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E-raamat: Modern Applied Regressions: Bayesian and Frequentist Analysis of Categorical and Limited Response Variables with R and Stan [Taylor & Francis e-raamat]

(Ball State University, Muncie, Indiana, USA)
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Modern Applied Regressions: Bayesian and Frequentist Analysis of Categorical and Limited Response Variables with R and StanSuurem pilt
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Modern Applied Regressions creates an intricate and colorful mural with mosaics of categorical and limited response variable (CLRV) models using both Bayesian and Frequentist approaches. Written for graduate students, junior researchers, and quantitative analysts in behavioral, health, and social sciences, this text provides details for doing Bayesian and frequentist data analysis of CLRV models. Each chapter can be read and studied separately with R coding snippets and template interpretation for easy replication. Along with the doing part, the text provides basic and accessible statistical theories behind these models and uses a narrative style to recount their origins and evolution.

This book first scaffolds both Bayesian and frequentist paradigms for regression analysis, and then moves onto different types of categorical and limited response variable models, including binary, ordered, multinomial, count, and survival regression. Each of the middle four chapters discusses a major type of CLRV regression that subsumes an array of important variants and extensions. The discussion of all major types usually begins with the history and evolution of the prototypical model, followed by the formulation of basic statistical properties and an elaboration on the doing part of the model and its extension. The doing part typically includes R codes, results, and their interpretation. The last chapter discusses advanced modeling and predictive techniquesmultilevel modeling, causal inference and propensity score analysis, and machine learningthat are largely built with the toolkits designed for the CLRV models previously covered.

The online resources for this book, including R and Stan codes and supplementary notes, can be accessed at https://sites.google.com/site/socjunxu/home/statistics/modern-applied-regressions.
Preface xi
1 Introduction
1(36)
1.1 Categorical and Limited Response Variables
1(3)
1.1.1 A Brief History of CLRV Models
2(1)
1.1.2 Overview of CLRVs
3(1)
1.2 Approaches to Regression Analysis
4(4)
1.2.1 Frequentist Approach to Regression Modeling
4(1)
1.2.2 Bayesian Approach to Regression Modeling
4(1)
1.2.2.1 The Example of COVID-19
5(1)
1.2.3 Priors
6(1)
1.2.3.1 Conjugate Priors
6(1)
1.2.3.2 Informative, Non-informative, and Other Priors
7(1)
1.2.4 Markov Chain Monte Carlo (MCMC)
8(1)
1.3 Introduction to R
8(13)
1.3.1 RStudio
9(1)
1.3.2 Use R as Calculator
10(1)
1.3.3 Set Up Working Directory
11(1)
1.3.4 Open Log File
12(1)
1.3.5 Load Data
12(1)
1.3.6 Subset Data
13(1)
1.3.7 Examine Data
13(1)
1.3.8 Examine Individual Variables
14(1)
1.3.9 Save Graphs
15(1)
1.3.10 Add Comments
15(1)
1.3.11 Create Dummy Variables and Check Transformation
16(1)
1.3.12 Label Variables
17(1)
1.3.13 Label Values
17(1)
1.3.14 Create Ordinal Variables
18(1)
1.3.15 Check Transformation
18(1)
1.3.16 Drop Missing Cases
19(1)
1.3.17 Graph Matrix
19(1)
1.3.18 Save Data
20(1)
1.3.19 Close Log
20(1)
1.3.20 Source Codes
20(1)
1.4 Review of Linear Regression Models
21(16)
1.4.1 A Brief History of OLS Rregression
21(1)
1.4.2 Main Results of OLS Regression
22(1)
1.4.2.1 OLS Estimator and Variance-Covariance Matrix
23(1)
1.4.3 Major Assumptions of OLS Regression
23(1)
1.4.3.1 Zero Conditional Mean and Linearity
24(1)
1.4.3.2 Spherical Disturbance
24(1)
1.4.3.3 Identifiability
24(1)
1.4.3.4 Nonstochastic Covariates
25(1)
1.4.3.5 Normality
25(1)
1.4.4 Estimation and Interpretation
25(6)
1.4.5 A Brief Introduction to Stan and Other BUGS-like Software
31(1)
1.4.6 Bayesian Approach to Linear Regression
32(5)
2 Binary Regression
37(50)
2.1 Introduction
37(3)
2.1.1 A Brief History of Binary Regression
37(1)
2.1.2 Linear Probability Regression
38(2)
2.2 Maximum Likelihood Estimation
40(9)
2.2.1 Simple MLE Examples
41(4)
2.2.2 MLE for Binary Regression
45(1)
2.2.3 Numerical Methods for MLE
46(2)
2.2.4 Normality, Consistency, and Efficiency
48(1)
2.2.5 Nonlinear Probability
49(1)
2.3 Hypothesis Testing and Model Comparisons
49(13)
2.3.1 Wald, Likelihood Ratio, and Score Tests
51(4)
2.3.1.1 Graphical Comparison of Wald, LR, and Score Tests
55(1)
2.3.2 Scalar Measures
56(3)
2.3.3 ROC Curve
59(2)
2.3.4 Goodness of Fit Measures: The Hosmer-Lemeshow Test
61(1)
2.3.5 Limitations of NHST
61(1)
2.4 Interpretation of Results
62(12)
2.4.1 Precision Estimates
63(1)
2.4.1.1 End-Point Transformation
64(1)
2.4.1.2 Delta Method
64(1)
2.4.1.3 Re-sampling Methods
64(1)
2.4.2 Interpretation Based on Predictions
65(3)
2.4.3 Interpretations Based on Effects
68(1)
2.4.3.1 Odds Ratios
68(1)
2.4.3.2 Discrete Rates of Change in Prediction
69(2)
2.4.3.3 Marginal Effects
71(2)
2.4.4 Group Comparisons
73(1)
2.5 Bayesian Binary Regression
74(13)
2.5.1 Priors for Binary Regression
75(3)
2.5.2 Bayesian Estimation of Binary Regression
78(4)
2.5.3 Bayesian Post-estimation Analysis
82(2)
2.5.4 Bayesian Assessment of Null Values
84(3)
3 Polytomous Regression
87(50)
3.1 Ordered Regression
88(28)
3.1.1 Types of Ordinal Measures and Regression Models
88(1)
3.1.2 A Brief History of Ordered Regression Models
89(1)
3.1.3 Cumulative Regression
89(1)
3.1.3.1 Model Setup and Estimation
89(4)
3.1.3.2 Hypothesis Testing and Model Comparison
93(2)
3.1.3.3 Interpretation
95(3)
3.1.4 Testing the Proportional Odds/Parallel Lines Assumption
98(3)
3.1.5 Partial, Proportional Constraint, and Non-parallel Models
101(5)
3.1.6 Continuation Ratio Regression
106(6)
3.1.7 Adjacent Category Regression
112(2)
3.1.8 Stereotype Logit
114(2)
3.2 Extentions to Classical Ordered Regression Models
116(7)
3.2.1 Inflated Ordered Regression
116(4)
3.2.2 Heterogeneous Choice Models
120(2)
3.2.3 General Guidelines for Model Selection
122(1)
3.3 Multinomial Regression
123(7)
3.3.1 Multinomial Logit Regression
123(6)
3.3.2 Multinomial Probit Regression
129(1)
3.4 Bayesian Polytomous Regression
130(7)
3.4.1 Bayesian Estimation
130(1)
3.4.1.1 Bayesian Parallel Cumulative Ordered Regression
131(1)
3.4.1.2 Bayesian Non-Parallel Cumulative Ordered Regression
132(2)
3.4.1.3 Bayesian Stereotype Logit Model
134(3)
4 Count Regression
137(32)
4.1 Poisson Distribution
137(2)
4.2 Basic Count Regression Models
139(18)
4.2.1 Explore the Count Response Variable
140(1)
4.2.2 Plot Observed vs. Predicted Count Proportions
141(1)
4.2.3 Poisson Regression
142(8)
4.2.4 Contagion, Heterogeneity, and Over-Dispersion
150(2)
4.2.5 Quasi-Poisson Regression
152(1)
4.2.6 Negative Binomial Regression
152(5)
4.3 Zero-Modified Count Regression
157(5)
4.3.1 Zero-Truncated Models
158(1)
4.3.2 Hurdle Models
159(1)
4.3.3 Zero-Inflated Models
160(2)
4.4 Bayesian Estimation of Count Regression
162(7)
4.4.1 Bayesian Estimation of Negative Binomial Regression
162(5)
4.4.2 Bayesian Estimation of Zero-Inflated Poisson Regression
167(2)
5 Survival Regression
169(36)
5.1 Introduction
169(3)
5.1.1 Censoring and Truncation
170(2)
5.2 Basic Concepts
172(2)
5.2.1 Time and Survival Function
172(1)
5.2.2 Hazard Function
173(1)
5.3 Descriptive Survival Analysis
174(6)
5.3.1 The Kaplan-Meier Estimator
174(3)
5.3.2 The Log-Rank Test
177(3)
5.4 Accelerated Failure Time Model
180(6)
5.4.1 Exponential AFT Regression
181(2)
5.4.2 Weibull AFT Regression
183(3)
5.5 Parametric Proportional Hazard Regression
186(4)
5.5.1 Exponential PH Regression
187(1)
5.5.2 Weibull PH Regression
188(2)
5.6 Cox Regression
190(2)
5.7 Testing the PH Assumption
192(2)
5.8 Bayesian Approaches to Survival Regression
194(11)
5.8.1 Bayesian Estimation of Weibull PH Model Using rstan
195(7)
5.8.2 Bayesian Estimation of Survival Models Using sp BayesSurv
202(3)
6 Extensions
205(52)
6.1 Multilevel Regression
205(11)
6.1.1 Multilevel Logit Regression
206(5)
6.1.2 Multilevel Count Regression
211(3)
6.1.3 Bayesian Multilevel Regression
214(2)
6.2 Causal Inference
216(12)
6.2.1 Average Treatment Effects
217(1)
6.2.1.1 Average Treatment Effects
217(1)
6.2.1.2 Average Treatment Effects for the Treated
218(1)
6.2.1.3 (Strong) Ignorability of Treatment Assumption
218(1)
6.2.2 Propensity Score Analysis
219(1)
6.2.2.1 Propensity Score Matching
219(4)
6.2.2.2 Mahalanobis Distance Matching
223(1)
6.2.2.3 Genetic Matching
224(2)
6.2.2.4 Coarsened (Exact) Matching
226(2)
6.3 Machine Learning
228(29)
6.3.1 Basic Concepts
229(1)
6.3.1.1 Machine Learning and Statistical Learning
229(1)
6.3.1.2 Supervised Learning and Unsupervised Learning
230(1)
6.3.1.3 Regression and Classification
230(1)
6.3.1.4 Training, Validation, and Test
230(1)
6.3.2 Supervised Learning
230(1)
6.3.2.1 Regularization: Ridge and Lasso Regression
230(11)
6.3.2.2 Penalized Binary Logit
241(2)
6.3.2.3 Decision/Regression Trees
243(7)
6.3.2.4 Bagging and Random Forests
250(2)
6.3.2.5 Classification Trees
252(5)
Bibliography 257(16)
Index 273
Dr. Jun Xu is professor of sociology and data science at Ball State University. His quantitative research interests include Bayesian statistics, categorical data analysis, causal inference, machine learning, and statistical programming. His methodological works have appeared in journals such as Sociological Methods and Research, Social Science Research, and The Stata Journal. He is an author of Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives (with Dr. Andrew S. Fullerton by Chapman & Hall). In the past two decades or so, he has authored or co-authored several statistical application commands and packages, including gencrm, grcompare and the popular SPost9.0 package in Stata, and stdcoef in R.
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