Generalized linear models and extensions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
College Station, Tex.
Stata Press
2007
|
| Edition: | 2. ed. |
| Series: | A Stata Press publication
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015579559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XXII, 387 S. graph. Darst. |
| ISBN: | 1597180149 9781597180146 |
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| 245 | 1 | 0 | |a Generalized linear models and extensions |c James W. Hardin ; Joseph M. Hilbe |
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 627f 2007 A 10032(2) |
|---|---|
| DE-BY-TUM_katkey | 1612394 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010083213 |
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| adam_text | Titel: Generalized linear models and extensions
Autor: Hardin, James W.
Jahr: 2007
Contents
List of Tables xvii
List of Figures xix
List of Listings xxii
Preface xxiii
1 Introduction 1
1.1 Origins and motivation........................... 1
1.2 Notational conventions........................... 3
1.3 Applied or theoretical?........................... 4
1.4 Road map.................................. 4
1.5 Installing the support materials...................... 6
1 Foundations of Generalized Linear Models 7
2 GLMs 9
2.1 Components................................. 11
2.2 Assumptions................................. 12
2.3 Exponential family............................. 13
2.4 Example: Using an offset in a GLM.................... 15
2.5 Summary................................... 16
3 GLM estimation algorithms 19
3.1 Newton-Raphson (using the observed Hessian).............. 25
3.2 Starting values for Newton-Raphson................... 27
3.3 IRLS (using the expected Hessian) .................... 28
3.4 Starting values for IRLS.......................... 31
3.5 Goodness of fit ............................... 31
3.6 Estimated variance matrices........................ 32
Contents
Vill
3.6.1 Hessian............................... 34
3.6.2 Outer product of the gradient.................. 35
3.6.3 Sandwich.............................. 35
3.6.4 Modified sandwich......................... 36
3.6.5 Unbiased sandwich........................ 37
3.6.6 Modified unbiased sandwich................... 38
3.6.7 Weighted sandwich: Newey-West................ 38
3.6.8 Jackknife...................*........... 40
3.6.8.1 Usual jackknife..................... 40
3.6.8.2 One-step jackknife ................... 41
3.6.8.3 Weighted jackknife................... 41
3.6.8.4 Variable jackknife.................... 41
3.6.9 Bootstrap ............................. 42
3.6.9.1 Usual bootstrap..................... 42
3.6.9.2 Grouped bootstrap................... 43
3.7 Estimation algorithms ........................... 43
3.8 Summary................................... 44
4 Analysis of fit 47
4.1 Deviance................................... 48
4.2 Diagnostics.................................. 49
4.2.1 Cook s distance.......................... 49
4.2.2 Overdispersion........................... 49
4.3 Assessing the link function......................... 50
4.4 Checks for systematic departure from the model............. 51
4.5 Residual analysis.............................. 52
4.5.1 Response residuals......................... 53
4.5.2 Working residuals......................... 53
4.5.3 Pearson residuals......................... 54
4.5.4 Partial residuals.......................... 54
4.5.5 Anscombe residuals........................ 54
Contents ix
4.5.6 Deviance residuals......................... 55
4.5.7 Adjusted deviance residuals ................... 55
4.5.8 Likelihood residuals........................ 55
4.5.9 Score residuals........................... 55
4.6 Model statistics............................... 55
4.6.1 Criterion measures ........................ 56
4.6.1.1 AIC ........................... 56
4.6.1.2 BIC............................ 57
4.6.2 The interpretation of R2 in linear regression.......... 58
4.6.2.1 Percent variance explained............... 58
4.6.2.2 The ratio of variances.................. 58
4.6.2.3 A transformation of the likelihood ratio ....... 59
4.6.2.4 A transformation of the F test............. 59
4.6.2.5 Squared correlation................... 59
4.6.3 Generalizations of linear regression R2 interpretations..... 59
4.6.3.1 Efron s pseudo-R2.................... 60
4.6.3.2 McFadden s likelihood-ratio index........... 60
4.6.3.3 Ben-Akiva and Lerman adjusted likelihood-ratio index 60
4.6.3.4 McKelvey and Zavoina ratio of variances....... 61
4.6.3.5 Transformation of likelihood ratio........... 61
4.6.3.6 Cragg and Uhler normed measure........... 61
4.6.4 More R2 measures......................... 62
4.6.4.1 The count R2...................... 62
4.6.4.2 The adjusted count R2................. 62
4.6.4.3 Veall and Zimmermann R2............... 62
4.6.4.4 Cameron-Windmeijer R2................ 62
II Continuous-Response Models 65
5 The Gaussian family 67
5.1 Derivation of the GLM Gaussian family.................. 68
Contents
÷
5.2 Derivation in terms of the mean...................... 68
5.3 IRLS GLM algorithm (nonbinomial) ................... 70
5.4 Maximum likelihood estimation...................... 73
5.5 GLM log-normal models.......................... 74
5.6 Expected versus observed information matrix .............. 75
5.7 Other Gaussian links............................ 77
5.8 Example: Relation to OLS......................... 77
5.9 Example: Beta-carotene.......................... 79
6 The gamma family 89
6.1 Derivation of the gamma model...................... 90
6.2 Example: Reciprocal link.......................... 92
6.3 Maximum likelihood estimation...................... 95
6.4 Log-gamma models............................. 96
6.5 Identity-gamma models........................... 100
6.6 Using the gamma model for survival analysis............... 101
7 The inverse Gaussian family 105
7.1 Derivation of the inverse Gaussian model................. 105
7.2 The inverse Gaussian algorithm...................... 107
7.3 Maximum likelihood algorithm....................... 107
7.4 Example: The canonical inverse Gaussian ................ 108
7.5 Noncanonical links............................. 109
8 The power family and link 113
8.1 Power links.................................. 113
8.2 Example: Power link............................ 114
8.3 The power family.............................. 115
III Binomial Response Models 117
9 The binomial-logit family 119
9.1 Derivation of the binomial model..................... 120
9.2 Derivation of the Bernoulli model..................... 123
Contents xi
9.3 The binomial regression algorithm..................... 124
9.4 Example: Logistic regression........................ 126
9.4.1 Model producing logistic coefficients: The heart data..... 127
9.4.2 Model producing logistic odds ratios............... 128
9.5 GOF statistics................................ 129
9.6 Interpretation of parameter estimates................... 132
10 The general binomial family 141
10.1 Noncanonical binomial models....................... 141
10.2 Noncanonical binomial links (binary form)................ 142
10.3 The probit model.............................. 143
10.4 The clog-log and log-log models...................... 148
10.5 Other links.................................. 155
10.6 Interpretation of coefficients........................ 156
10.6.1 Identity link............................ 156
10.6.2 Logit link.............................. 156
10.6.3 Log link .............................. 157
10.6.4 Log complement link....................... 158
10.6.5 Summary.............................. 159
10.7 Generalized binomial regression...................... 159
11 The problem of overdispersion 165
11.1 Overdispersion................................ 165
11.2 Scaling of standard errors ......................... 170
11.3 Williams procedure............................. 175
11.4 Robust standard errors........................... 178
IV Count Response Models 181
12 The Poisson family 183
12.1 Count response regression models..................... 183
12.2 Derivation of the Poisson algorithm.................... 184
12.3 Poisson regression: Examples ....................... 189
Contents
Xll
12.4 Example: Testing overdispersion in the Poisson model ......... 192
12.5 Using the Poisson model for survival analysis............... 194
12.6 Using offsets to compare models...................... 195
12.7 Interpretation of coefficients........................ 197
13 The negative binomial family 199
13.1 Constant overdispersion .......................... 201
13.2 Variable overdispersion........................... 203
13.2.1 Derivation in terms of a Poisson-gamma mixture.......203
13.2.2 Derivation in terms of the negative binomial probability function 206
13.2.3 The canonical link negative binomial parameterization .... 207
13.3 The log-negative binomial parameterization ............... 209
13.4 Negative binomial examples........................ 211
13.5 The geometric family............................ 215
13.6 Interpretation of coefficients........................ 218
14 Other count data models 221
14.1 Count response regression models..................... 221
14.2 Zero-truncated models........................... 224
14.3 Zero-inflated models ............................ 227
14.4 Hurdle models................................ 232
14.5 Heterogeneous negative binomial models................. 235
14.6 Generalized Poisson regression models .................. 239
14.7 Censored count response models...................... 241
V Multinomial Response Models 249
15 The ordered-response family 251
15.1 Ordered outcomes for general link..................... 252
15.2 Ordered outcomes for specific links.................... 254
15.2.1 Ordered logit............................ 254
15.2.2 Ordered probit........................... 255
15.2.3 Ordered clog-log.......................... 255
Contents xiii
15.2.4 Ordered log-log.......................... 256
15.2.5 Ordered cauchit.......................... 256
15.3 Generalized ordered outcome models................... 257
15.4 Example: Synthetic data.......................... 258
15.5 Example: Automobile data......................... 263
15.6 Partial proportional-odds models..................... 269
15.7 Continuation ratio models......................... 273
16 Unordered-response family 279
16.1 The multinomial logit model........................ 280
16.1.1 Example: Relation to logistic regression............. 280
16.1.2 Example: Relation to conditional logistic regression...... 281
16.1.3 Example: Extensions with conditional logistic regression . . . 283
16.1.4 The independence of irrelevant alternatives........... 284
16.1.5 Example: Assessing the IIA ................... 285
16.1.6 Interpreting coefficients...................... 287
16.1.7 Example: Medical admissions—introduction.......... 287
16.1.8 Example: Medical admissions—summary............ 289
16.2 The multinomial probit model....................... 295
16.2.1 Example: A comparison of the models ............. 297
16.2.2 Example: Comparing probit and multinomial probit...... 299
16.2.3 Example: Concluding remarks.................. 302
VI Extensions to the GLM 305
17 Extending the likelihood 307
17.1 The quasilikelihood............................. 307
17.2 Example: Wedderburn s leaf blotch data................. 308
17.3 Generalized additive models........................ 316
18 Clustered data 319
18.1 Generalization from individual to clustered data............. 319
18.2 Pooled estimators.............................. 320
xiy Contents
18.3 Fixed effects.............·................... 321
18.3.1 Unconditional fixed-effects estimators.............. 322
18.3.2 Conditional fixed-effects estimators............... 323
18.4 Random effects............................... 325
18.4.1 Maximum likelihood estimation................. 325
18.4.2 Gibbs sampling.......................... 329
18.5 GEEs..................................... 330
18.6 Other models................................ 333
VII Stata Software 337
19 Programs for Stata 339
19.1 The glm command............................. 340
19.1.1 Syntax............................... 340
19.1.2 Description............................. 341
19.1.3 Options............................... 341
19.2 The predict command after glm...................... 345
19.2.1 Syntax............................... 345
19.2.2 Options............................... 345
19.3 User-written programs........................... 347
19.3.1 Global macros available for user-written programs....... 347
19.3.2 User-written variance functions ................. 348
19.3.3 User-written programs for link functions............ 350
19.3.4 User-written programs for Newey-West weights........ 352
19.4 Remarks................................... 353
19.4.1 Equivalent commands....................... 353
19.4.2 Special comments on family(Gaussian) models......... 353
19.4.3 Special comments on family(binomial) models......... 353
19.4.4 Special comments on family(nbinomial) models ........ 354
19.4.5 Special comment on family(gamma) link(log) models..... 354
A Tables 355
Contents xv
References 369
Author index 379
Subject index 383
|
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| id | DE-604.BV022370369 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:53:54Z |
| institution | BVB |
| isbn | 1597180149 9781597180146 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015579559 |
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| owner_facet | DE-824 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-522 DE-N2 |
| physical | XXII, 387 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Stata Press |
| record_format | marc |
| series2 | A Stata Press publication |
| spellingShingle | Hardin, James W. 1963- Generalized linear models and extensions Lineaire modellen gtt Software gtt Statistische analyse gtt Statistik Linear Models Linear models (Statistics) Statistics Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| subject_GND | (DE-588)4124382-1 |
| title | Generalized linear models and extensions |
| title_auth | Generalized linear models and extensions |
| title_exact_search | Generalized linear models and extensions |
| title_full | Generalized linear models and extensions James W. Hardin ; Joseph M. Hilbe |
| title_fullStr | Generalized linear models and extensions James W. Hardin ; Joseph M. Hilbe |
| title_full_unstemmed | Generalized linear models and extensions James W. Hardin ; Joseph M. Hilbe |
| title_short | Generalized linear models and extensions |
| title_sort | generalized linear models and extensions |
| topic | Lineaire modellen gtt Software gtt Statistische analyse gtt Statistik Linear Models Linear models (Statistics) Statistics Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| topic_facet | Lineaire modellen Software Statistische analyse Statistik Linear Models Linear models (Statistics) Statistics Verallgemeinertes lineares Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015579559&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hardinjamesw generalizedlinearmodelsandextensions AT hilbejosephm generalizedlinearmodelsandextensions |
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