Analysis of Ordinal Categorical Data / Edition 2

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Categorical data having ordered categories are common in practice, especially in applications throughout the biomedical and social sciences. Thoroughly updated to reflect developments since the publication of its predecessor, Analysis of Ordinal Categorical Data, Second Edition presents a comprehensive survey of methods for analyzing ordinal categorical data, complete with coverage of the most recent research.

The author highlights various modeling techniques, including cumulative logit models with and without proportional odds structure, adjacent-categories logit and continuation-ratio logit models, stereotype models, association models for ordinal odds ratios, and models for clustered ordinal data. Additional features of this Second Edition include:

A new chapter on marginal models for multivariate ordinal responses, using maximum likelihood and generalized estimating equations for model fitting

A new chapter on random effects models for clustered ordinal data

A new chapter on Bayesian approaches for analyzing ordinal data

Models and order-restricted inference methods for various types of ordinal odds ratios, including local odds ratios, cumulative odds ratios, and global odds ratios

Presentation of non-model-based methods, such as nonparametric rank methods that also apply to ordered categorical data

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Product Details

Meet the Author

ALAN AGRESTI, PhD, is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida and Visiting Professor in the Department of Statistics at Harvard University. A Fellow of the American Statistical Association and the Institute of Mathematical Statistics, Dr. Agresti has published extensively on the topic of categorical data analysis and has presented lectures and short courses on the subject in more than thirty countries. He is the author of Categorical Data Analysis, Second Edition and An Introduction to Categorical Data Analysis, Second Edition, both published by Wiley.

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Table of Contents

Preface ix

1 Introduction 1

1.1 Ordinal Categorical Scales 1

1.2 Advantages of Using Ordinal Methods 2

1.3 Ordinal Modeling Versus Ordinary Regession Analysis 4

1.4 Organization of This Book 8

2 Ordinal Probabilities, Scores, and Odds Ratios 9

2.1 Probabilities and Scores for an Ordered Categorical Scale 9

2.2 Ordinal Odds Ratios for Contingency Tables 18

2.3 Confidence Intervals for Ordinal Association Measures 26

2.4 Conditional Association in Three-Way Tables 35

2.5 Category Choice for Ordinal Variables 37

Chapter Notes 41

Exercises 42

3 Logistic Regression Models Using Cumulative Logits 44

3.1 Types of Logits for An Ordinal Response 44

3.2 Cumulative Logit Models 46

3.3 Proportional Odds Models: Properties and Interpretations 53

3.4 Fitting and Inference for Cumulative Logit Models 58

3.5 Checking Cumulative Logit Models 67

3.6 Cumulative Logit Models Without Proportional Odds 75

3.7 Connections with Nonparametric Rank Methods 80

Chapter Notes 84

Exercises 87

4 Other Ordinal Logistic Regression Models 88

4.1 Adjacent-Categories Logit Models 88

4.2 Continuation-Ratio Logit Models 96

4.3 Stereotype Model: Multiplicative Paired-Category Logits 103

Chapter Notes 115

Exercises 117

5 Other Ordinal Multinomial Response Models 118

5.1 Cumulative Link Models 118

5.2 Cumulative Probit Models 122

5.3 Cumulative Log-Log Links: Proportional Hazards Modeling 125

5.4 Modeling Location and Dispersion Effects 130

5.5 Ordinal ROC Curve Estimation 132

5.6 Mean Response Models 137

Chapter Notes 140

Exercises 142

6 Modeling Ordinal Association Structure 145

6.1 Ordinary Loglinear Modeling 145

6.2 Loglinear Model of Linear-by-Linear Association 147

6.3 Row or Column Effects Association Models 154

6.4 Association Models for Multiway Tables 160

6.5 Multiplicative Association and Correlation Models 167

6.6 Modeling Global Odds Ratios and Other Associations 176

Chapter Notes 180

Exercises 182

7 Non-Model-Based Analysis of Ordinal Association 184

7.1 Concordance and Discordance Measures of Association 184

7.2 Correlation Measures for Contingency Tables 192

7.3 Non-Model-Based Inference for Ordinal Association Measures 194

7.4 Comparing Singly Ordered Multinomials 199

7.5 Order-Restricted Inference with Inequality Constraints 206

7.6 Small-Sample Ordinal Tests of Independence 211

7.7 Other Rank-Based Statistical Methods for Ordered Categories 214

Appendix: Standard Errors for Ordinal Measures 216

Chapter Notes 219

Exercises 222

8 Matched-Pairs Data with Ordered Categories 225

8.1 Comparing Marginal Distributions for Matched Pairs 226

8.2 Models Comparing Matched Marginal Distributions 231

8.3 Models for The Joint Distribution in A Square Table 235

8.4 Comparing Marginal Distributions for Matched Sets 240

8.5 Analyzing Rater Agreement on an Ordinal Scale 247

8.6 Modeling Ordinal Paired Preferences 252

Chapter Notes 258

Exercises 260

9 Clustered Ordinal Responses: Marginal Models 262

9.1 Marginal Ordinal Modeling with Explanatory Variables 263

9.2 Marginal Ordinal Modeling: GEE Methods 268

9.3 Transitional Ordinal Modeling, Given the Past 274

Chapter Notes 277

Exercises 279

10 Clustered Ordinal Responses: Random Effects Models 281

10.1 Ordinal Generalized Linear Mixed Models 282

10.2 Examples of Ordinal Random Intercept Models 288

10.3 Models with Multiple Random Effects 294

10.4 Multilevel (Hierarchical) Ordinal Models 303

10.5 Comparing Random Effects Models and Marginal Models 306

Chapter Notes 312

Exercises 314

11 Bayesian Inference for Ordinal Response Data 315

11.1 Bayesian Approach to Statistical Inference 316

11.2 Estimating Multinomial Parameters 319

11.3 Bayesian Ordinal Regression Modeling 327

11.4 Bayesian Ordinal Association Modeling 335

11.5 Bayesian Ordinal Multivariate Regression Modeling 339

11.6 Bayesian Versus Frequentist Approaches to Analyzing Ordinal Data 341

Chapter Notes 342

Exercises 344

Appendix: Software for Analyzing Ordinal Categorical Data 345

Bibliography 359

Example Index 389

Subject Index 391

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