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
