Log-linear models and logistic regression
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| Vorheriger Titel: | Christensen, Ronald Log linear models |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Christensen, Ronald |d 1951- |e Verfasser |0 (DE-588)111351820 |4 aut | |
| 245 | 1 | 0 | |a Log-linear models and logistic regression |c Ronald Christensen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a XV, 483 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 780 | 0 | 0 | |i 1. Aufl. u.d.T. |a Christensen, Ronald |t Log linear models |w (DE-604)BV004262312 |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0048 MAT 628f 2001 A 10569(2) 0102 MAT 628f 2001 A 10569 |
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| DE-BY-TUM_katkey | 859753 |
| DE-BY-TUM_location | LSB 01 |
| DE-BY-TUM_media_number | 040010227295 040020188027 |
| _version_ | 1820815268098605056 |
| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
1 Introduction 1
1.1 Conditional Probability and Independence 2
1.2 Random Variables and Expectations 11
1.3 The Binomial Distribution 13
1.4 The Multinomial Distribution 14
1.5 The Poisson Distribution 18
1.6 Exercises 20
2 Two-Dimensional Tables and Simple Logistic Regression 23
2.1 Two Independent Binomials 23
2.1.1 The Odds Ratio 29
2.2 Testing Independence in a 2 x 2 Table 30
2.2.1 The Odds Ratio 32
2.3 IxJ Tables 33
2.3.1 Response Factors 37
2.3.2 Odds Ratios 38
2.4 Maximum Likelihood Theory for Two-Dimensional
Tables 42
2.5 Log-Linear Models for Two-Dimensional Tables 47
2.5.1 Odds Ratios 51
xii Contents
2.6 Simple Logistic Regression 54
2.6.1 Computer Commands 61
2.7 Exercises 61
3 Three-Dimensional Tables 69
3.1 Simpson s Paradox and the Need for Higher-Dimensional
Tables 70
3.2 Independence and Odds Ratio Models 72
3.2.1 The Model of Complete Independence 72
3.2.2 Models with One Factor Independent of the
Other Two 75
3.2.3 Models of Conditional Independence 79
3.2.4 A Final Model for Three-Way Tables 83
3.2.5 Odds Ratios and Independence Models 85
3.3 Iterative Computation of Estimates 87
3.4 Log-Linear Models for Three-Dimensional Tables 89
3.4.1 Estimation 92
3.4.2 Testing Models 94
3.5 Product-Multinomial and Other Sampling Plans 99
3.5.1 Other Sampling Models 102
3.6 Model Selection Criteria 104
3.6.1 R2 104
3.6.2 Adjusted R2 105
3.6.3 Akaike s Information Criterion 106
3.7 Higher-Dimensional Tables 108
3.7.1 Computer Commands 110
3.8 Exercises 113
4 Logistic Regression, Logit Models, and Logistic Discrimination 116
4.1 Multiple Logistic Regression 120
4.1.1 Informal Model Selection 122
4.2 Measuring Model Fit 127
4.2.1 Checking Lack of Fit 129
4.3 Logistic Regression Diagnostics 130
4.4 Model Selection Methods 136
4.4.1 Computations for Nonbinary Data 138
4.4.2 Computer Commands 139
4.5 ANOVA Type Logit Models 141
4.5.1 Computer Commands 149
4.6 Logit Models for a Multinomial Response 150
4.7 Logistic Discrimination and Allocation 159
4.8 Exercises 170
5 Independence Relationships and Graphical Models 178
5.1 Model Interpretations 178
Contents xiii
5.2 Graphical and Decomposable Models 182
5.3 Collapsing Tables 192
5.4 Recursive Causal Models 195
5.5 Exercises 209
6 Model Selection Methods and Model Evaluation 211
6.1 Stepwise Procedures for Model Selection 212
6.2 Initial Models for Selection Methods 215
6.2.1 All s-Factor Effects 215
6.2.2 Examining Each Term Individually 217
6.2.3 Tests of Marginal and Partial Association 217
6.2.4 Testing Each Term Last 218
6.3 Example of Stepwise Methods 224
6.3.1 Forward Selection 226
6.3.2 Backward Elimination 230
6.3.3 Comparison of Stepwise Methods 232
6.3.4 Computer Commands 233
6.4 Aitkin s Method of Backward Selection 234
6.5 Model Selection Among Decomposable and Graphical
Models 240
6.6 Use of Model Selection Criteria 246
6.7 Residuals and Influential Observations 247
6.7.1 Computations 249
6.7.2 Computing Commands 253
6.8 Drawing Conclusions 254
6.9 Exercises 256
7 Models for Factors with Quantitative Levels 258
7.1 Models for Two-Factor Tables 259
7.1.1 Log-Linear Models with Two Quantitative
Factors 260
7.1.2 Models with One Quantitative Factor 262
7.2 Higher-Dimensional Tables 266
7.2.1 Computing Commands 268
7.3 Unknown Factor Scores 269
7.4 Logit Models 275
7.5 Exercises 277
8 Fixed and Random Zeros 279
8.1 Fixed Zeros 279
8.2 Partitioning Polytomous Variables 282
8.3 Random Zeros 286
8.4 Exercises 293
xiv Contents
9 Generalized Linear Models 297
9.1 Distributions for Generalized Linear Models 299
9.2 Estimation of Linear Parameters 304
9.3 Estimation of Dispersion and Model Fitting 306
9.4 Summary and Discussion 311
9.5 Exercises 313
10 The Matrix Approach to Log-Linear Models 314
10.1 Maximum Likelihood Theory for Multinomial Sampling . 318
10.2 Asymptotic Results 322
10.3 Product-Multinomial Sampling 339
10.4 Inference for Model Parameters 342
10.5 Methods for Finding Maximum Likelihood Estimates . . . 345
10.6 Regression Analysis of Categorical Data 347
10.7 Residual Analysis and Outliers 354
10.8 Exercises 360
11 The Matrix Approach to Logit Models 363
11.1 Estimation and Testing for Logistic Models 363
11.2 Model Selection Criteria for Logistic Regression 371
11.3 Likelihood Equations and Newton-Raphson 372
11.4 Weighted Least Squares for Logit Models 375
11.5 Multinomial Response Models 377
11.6 Asymptotic Results 378
11.7 Discrimination, Allocation, and Retrospective Data .... 387
11.8 Exercises 394
12 Maximum Likelihood Theory for Log-Linear Models 396
12.1 Notation 396
12.2 Fixed Sample Size Properties 397
12.3 Asymptotic Properties 402
12.4 Applications 412
12.5 Proofs of Lemma 12.3.2 and Theorem 12.3.8 418
13 Bayesian Binomial Regression 422
13.1 Introduction 422
13.2 Bayesian Inference 424
13.2.1 Specifying the Prior and Approximating the
Posterior 424
13.2.2 Predictive Probabilities 434
13.2.3 Inference for Regression Coefficients 436
13.2.4 Inference for LDa 438
13.3 Diagnostics 440
13.3.1 Case Deletion Influence Measures 441
13.3.2 Model Checking 446
Contents xv
13.3.3 Link Selection 447
13.3.4 Sensitivity Analysis 448
13.4 Posterior Computations and Sample Size Calculation . . . 449
Appendix: Tkbles 455
A.I The Greek Alphabet 455
A.2 Tables of the x2 Distribution 456
References 458
Author Index 475
Subject Index 479
|
| any_adam_object | 1 |
| author | Christensen, Ronald 1951- |
| author_GND | (DE-588)111351820 |
| author_facet | Christensen, Ronald 1951- |
| author_role | aut |
| author_sort | Christensen, Ronald 1951- |
| author_variant | r c rc |
| building | Verbundindex |
| bvnumber | BV011604009 |
| classification_rvk | QH 234 SK 840 |
| classification_tum | MAT 628f MAT 620f |
| ctrlnum | (OCoLC)263659198 (DE-599)BVBBV011604009 |
| dewey-full | 519.535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.535 |
| dewey-search | 519.535 |
| dewey-sort | 3519.535 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV011604009 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T14:36:28Z |
| institution | BVB |
| isbn | 0387982477 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007817251 |
| oclc_num | 263659198 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-N2 DE-29T DE-739 DE-20 DE-824 DE-384 DE-83 DE-11 DE-188 DE-578 DE-521 |
| owner_facet | DE-91G DE-BY-TUM DE-N2 DE-29T DE-739 DE-20 DE-824 DE-384 DE-83 DE-11 DE-188 DE-578 DE-521 |
| physical | XV, 483 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spellingShingle | Christensen, Ronald 1951- Log-linear models and logistic regression Log-linear models Regressionsanalyse (DE-588)4129903-6 gnd Kontingenztafel (DE-588)4165159-5 gnd Logistische Verteilung (DE-588)4299453-6 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Log-lineares Modell (DE-588)4036197-4 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4165159-5 (DE-588)4299453-6 (DE-588)4124382-1 (DE-588)4036197-4 |
| title | Log-linear models and logistic regression |
| title_auth | Log-linear models and logistic regression |
| title_exact_search | Log-linear models and logistic regression |
| title_full | Log-linear models and logistic regression Ronald Christensen |
| title_fullStr | Log-linear models and logistic regression Ronald Christensen |
| title_full_unstemmed | Log-linear models and logistic regression Ronald Christensen |
| title_old | Christensen, Ronald Log linear models |
| title_short | Log-linear models and logistic regression |
| title_sort | log linear models and logistic regression |
| topic | Log-linear models Regressionsanalyse (DE-588)4129903-6 gnd Kontingenztafel (DE-588)4165159-5 gnd Logistische Verteilung (DE-588)4299453-6 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Log-lineares Modell (DE-588)4036197-4 gnd |
| topic_facet | Log-linear models Regressionsanalyse Kontingenztafel Logistische Verteilung Verallgemeinertes lineares Modell Log-lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007817251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT christensenronald loglinearmodelsandlogisticregression |