression With the mlogit() Function in the mlogit Package
297(3)
7.7 Making Publication-Quality Tables
300(3)
7.7.1 Presenting the Results of the vglm Models Using the texreg Package
300(3)
7.8 Reporting the Results
303(2)
7.9 Summary of R Commands in This
Chapter
305(4)
Glossary
308(1)
Exercises
308(1)
8 Poisson Regression Models
309(32)
Objectives of This
Chapter
309(1)
8.1 Poisson Regression Models: An Introduction
310(3)
8.1.1 The Poisson Distribution
311(1)
8.1.2 Incidence Rate Ratios in Poisson Regression Models
311(1)
8.1.3 Model Fit Statistics
312(1)
8.1.4 Interpretation of Model Parameter Estimates
312(1)
8.1.5 Interpreting an Incidence Rate Ratio as a Percentage Change in an Incidence Rate
312(1)
8.1.6 Interpreting Marginal Effects as Changes in Predicted Counts
313(1)
8.2 Research Example and Description of the Data and Sample
313(1)
8.3 Fitting a One-Predictor Poisson Regression Model With R
314(6)
8.3.1 Packages and Functions for Poisson Regression Models in R
314(1)
8.3.2 Theglm() Function
314(1)
8.3.3 The Poisson Regression Model: One-Predictor Model
314(1)
8.3.4 Interpreting the Output
315(1)
8.3.5 Interpreting the Incidence Rate Ratios in the One-Predictor Poisson Regression Model
316(1)
8.3.6 Model Fit Statistics
317(3)
8.4 Fitting a Multiple-Predictor Poisson Regression Model With R
320(10)
8.4.1 The Poisson Regression Model: Multiple-Predictor Model
320(1)
8.4.2 Interpreting R Output
321(1)
8.4.3 Interpreting the Incidence Rate Ratios (IRRs) in the Multiple-Predictor Poisson Model
322(1)
8.4.4 Model Fit Statistics
323(3)
8.4.5 Interpreting the Marginal Effects in the Poisson Regression Model
326(1)
8.4.6 Interpreting the Predicted Counts With the ggpredict() Function in the ggeffects Package
326(3)
8.4.7 Model Comparisons Using the Likelihood Ratio Test
329(1)
8.5 Poisson Regression With the vglm () Function in the VGAM Package
330(3)
8.6 Making Publication-Quality Tables
333(2)
8.6.1 Presenting the Results Using the stargazer Package
333(2)
8.7 Reporting the Results
335(1)
8.8 Summary of R Commands in This
Chapter
336(5)
Glossary
339(1)
Exercises
339(2)
9 Negative Binomial Regression Models and Zero-Inflated Models
341(40)
Objectives of This
Chapter
341(1)
9.1 Negative Binomial Regression Models: An Introduction
342(3)
9.1.1 The Negative Binomial Distribution
343(1)
9.1.2 Incidence Rate Ratios in Negative Binomial Regression Models
344(1)
9.1.3 Model Fit Statistics
344(1)
9.1.4 Interpretation of Model Parameter Estimates
345(1)
9.2 Research Example and Description of the Data and Sample
345(1)
9.3 Fitting a Multiple-Predictor Negative Binomial Regression Model With R
345(13)
9.3.1 Packages and Functions for Negative Binomial Regression Models in R
345(1)
9.3.2 The glm.nb() Function
346(1)
9.3.3 The Negative Binomial Regression Model: Multiple-Predictor Model
346(1)
9.3.4 Interpreting the Output
347(2)
9.3.5 Interpreting the Incidence Rate Ratios in the Negative Binomial Regression Model
349(1)
9.3.6 Interpreting the Marginal Effects in the Negative Binomial Regression Model
350(1)
9.3.7 Model Fit Statistics
350(4)
9.3.8 Interpreting the Predicted Counts With the ggpredict() Function in the ggeffects Package
354(2)
9.3.9 Testing the Dispersion Parameter Using the Likelihood Ratio Test
356(2)
9.4 Negative Binomial Regression With the vglm () Function in the VGAM Package
358(3)
9.5 Zero-Inflated Poisson Regression With the zeroinf() Function in the pscl Package
361(6)
9.6 Zero-Inflated Negative Binomial Regression With the zeroinf() Function in the pscl Package
367(5)
9.7 Making Publication-Quality Tables
372(2)
9.7.1 Presenting the Results Using the stargazer Package
372(1)
9.7.2 Presenting the Results Using the texreg Package
373(1)
9.8 Reporting the Results
374(2)
9.9 Summary of R Commands in This
Chapter
376(5)
Glossary
380(1)
Exercises
380(1)
10 Multilevel Modeling for Continuous Response Variables
381(38)
Objectives of This
Chapter
381(1)
10.1 Multilevel Modeling: An Introduction
382(5)
10.1.1 Multilevel Data Structure
382(1)
10.1.2 Intraclass Correlation
382(1)
10.1.3 Overview of a Basic Two-Level Model
383(1)
10.1.4 Model-Building Strategies
384(1)
10.1.5 Model Fit Statistics
385(1)
10.1.6 Centering
386(1)
10.1.7 Sample Size
386(1)
10.1.8 Data Structure for Model Fitting
387(1)
10.2 Multilevel Modeling for Continuous Outcome Variables
387(1)
10.2.1 Research Example and Research Questions
387(1)
10.2.2 Description of the Data and Sample
388(1)
10.3 Multilevel Modeling for Continuous Response Variables With R
388(14)
10.3.1 The lme () Function in the nlme Package
388(1)
10.3.2 Unconditional Means Model (Model 1: Null Model)
389(2)
10.3.3 Random-Intercept Model (Model 21
391(3)
10.3.4 Random-Coefficient Model: Random-Intercept and Slope Model With Level 1 Variable (Model 3)
394(2)
10.3.5 Contextual Model With Level 1 and Level 2 Variables (Model 4)
396(3)
10.3.6 Contextual Model With Cross-Level Interactions (Model 5)
399(3)
10.4 Multilevel Modeling for Continuous Response Variables With the liner () Function in the lme4 Package
402(7)
10.4.1 The lmero Function in the lme4 Package
402(2)
10.4.2 Interpreting the Predicted Values With the ggpredict() Function in the ggeffects Package
404(5)
10.5 Making Publication-Quality Tables
409(3)
10.5.1 Presenting the Results Using the stargazer Package
409(1)
10.5.2 Presenting the Results Using the texreg Package
410(2)
10.6 Reporting the Results
412(2)
10.7 Summary of R Commands in This
Chapter
414(5)
Glossary
416(1)
Exercises
416(3)
11 Multilevel Modeling for Binary Response Variables
419(40)
Objectives of This
Chapter
419(1)
11.1 Multilevel Modeling for Binary Outcome Variables
420(2)
11.1.1 Model Specification
420(1)
11.1.2 Odds and Odds Ratios in Multilevel Logistic Regression Models
421(1)
11.2 Research Example and Description of the Data and Sample
422(1)
11.2.1 Research Example and Research Questions
422(1)
11.2.2 Description of the Data and Sample
422(1)
11.3 Multilevel Modeling for Binary Response Variables With R
423(20)
11.3.1 Packages and Functions for Multilevel Modeling for Binary Response Variables in R
423(1)
11.3.2 TheglmerO Function in the lme4 Package
423(1)
11.3.3 Unconditional Model or Null Model (Model 11
424(2)
11.3.4 Random-Intercept Model (Model 21
426(3)
11.3.5 Random-Coefficient Model With a Level-1 Variable (Model 3)
429(3)
11.3.6 Contextual Model With Level-2 Variables (Model 4)
432(3)
11.3.7 Contextual Model With Cross-Level Interactions (Model 5)
435(4)
11.3.8 Interpreting the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
439(4)
11.4 Multilevel Modeling for Binary Outcome Variables With the clmm() Function in the ordinal Package
443(4)
11.5 Making Publication-Quality Tables
447(5)
11.5.1 Presenting the Results Using the stargazer Package
447(1)
11.5.2 Presenting the Results Using the texreg Package
448(4)
11.6 Reporting the Results
452(1)
11.7 Summary of R Commands in This
Chapter
453(6)
Glossary
457(1)
Exercises
457(2)
12 Multilevel Modeling for Ordinal Response Variables
459(44)
Objectives of This
Chapter
459(1)
12.1 Multilevel Modeling for Ordinal Response Variables: An Introduction
460(4)
12.1.1 Model Specification
460(3)
12.1.2 Odds and Odds Ratios in Multilevel PO Models
463(1)
12.1.3 Likelihood Ratio Test
463(1)
12.2 Research Example: Research Problem and Questions
464(1)
12.2.1 Description of the Data and Sample
464(1)
12.3 Multilevel Modeling for Ordinal Response Variables With R
464(22)
12.3.1 Packages and Functions for Multilevel Modeling for Ordinal Response Variables in R
464(1)
12.3.2 The clmmO Function in the ordinal Package
465(1)
12.3.3 Unconditional Model or Null Model (Model 1)
466(2)
12.3.4 Random-Intercept Model (Model 2)
468(3)
12.3.5 Random-Coefficient Model With a Level 1 Variable (Model 3l
471(4)
12.3.6 Contextual Model With Both Level 1 and Level 2 Variables (Model 41
475(4)
12.3.7 Contextual Model With Cross-Level Interactions (Model 5)
479(3)
12.3.8 Model Comparisons Using the AIC and the Log-Likelihood Statistics
482(1)
12.3.9 Interpreting the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
483(3)
12.4 Multilevel Modeling for Ordinal Response Variables With the mixor() Function in the mixor Package
486(7)
12.4.1 The mixor () Function in the mixor Package
486(2)
12.4.2 Multilevel Model for Ordinal Response Variables With Nonadaptive Gauss-Hermite Quadrature Using the mixor () Function
488(2)
12.4.3 Multilevel Model for Ordinal Response Variables With Adaptive Gauss-Hermite Quadrature Using the mixor () Function
490(3)
12.5 Making Publication-Quality Tables Using the texreg Package
493(2)
12.6 Reporting the Results
495(2)
Results for the Unconditional Model (Model 1)
496(1)
Results for the Contextual Model Without Cross-Level Interactions (Model 4)
496(1)
12.7 Summary of R Commands in This
Chapter
497(6)
Glossary
500(1)
Exercises
500(3)
13 Multilevel Modeling for Count Response Variables
503(48)
Objectives of This
Chapter
503(1)
13.1 Multilevel Modeling for Count Response Variables
504(1)
13.1.1 Model Specification
504(1)
13.1.2 Incidence Rate Ratios in Multilevel Poisson Regression Models
505(1)
13.2 Research Example and Description of the Data and Sample
505(2)
13.2.1 Research Example and Research Questions
505(1)
13.2.2 Description of the Data and Sample
506(1)
13.3 Multilevel Modeling for Count Response Variables With R
507(22)
13.3.1 Packages and Functions for Multilevel Modeling for Count Response Variables in R
507(1)
13.3.2 The glmer() Function in the lme4 Package
507(1)
13.3.3 Unconditional Model or Null Model (Model 1)
508(4)
13.3.4 Random-Intercept Model (Model 2)
512(3)
13.3.5 Random-Coefficient Model With a Level-1 Variable (Model 3)
515(5)
13.3.6 Contextual Model With Level-2 Variables (Model 4)
520(4)
13.3.7 Interpreting the Marginal Effects With the margins () Function in the margins Package
524(1)
13.3.8 Interpreting the Predicted Counts With the ggpredict() Function in the ggeffects Package
525(4)
13.4 Multilevel Modeling for Count Response Variables With the glmmTMB () Function in the glmmTMB Package
529(3)
13.5 Multilevel Modeling for Count Response Variables With the glmmPQL () Function in the MASS Package
532(4)
13.6 Multilevel Negative Binomial Models With the glmmTMB () Function in the glmmTMB Package
536(2)
13.7 Making Publication-Quality Tables
538(4)
13.7.1 Presenting the Results Using the stargazer Package
538(2)
13.7.2 Presenting the Results Using the texreg Package
540(2)
13.8 Reporting the Results
542(2)
13.9 Summary of R Commands in This
Chapter
544(7)
Glossary
548(1)
Exercises
548(3)
14 Multilevel Modeling for Nominal Response Variables
551(48)
Objectives of This
Chapter
551(1)
14.1 Multilevel Modeling for Nominal Outcome Variables
552(2)
14.1.1 Model Specification
552(2)
14.1.2 Odds and Odds Ratios in Multilevel Multinomial Logistic Regression Models
554(1)
14.2 Research Example and Description of the Data and Sample
554(2)
14.2.1 Research Example and Research Questions
554(1)
14.2.2 Description of the Data and Sample
555(1)
14.3 Multilevel Modeling for Nominal Response Variables With R
556(13)
14.3.1 Packages and Functions for Multilevel Modeling for Nominal Response Variables in R
556(1)
14.3.2 The mblogit() Function in the mclogit Package
556(1)
14.3.3 Unconditional Model or Null Model (Model 1)
557(3)
14.3.4 Random-Intercept Model (Model 2)
560(4)
14.3.5 Random-Intercept Model With Level-2 Variables (Model 3)
564(5)
14.4 Bayesian Multilevel Modeling for Nominal Outcome Variables With the MCMCglmm () Function in the MCMCglmm Package
569(7)
14.4.1 The MCMCglmm () Function in the MCMCglmm Package: Syntax for Bayesian Multilevel Multinomial Regression Models
569(2)
14.4.2 Multilevel Multinomial Regression Models With MCMCglmm(): Correlated Random Effects
571(3)
14.4.3 Multilevel Multinomial Regression Models With MCMCglmm (): Uncorrected Random Effects
574(2)
14.5 Bayesian Multilevel Modeling for Nominal Outcome Variables With the brm() Function in the brms Package
576(11)
14.5.1 The brm() Function in the brms Package: Syntax for Bayesian Multilevel Multinomial Regression Models
576(1)
14.5.2 Multilevel Multinomial Regression Models With brm(): Uncorrected Random Effects
577(3)
14.5.3 Multilevel Multinomial Regression Models With brm(): Correlated Random Effects
580(3)
14.5.4 Multilevel Multinomial Regression Models With brm(): Model Diagnostics With plot ()
583(1)
14.5.5 Conditional Effects With conditional effects ()
584(1)
14.5.6 Interpreting the Predicted Probabilities With the ggpredict() Function in the ggeffects Package
584(3)
14.6 Making Publication-Quality Tables
587(3)
14.6.1 Presenting the Results Using the texreg Package
587(3)
14.7 Reporting the Results
590(2)
14.8 Summary of R Commands in This
Chapter
592(7)
Glossary
596(1)
Exercises
596(3)
15 Bayesian Generalized Linear Models
599(48)
Objectives of This
Chapter
599(1)
15.1 Bayesian Generalized Linear Models
600(4)
15.1.1 Bayesian Inference: A Brief Introduction
600(1)
15.1.2 Specifying Priors
601(1)
15.1.3 Number of Iterations and Warm-Up
601(1)
15.1.4 Evaluating MCMC Convergence
602(1)
15.1.5 Point Estimates and Credible Intervals
602(1)
15.1.6 A Review of Generalized Linear Models
603(1)
15.2 Bayesian Logistic Regression With R
604(14)
15.2.1 Description of the Data and Sample
604(1)
15.2.2 Packages and Functions for Bayesian Logistic Regression With R
605(1)
15.2.3 The stan glm () Function in the rstanarm Package
605(9)
15.2.4 The brm() Function in the brms Package: Syntax for Bayesian Logistic Regression Models
614(4)
15.3 Bayesian Ordinal and Multinomial Logistic Regression With R
618(5)
15.3.1 Packages and Functions for Bayesian Ordinal Logistic Regression With R
618(1)
15.3.2 The stan_ glm () Function in the rstanarm Package
618(2)
15.3.3 The brm() Function in the brms Package: Syntax for Bayesian Ordinal Logistic Regression Models
620(1)
15.3.4 Packages and Functions for Bayesian Multinomial Logistic Regression With R
621(1)
15.3.5 The brm() Function in the brms Package: Syntax for Bayesian Multinomial Logistic Regression Models
622(1)
15.4 Bayesian Poisson Regression With R
623(7)
15.4.1 Description of the Data and Sample
623(1)
15.4.2 The Poisson Regression Model With the glm() Function
623(1)
15.4.3 Packages and Functions for Bayesian Poisson Regression With R
624(1)
15.4.4 The stan glm () Function in the rstanarm Package
624(4)
15.4.5 ThebrmO Function in the brms Package: Syntax for Bayesian Poisson Regression Models
628(2)
15.5 Bayesian Negative Binomial Regression With R
630(7)
15.5.1 Description of the Data and Sample
630(1)
15.5.2 The Negative Binomial Regression Model With the glm.nb() Function
630(1)
15.5.3 Packages and Functions for Bayesian Negative Binomial Regression With R
631(1)
15.5.4 The stan glm () Function in the rstanarm Package
631(5)
15.5.5 Thebrm() Function in the brms Package: Syntax for Bayesian Negative Binomial Regression Models
636(1)
15.6 Making Publication-Quality Tables
637(2)
15.6.1 Presenting the Results Using the texreg Package
637(2)
15.7 Reporting the Results
639(1)
15.8 Summary of R Commands in This
Chapter
640(7)
Glossary
645(1)
Exercises
646(1)
16 Bayesian Multilevel Modeling of Categorical Response Variables
647(42)
Objectives of This
Chapter
647(1)
16.1 Bayesian Multilevel Logistic Regression With R
648(9)
16.1.1 Model Specification
648(1)
16.1.2 Description of the Data and Sample
648(1)
16.1.3 Packages and Functions for Bayesian Multilevel Modeling for Binary Response Variables in R
649(1)
16.1.4 The brm() Function in the brms Package: Syntax for Bayesian Multilevel Logistic Regression Models
649(4)
16.1.5 The MCMCglmm () Function in the MCMCglmm Package: Syntax for Bayesian Multilevel Logistic Regression Models
653(4)
16.2 Bayesian Multilevel Ordinal Logistic Regression With R
657(7)
16.2.1 Model Specification
657(1)
16.2.2 Description of the Data and Sample
658(1)
16.2.3 Packages and Functions for Bayesian Multilevel Ordinal Logistic Regression With R
658(1)
16.2.4 The brm() Function in the brms Package: Syntax for Bayesian Multilevel Ordinal Logistic Regression Models
659(5)
16.3 Bayesian Multilevel Poisson Regression With R
664(11)
16.3.1 Model Specification
664(2)
16.3.2 Description of the Data and Sample
666(1)
16.3.3 Packages and Functions for Bayesian Multilevel Poisson Regression Models in R
666(1)
16.3.4 The brm() Function in the brms Package: Syntax for Bayesian Multilevel Poisson Regression Models
666(4)
16.3.5 The MCMCglmm () Function in the MCMCglmm Package: Syntax for Bayesian Multilevel Poisson Regression Models
670(5)
16.4 Bayesian Multilevel Negative Binomial Regression With R
675(4)
16.4.1 The brm() Function in the brms Package: Syntax for Bayesian Multilevel Negative Binomial Regression Models
675(4)
16.5 Making Publication-Quality Tables
679(2)
16.5.1 Presenting the Results Using the texreg Package
679(2)
16.6 Reporting the Results
681(2)
16.7 Summary of R Commands in This
Chapter
683(6)
Glossary
687(1)
Exercises
687(2)
References 689(6)
Index 695
Xing Liu Ph.D., is a professor of educational research and assessment at Eastern Connecticut State University. He received his Ph.D. in measurement, evaluation, and assessment in the field of educational psychology from the University of Connecticut, Storrs. His interests include categorical data analysis, multilevel modeling, longitudinal data analysis, structural equation modeling, educational assessment, propensity score methods, data science, and Bayesian methods. He is the author of Applied Ordinal Logistic Regression Using Stata: From Single-Level to Multilevel Modeling (2016). His major publications focus on advanced statistical models. His articles have been recognized among the most popular papers published in the Journal of Modern Applied Statistical Methods (JMASM). Dr. Liu is the recipient of the Excellence Award in Creativity/Scholarship at Eastern Connecticut State University.
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