Generalized linear models and extensions:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
College Station, Tex.
Stata Press
2012
|
| Edition: | 3. 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=025050582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XXIV, 455 S. graph. Darst. |
| ISBN: | 9781597181051 1597181056 |
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| 245 | 1 | 0 | |a Generalized linear models and extensions |c James W. Hardin ; Joseph M. Hilbe |
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|---|---|
| adam_text | Titel: Generalized linear models and extensions
Autor: Hardin, James W
Jahr: 2012
Contents
List of tables xvii
List of figures xix
Preface xxiii
1 Introduction 1
1.1 Origins and motivation.......................... 2
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 ................................. 17
3 GLM estimation algorithms 19
3.1 Newton Raphson (using the observed Hessian) ............ 25
3.2 Starting values for Newton-Raphson.................. 26
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
3.6.1 Hessian.............................. 34
Contents
3.6.2 Outer product of the gradient................. 35
3.6.3 Sandwich ............................ ?*¦
3.6.4 Modified sandwich ....................... 30
3.6.5 Unbiased sandwich....................... 3
3.6.6 Modified unbiased sandwich.................. 38
3.6.7 Weighted sandwich: Newev West............... 39
3.6.8 Jackknife............................. 40
3.6.8.1 Usual jackknife.................... 10
3.6.8.2 One-step jackknife.................. 41
3.6.8.3 Weighted jackknife.................. 41
3.6.8.4 Variable jackknife .................. 42
3.6.9 Bootstrap............................ 42
3.6.9.1 Usual bootstrap ................... 13
3.6.9.2 Grouped bootstrap.................. 43
3.7 Estimation algorithms.......................... 43
3.8 Summary................................. 14
Analysis of fit 47
4.1 Deviance.................................. 48
4.2 Diagnostics................................ 19
4.2.1 Cook s distance......................... 10
4.2.2 Overdispersion ......................... 19
4.3 Assessing the link function........................ 50
4.4 Residual analysis............................. 5.1
4.4.1 Response residuals....................... 53
4.4.2 Working residuals........................ 53
4.4.3 Pearson residuals........................ 53
4.4.4 Partial residuals......................... 53
4.4.5 Anscombe residuals....................... 54
4.4.6 Deviance residuals ....................... 54
4.4.7 Adjusted deviance residuals.................. 54
Contents ix
4.4.8 Likelihood residuals....................... 55
4.4.9 Score residuals ......................... 55
4.5 Checks for systematic departure from the model............ 55
4.6 Model statistics.............................. 56
4.6.1 Criterion measures....................... 56
4.6.1.1 AIC.......................... 56
4.6.1.2 BIC.......................... 58
4.6.2 The interpretation of R2 in linear regression......... 59
4.6.2.1 Percentage variance explained............ 59
4.6.2.2 The ratio of variances................ 60
4.6.2.3 A transformation of the likelihood ratio...... 60
4.6.2.4 A transformation of the F test ........... 60
4.6.2.5 Squared correlation.................. 60
4.6.3 Generalizations of linear regression R2 interpretations .... 60
4.6.3.1 Efron s pseudo-R2 .................. 61
4.6.3.2 McFadden s likelihood-ratio index ......... 61
4.6.3.3 Ben-Akiva and Lerman adjusted likelihood-ratio
index ......................... 61
4.6.3.4 McKelvcy and Zavoina ratio of variances...... 62
4.6.3.5 Transformation of likelihood ratio ......... 62
4.6.3.6 Cragg and Uhler normed measure ......... 62
4.6.4 More R2 measures ....................... 63
4.6.4.1 The count R2..................... 63
4.6.4.2 The adjusted count R2................ 63
4.6.4.3 Veall and Zimmermann R2 ............. 63
4.6.4.4 Cameron-Windmeijer R2 .............. 64
4.7 Marginal effects.............................. 64
4.7.1 Marginal effects for GLMs................... 64
4.7.2 Discrete change for GLMs................... 68
x Contents
5 Data synthesis 71
5.1 Generating correlated data........................ 71
5.2 Generating data from a specified population.............. 75
5.2.1 Generating data for linear regression............. 76
5.2.2 Generating data for logistic regression ............ 78
5.2.3 Generating data for probit regression............. 80
5.2.4 Generating data for cloglog regression ............ 81
5.2.5 Generating data for Gaussian variance and log link..... 82
5.2.6 Generating underdispersed count data............ 83
5.3 Simulation................................. 85
5.3.1 Heteroskedasticity in linear regression............. 85
5.3.2 Power analysis.......................... 88
5.3.3 Comparing fit of Poisson and negative binomial....... 90
5.3.4 Effect of omitted covariate on R.Efron m Poisson regression . 93
II Continuous Response Models 95
6 The Gaussian family 97
6.1 Derivation of the GLM Gaussian family................ 98
6.2 Derivation in terms of the mean..................... 98
6.3 IRLS GLM algorithm (nonbinomial).................. 100
6.4 ML estimation .............................. 103
6.5 GLM log-normal models......................... 104
6.6 Expected versus observed information matrix............. 105
6.7 Other Gaussian links........................... 107
6.8 Example: Relation to OLS........................ 107
6.9 Example: Beta-carotene......................... 109
7 The gamma family 121
7.1 Derivation of the gamma model..................... 122
7.2 Example: Reciprocal link ........................ 124
7.3 ML estimation .............................. 127
Contents xi
7.4 Log-gamma models............................ 128
7.5 Identity-gamma models ......................... 132
7.6 Using the gamma model for survival analysis ............. 133
8 The inverse Gaussian family 137
8.1 Derivation of the inverse Gaussian model................ 137
8.2 The inverse Gaussian algorithm..................... 139
8.3 Maximum likelihood algorithm..................... 139
8.4 Example: The canonical inverse Gaussian............... 140
8.5 Noncanonical links............................ 141
9 The power family and link 147
9.1 Power links................................ 147
9.2 Example: Power link........................... 148
9.3 The power family............................. 149
III Binomial Response Models 151
10 The binomial-logit family 153
10.1 Derivation of the binomial model.................... 154
10.2 Derivation of the Bernoulli model.................... 157
10.3 The binomial regression algorithm ................... 158
10.4 Example: Logistic regression....................... 160
10.4.1 Model producing logistic coefficients: The heart data .... 161
10.4.2 Model producing logistic odds ratios............. 162
10.5 GOF statistics .............................. 163
10.6 Proportional data............................. 167
10.7 Interpretation of parameter estimates.................. 167
11 The general binomial family 177
11.1 Noncanonical binomial models...................... 177
11.2 Noncanonical binomial links (binary form)............... 178
11.3 The probit model............................. 179
11.4 The clog-log and log-log models..................... 185
xjj Contents
11.5 Other links ................................ 102
11.6 Interpretation of coefficients....................... 103
11.6.1 Identity link........................... 103
11.6.2 Logit link............................ 103
11.6.3 Log link............................. 194
11.6.4 Log complement link...................... 195
11.6.5 Summary ............................ 106
11.7 Generalized binomial regression..................... 196
12 The problem of overdispersion 203
12.1 Overdispersion .............................. 203
12.2 Scaling of standard errors........................ 209
12.3 Williams procedure ........................... 215
12.4 Robust standard errors.......................... 218
IV Count Response Models 221
13 The Poisson family 223
13.1 Count response regression models.................... 223
13.2 Derivation of the Poisson algorithm................... 224
13.3 Poisson regression: Examples...................... 228
13.4 Example: Testing overdispersion in the Poisson model........ 232
13.5 LTsing the Poisson model for survival analysis............. 234
13.6 Using offsets to compare models..................... 235
13.7 Interpretation of coefficients....................... 238
14 The negative binomial family 241
14.1 Constant overdispersion......................... 243
14.2 Variable overdispersion.......................... 245
14.2.1 Derivation in terms of a Poisson-gamma mixture...... 245
14.2.2 Derivation in terms of the negative binomial probability
function............................. 248
14.2.3 The canonical link negative binomial parameterization . . . 249
14.3 The log-negative binomial parameterization .............. 251
Contents xiii
14.4 Negative binomial examples....................... 254
14.5 The geometric family........................... 260
14.6 Interpretation of coefficients....................... 264
15 Other count data models 267
15.1 Count response regression models.................... 267
15.2 Zero-truncated models.......................... 270
15.3 Zero-inflated models........................... 273
15.4 Hurdle models............................... 280
15.5 Negative binomial(P) models...................... 284
15.6 Heterogeneous negative binomial models................ 289
15.7 Generalized Poisson regression models................. 293
15.8 Poisson inverse Gaussian models .................... 295
15.9 Censored count response models .................... 297
15.10 Finite mixture models.......................... 306
V Multinomial Response Models 311
16 The ordered-response family 313
16.1 Interpretation of coefficients: Single binary predictor......... 314
16.2 Ordered outcomes for general link.................... 316
16.3 Ordered outcomes for specific links................... 319
16.3.1 Ordered logit .......................... 319
16.3.2 Ordered probit ......................... 320
16.3.3 Ordered clog-log......................... 320
16.3.4 Ordered log-log......................... 321
16.3.5 Ordered cauchit......................... 321
16.4 Generalized ordered outcome models.................. 322
16.5 Example: Synthetic data......................... 323
16.6 Example: Automobile data ....................... 329
16.7 Partial proportional-odds models.................... 335
16.8 Continuation-ratio models........................339
xiv Contents
17 Unordered-response family 345
17.1 The multinomial logit model....................... 346
17.1.1 Interpretation of coefficients: Single binary predictor .... 346
17.1.2 Example: Relation to logistic regression ........... 348
17.1.3 Example: Relation to conditional logistic regression..... 349
17.1.4 Example: Extensions with conditional logistic regression . . 351
17.1.5 The independence of irrelevant alternatives ......... 351
17.1.6 Example: Assessing the IIA.................. 352
17.1.7 Interpreting coefficients..................... 354
17.1.8 Example: Medical admissions -introduction......... 355
17.1.9 Example: Medical admissions?summary........... 357
17.2 The multinomial probit model...................... 361
17.2.1 Example: A comparison of the models............ 362
17.2.2 Example: Comparing probit and multinomial probit .... 364
17.2.3 Example: Concluding remarks................. 368
VI Extensions to the GLM 369
18 Extending the likelihood 371
18.1 The quasilikelihood............................ 371
18.2 Example: Wedderbunrs leaf blotch data................ 372
18.3 Generalized additive models....................... 381
19 Clustered data 383
19.1 Generalization from individual to clustered data............ 383
19.2 Pooled estimators............................. 384
19.3 Fixed effects................................ 386
19.3.1 Unconditional fixed-effects estimators............. 386
19.3.2 Conditional fixed-effects estimators.............. 387
19.4 Random effects.............................. 390
19.4.1 Maximum likelihood estimation................ 390
19.4.2 Gibbs sampling................ . ........ 394
Contents xv
19.5 GEEs ................................... 395
19.6 Other models............................... 398
VII Stata Software 403
20 Programs for Stata 405
20.1 The glm command............................ 406
20.1.1 Syntax.............................. 406
20.1.2 Description ........................... 408
20.1.3 Options ............................. 408
20.2 The predict command after glm..................... 412
20.2.1 Syntax.............................. 412
20.2.2 Options ............................. 412
20.3 User-written programs.......................... 414
20.3.1 Global macros available for user-written programs...... 414
20.3.2 User-written variance functions................ 415
20.3.3 User-written programs for link functions........... 417
20.3.4 User-written programs for Newey-West weights....... 419
20.4 Remarks.................................. 420
20.4.1 Equivalent commands ..................... 420
20.4.2 Special comments on family(Gaussian) models........ 120
20.4.3 Special comments on family(binomial) models........ 421
20.4.4 Special comments on family(nbinoniial) models....... 421
20.4.5 Special comment on family(gamma) link (log) models .... 421
A Tables 423
References 437
Author index 447
Subject index 451
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| id | DE-604.BV040194057 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:09:54Z |
| institution | BVB |
| isbn | 9781597181051 1597181056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025050582 |
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| physical | XXIV, 455 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| 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=025050582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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