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An Introduction to Categorical Data Analysis

Second Edition

ALAN AGRESTI

Department of Statistics

University of Florida

Gainesville, Florida

1. Introduction 1

1.1 Categorical Response Data, 1

1.1.1 Response/Explanatory Variable Distinction, 2

1.1.2 Nominal/Ordinal Scale Distinction, 2

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

1.1.2 Nominal/Ordinal Scale Distinction, 2

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

/Explanatory Variable Distinction, 2

1.1.2 Nominal/Ordinal Scale Distinction, 2

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

/Ordinal Scale Distinction, 2

1.1.3 Organization of this Book, 3

1.2 Probability Distributions for Categorical Data, 3

1.2.1 Binomial Distribution, 4

1.2.2 Multinomial Distribution, 5

1.3 Statistical Inference for a Proportion, 6

1.3.1 Likelihood Function and Maximum Likelihood Estimation, 6

1.3.2 Significance Test About a Binomial Proportion, 8

1.3.3 Example: Survey Results on Legalizing Abortion, 8

1.3.4 Confidence Intervals for a Binomial Proportion, 9

1.4 More on Statistical Inference for Discrete Data, 11

1.4.1 Wald, Likelihood-Ratio, and Score Inference, 11

1.4.2 Wald, Score, and Likelihood-Ratio Inference for

Binomial Parameter, 12

1.4.3 Small-Sample Binomial Inference, 13

1.4.4 Small-Sample Discrete Inference is Conservative, 14

1.4.5 Inference Based on the Mid P-value, 15

1.4.6 Summary, 16

Problems, 16

1.4.6 Summary, 16

Problems, 16

P-value, 15

1.4.6 Summary, 16

Problems, 16

2. Contingency Tables 21

2.1 Probability Structure for Contingency Tables, 21

2.1.1 Joint, Marginal, and Conditional Probabilities, 22

2.1.2 Example: Belief in Afterlife, 22

3. Generalized Linear Models 65

3.1 Components of a Generalized Linear Model, 66

3.1.1 Random Component, 66

3.1.2 Systematic Component, 66

3.1.3 Link Function, 66

3.1.4 Normal GLM, 67

3.2 Generalized Linear Models for Binary Data, 68

3.2.1 Linear Probability Model, 68

3.2.2 Example: Snoring and Heart Disease, 69

3.2.3 Logistic Regression Model, 70

3.2.4 Probit Regression Model, 72

3.2.5 Binary Regression and Cumulative Distribution

Functions, 72

3.3 Generalized Linear Models for Count Data, 74

3.3.1 Poisson Regression, 75

3.3.2 Example: Female Horseshoe Crabs and their Satellites, 75

3.3.3 Overdispersion: Greater Variability than Expected, 80

3.3.4 Negative Binomial Regression, 81

3.3.5 Count Regression for Rate Data, 82

3.3.6 Example: British Train Accidents over Time, 83

3.4 Statistical Inference and Model Checking, 84

3.4.1 Inference about Model Parameters, 84

3.4.2 Example: Snoring and Heart Disease Revisited, 85

3.4.3 The Deviance, 85

3.4.4 Model Comparison Using the Deviance, 86

3.4.5 Residuals Comparing Observations to the Model Fit, 87

3.5 Fitting Generalized Linear Models, 88

3.5.1 The Newton–Raphson Algorithm Fits GLMs, 88

3.5.2 Wald, Likelihood-Ratio, and Score Inference Use the

Likelihood Function, 89

3.5.3 Advantages of GLMs, 90 .................

11. A Historical Tour of Categorical Data Analysis 325

11.1 The Pearson–Yule Association Controversy, 325

11.2 R. A. Fisher’s Contributions, 326

11.3 Logistic Regression, 328

11.4 Multiway Contingency Tables and Loglinear Models, 329

11.5 Final Comments, 331

共计11章， 388页

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[此贴子已经被作者于2009-3-12 9:30:12编辑过]