Analyzing categorical data:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
2003
|
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 496 S. graph. Darst. |
| ISBN: | 0387007490 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Introduction 1
1.1 The Nature of Categorical Data 1
1.2 Organization of This Book 3
2 Gaussian Based Data Analysis 7
2.1 The Normal (Gaussian) Random Variable 7
2.1.1 The Gaussian Density Function 7
2.1.2 Large Sample Inference for the Gaussian
Random Variable 8
2.1.3 Exact Inference for the Gaussian Random Variable . 11
2.2 Linear Regression and Least Squares 12
2.2.1 The Linear Regression Model 12
2.2.2 Least Squares Estimation 14
2.2.3 Interpreting Regression Coefficients 15
2.2.4 Assessing the Strength of a Regression Relationship 17
2.3 Inference for the Least Squares Regression Model 18
2.3.1 Hypothesis Tests and Confidence Intervals for (3 . . 18
2.3.2 Interval Estimation for Predicted and Fitted Values 19
2.4 Checking Assumptions 20
2.5 An Example 21
2.6 Background Material 25
2.7 Exercises 26
xii Contents
3 Gaussian Based Model Building 29
3.1 Linear Contrasts and Hypothesis Tests 29
3.2 Categorical Predictors 31
3.2.1 One Categorical Predictor with Two Levels 31
3.2.2 One Categorical Predictor with More Than
Two Levels 32
3.2.3 More Than One Categorical Predictor 33
3.3 Regression Diagnostics 36
3.3.1 Identifying Outliers 36
3.3.2 Identifying Leverage Points 37
3.3.3 Identifying Influential Points 38
3.4 Model Selection 42
3.4.1 Choosing a Set of Candidate Models 44
3.4.2 Choosing the Best Model 45
3.4.3 Model Selection Uncertainty 46
3.5 Heteroscedasticity and Weighted Least Squares 49
3.6 Background Material 51
3.7 Exercises 52
4 Categorical Data and Goodness of Fit 55
4.1 The Binomial Random Variable 55
4.1.1 Large Sample Inference 56
4.1.2 Sample Size and Power Calculations 59
4.1.3 Inference from a Sample of Binomial
Random Variables 61
4.1.4 Exact Inference 61
4.2 The Multinomial Random Variable 68
4.2.1 Large Sample Inference 68
4.3 The Poisson Random Variable 69
4.3.1 Large Sample Inference 71
4.3.2 Exact Inference 73
4.3.3 The Connection Between the Poisson and
the Multinomial 74
4.4 Testing Goodness of Fit 75
4.4.1 Chi Squared Goodness of Fit Tests 75
4.4.2 Partitioning Pearson s X2 Statistic 80
4.4.3 Exact Inference 82
4.5 Overdispersion and Lack of Fit 84
4.5.1 The Zero Inflated Poisson Model 84
4.5.2 The Negative Binomial Model 88
4.5.3 Overdispersed Binomial Data and the
Beta Binomial Model 93
4.6 Underdispersion 98
4.7 Robust Estimation Using Hellinger Distance 100
4.8 Background Material 102
Contents xiii
4.9 Exercises 103
5 Regression Models for Count Data 125
5.1 The Generalized Linear Model 125
5.1.1 The Form of the Generalized Linear Model 125
5.1.2 Estimation in the Generalized Linear Model 127
5.1.3 Hypothesis Tests and Confidence Intervals for /3 . . 128
5.1.4 The Deviance and Lack of Fit 129
5.1.5 Model Selection 130
5.1.6 Model Checking and Regression Diagnostics 132
5.2 Poisson Regression 133
5.3 Overdispersion 147
5.3.1 The Robust Sandwich Covariance Estimator .... 149
5.3.2 Quasi Likelihood Estimation 149
5.4 Non Poisson Parametric Regression Models 154
5.4.1 Negative Binomial Regression 155
5.4.2 Zero Inflated Count Regression 162
5.4.3 Zero Truncated Poisson Regression 168
5.5 Nonparametric Count Regression 171
5.5.1 Local Likelihood Estimation Based on One Predictor 171
5.5.2 Smoothing Multinomial Data 175
5.5.3 Regression Smoothing with More Than
One Predictor 178
5.6 Background Material 181
5.7 Exercises 182
6 Analyzing Two Way Tables 197
6.1 Two by Two Tables 197
6.1.1 Two Sample Tests and Comparisons of Proportions . 197
6.1.2 Two by Two Tables and Tests of Independence ... 199
6.1.3 The Odds Ratio and the Relative Risk 203
6.2 Loglinear Models for Two Way Tables 208
6.2.1 2x2 Tables 208
6.2.2 IxJ Tables 210
6.3 Conditional Analyses 218
6.3.1 Two by Two Tables and Fisher s Exact Test 218
6.3.2 I x J Tables 221
6.4 Structural Zeroes and Quasi Independence 225
6.5 Outlier Identification and Robust Estimation 228
6.6 Background Material 234
6.7 Exercises 235
7 Tables with More Structure 247
7.1 Models for Tables with Ordered Categories 247
7.1.1 Linear by Linear (Uniform) Association 248
xiv Contents
7.1.2 Row, Column, and Row + Column Effects Models . 252
7.1.3 A Log Multiplicative Row and Column
Effects Model 261
7.1.4 Bivariate Discrete Distributions 264
7.2 Square Tables 270
7.2.1 Quasi Independence 270
7.2.2 Symmetry 270
7.2.3 Quasi Symmetry 273
7.2.4 Tables with Ordered Categories 276
7.2.5 Matched Pairs Data 278
7.2.6 Rater Agreement Tables 283
7.3 Conditional Analyses 289
7.4 Background Material 291
7.5 Exercises 293
8 Multidimensional Contingency Tables 309
8.1 2 x 2 x K Tables 309
8.1.1 Simpson s Paradox 310
8.1.2 Types of Independence 314
8.1.3 Tests of Conditional Association 316
8.2 Loglinear Models for Three Dimensional Tables 318
8.2.1 Hierarchical Loglinear Models 318
8.2.2 Association Diagrams, Conditional Independence,
and Collapsibility 323
8.2.3 Loglinear Model Fitting for
Three Dimensional Tables 324
8.3 Models for Tables with Ordered Categories 330
8.4 Higher Dimensional Tables 337
8.5 Conditional Analyses 344
8.6 Background Material 347
8.7 Exercises 348
9 Regression Models for Binary Data 365
9.1 The Logistic Regression Model 365
9.1.1 Why Logistic Regression? 365
9.1.2 Inference for the Logistic Regression Model 369
9.1.3 Model Fit and Model Selection 372
9.2 Retrospective (Case Control) Studies 380
9.3 Categorical Predictors 387
9.4 Other Link Functions 393
9.4.1 Dose Response Modeling and Logistic Regression . . 393
9.4.2 Probit Regression 394
9.4.3 Complementary Log Log and Log Log Regression . 396
9.5 Overdispersion 398
9.5.1 Nonparametric Approaches 398
Contents xv
9.5.2 Beta Binomial Regression 399
9.6 Smoothing Binomial Data 403
9.7 Conditional Analysis 407
9.8 Background Material 411
9.9 Exercises 412
10 Regression Models for Multiple Category
Response Data 427
10.1 Nominal Response Variable 427
10.1.1 Multinomial Logistic Regression 427
10.1.2 Independence of Irrelevant Alternatives 434
10.2 Ordinal Response Variable 435
10.2.1 The Proportional Odds Model 436
10.2.2 Other Link Functions 438
10.2.3 Adjacent Categories Logit Model 442
10.2.4 Continuation Ratio Models 443
10.3 Background Material 448
10.4 Exercises 449
A Some Basics of Matrix Algebra 455
References 459
Index 485
|
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| spelling | Simonoff, Jeffrey S. Verfasser aut Analyzing categorical data Jeffrey S. Simonoff New York u.a. Springer 2003 XV, 496 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Includes bibliographical references and index Kategoriale Daten - Datenanalyse Multivariate analysis Kategoriale Daten (DE-588)4327512-6 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Kategoriale Daten (DE-588)4327512-6 s Datenanalyse (DE-588)4123037-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010258070&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simonoff, Jeffrey S. Analyzing categorical data Kategoriale Daten - Datenanalyse Multivariate analysis Kategoriale Daten (DE-588)4327512-6 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4327512-6 (DE-588)4123037-1 |
| title | Analyzing categorical data |
| title_auth | Analyzing categorical data |
| title_exact_search | Analyzing categorical data |
| title_full | Analyzing categorical data Jeffrey S. Simonoff |
| title_fullStr | Analyzing categorical data Jeffrey S. Simonoff |
| title_full_unstemmed | Analyzing categorical data Jeffrey S. Simonoff |
| title_short | Analyzing categorical data |
| title_sort | analyzing categorical data |
| topic | Kategoriale Daten - Datenanalyse Multivariate analysis Kategoriale Daten (DE-588)4327512-6 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Kategoriale Daten - Datenanalyse Multivariate analysis Kategoriale Daten Datenanalyse |
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