목차 일부
CONTENTS
Preface ... ⅶ
1. Introduction ... 1
1.1. Categorical Response Data ... 2
1.2. Organization of This Book ... 5
Chapter Notes ... 6
Problems ... 6
2. Describing Two-Way Contingenc...
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목차 전체
CONTENTS
Preface ... ⅶ
1. Introduction ... 1
1.1. Categorical Response Data ... 2
1.2. Organization of This Book ... 5
Chapter Notes ... 6
Problems ... 6
2. Describing Two-Way Contingency Tables ... 8
2.1. Table Structure for Two Dimensions ... 8
2.2. Ways of Comparing Proportions ... 13
2.3. Summary Measures of Association ... 19
2.4. Historical Overview ... 26
Chapter Notes ... 28
Problems ... 29
3. Inference for Two-Way Contingency Tables ... 36
3.1. Sampling Distributions ... 37
3.2. Testing Goodness-of-Fit ... 42
3.3. Testing Independence ... 47
3.4. Large-Sample Confidence Intervals ... 54
3.5. Exact Tests for Small Samples ... 59
3.6. Exact Non-null Inference ... 66
Chapter Notes ... 68
Problems ... 70
4. Models for Binary Response Variables ... 79
4.1. Generalized Linear Models ... 80
4.2. Logistic Regression ... 84
4.3. Logit Models for Categorical Data ... 91
4.4. Using Models to Improve Inferential Power ... 97
4.5. Probit and Extreme Value Models ... 102
4.6. Model Diagnostics ... 107
4.7. Fitting Logit Models ... 112
4.8. Conditional Logistic Regression ... 117
Chapter Notes ... 119
Problems ... 122
5. Loglinear Models ... 130
5.1. Loglinear Model for Two Dimensions ... 130
5.2. Table Structure for Three Dimensions ... 135
5.3. Loglinear Models for Three Dimensions ... 143
5.4. Logiinear Models for Higher Dimensions ... 150
Chapter Notes ... 153
Problems ... 155
6. Fitting Loglinear and Logit Models ... 165
6.1. Sufficiency and Likelihood for Loglinear Models ... 165
6.2. Estimating Expected Frequencies ... 169
6.3. Testing Goodness of Fit ... 174
6.4. Estimating Model Parameters ... 178
6.5. Iterative Maximum Likelihood Estimation ... 184
6.6. Analyzing Rates and Survival Times Using Loglinear Models ... 189
6.7. Table Standardization ... 196
Chapter Notes ... 199
Problems ... 200
7. Building and Applying Loglinear Models ... 210
7.1. Partitioning Chi-Squared to Compare Models ... 210
7.2. Strategies in Model Selection ... 215
7.3. Analysis of Residuals ... 224
7.4. Testing Conditional Independence ... 228
7.5. Estimating and Comparing Conditional Associations ... 235
7.6. Sample Size and Power Considerations ... 239
7.7. Empty Cells and Sparseness in Contingency Tables ... 244
Chapter Notes ... 251
Problems ... 252
8. Loglinear-Logit Models for Ordinal Variables ... 261
8.1. Linear-by-Linear Association ... 263
8.2. Row Effects and Column Effects Models ... 269
8.3. Models for Ordinal Variables in Multidimensional Tables ... 274
8.4. Testing Independence for Ordinal Classifications ... 282
8.5. Other Models Having Parameter Scores ... 287
8.6. Model Selection for Ordinal Variables ... 293
Chapter Notes ... 295
Problems ... 297
9. Multinomial Response Models ... 306
9.1. Generalized Logit Models and Loglinear Models ... 307
9.2. Multinomial Logit Models ... 313
9.3. Logits for Ordinal Responses ... 318
9.4. Cumulative Logit Models ... 322
9.5. Cumulative Link Models ... 331
9.6. Mean Response Models ... 333
Chapter Notes ... 336
Problems ... 338
10. Models for Matched Pairs ... 347
10.1. Comparing Dependent Proportions ... 348
10.2. Symmetry Models ... 353
10.3. Marginal Homogeneity ... 358
10.4. Square Tables with Ordered Categories ... 361
10.5. Measuring Agreement ... 365
10.6. Bradley-Terry Model for Paired Comparisons ... 370
Chapter Notes ... 374
Problems ... 375
11. Analyzing Repeated Categorical Response Data ... 386
11.1. Symmetry ... 387
11.2. Marginal Homogeneity ... 390
11.3. Modeling a Repeated Categorical Response ... 395
11.4. Modeling a Repeated Ordinal Response ... 401
11.5. Markov Chain Models ... 406
Chapter Notes ... 410
Problems ... 412
12. Asymptotic Theory for Parametric Models ... 418
12.1. Delta Method ... 419
12.2. Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities ... 425
12.3. Asymptotic Distribution of Residuals and Goodness-of-Fit Statistics ... 431
12.4. Asymptotic Distributions for Loglinear Models ... 437
Chapter Notes ... 439
Problems ... 440
13. Estimation Theory for Parametric Models ... 445
13.1. Maximum Likelihood for Generalized Linear Models ... 445
13.2. Maximum Likelihood for Loglinear Models ... 453
13.3. Weighted Least Squares for Categorical Data ... 458
13.4. Bayesian Inference for Categorical Data ... 462
13.5. Other Methods of Estimation ... 471
Chapter Notes ... 476
Problems ... 477
Appendix A. Using Computer Software to Analyze Categorical Data ... 484
A.1. Software Packages ... 484
A.2. Listings of Computer Routines by Chapter ... 488
Appendix B. A Twentieth-Century Tour of Categorical Data Analysis ... 505
Appendix C. Chi-Squared Distribution Values for Various Right-Hand Tail Probabilities ... 506
Bibliography ... 508
Index of Examples ... 541
Index of Selected Notation ... 543
Author Index ... 544
Subject Index ... 549
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