An introduction to generalized linear models:
Saved in:
| Previous Title: | Dobson, Annette J. Introduction to statistical modelling |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Edition: | 3. ed. |
| Series: | Chapman & Hall/CRC Texts in statistical science series
[77] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 307 S. graph. Darst. |
| ISBN: | 9781584889502 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804138133413953536 |
|---|---|
| adam_text | Contents
Preface
1
Introduction
1
1.1
Background
1
1.2
Scope
1
1.3
Notation
5
1.4
Distributions related to the Normal distribution
7
1.5
Quadratic forms
11
1.6
Estimation
12
1.7
Exercises
15
2
Model Fitting
19
2.1
Introduction
19
2.2
Examples
19
2.3
Some principles of statistical modelling
32
2.4
Notation and coding for explanatory variables
37
2.5
Exercises
40
3
Exponential Family and Generalized Linear Models
45
3.1
Introduction
45
3.2
Exponential family of distributions
46
3.3
Properties of distributions in the exponential family
48
3.4
Generalized linear models
51
3.5
Examples
52
3.6
Exercises
55
4
Estimation
59
4.1
Introduction
59
4.2
Example: Failure times for pressure vessels
59
4.3
Maximum likelihood estimation
64
4.4
Poisson
regression example
66
4.5
Exercises
69
5
Inference
73
5.1
Introduction
73
5.2
Sampling distribution for score statistics
74
5.3 Taylor
series
approximations
76
5.4
Sampling
distribution for
MLEs
77
5.5
Log-likelihood ratio statistic
79
5.6
Sampling distribution for the deviance
80
5.7
Hypothesis testing
85
5.8
Exercises
87
Normal Linear Models
89
6.1
Introduction
89
6.2
Basic results
89
6.3
Multiple linear regression
95
6.4
Analysis of variance
102
6.5
Analysis of covariance
114
6.6
General linear models
117
6.7
Exercises
118
Binary Variables and Logistic Regression
123
7.1
Probability distributions
123
7.2
Generalized linear models
124
7.3
Dose response models
124
7.4
General logistic regression model
131
7.5
Goodness of fit statistics
135
7.6
Residuals
138
7.7
Other diagnostics
139
7.8
Example: Senility and WAIS
140
7.9
Exercises
143
Nominal and Ordinal Logistic Regression
149
8.1
Introduction
149
8.2
Multinomial distribution
149
8.3
Nominal logistic regression
151
8.4
Ordinal logistic regression
157
8.5
General comments
162
8.6
Exercises
163
Poisson
Regression and Log-Linear Models
165
9.1
Introduction
165
9.2
Poisson
regression
166
9.3
Examples of contingency tables
171
9.4
Probability models for contingency tables
175
9.5
Log-linear models
177
9.6
Inference for log-linear models
178
9.7
Numerical examples
179
9.8
Remarks
183
9.9
Exercises
183
10
Survival
Analysis
187
10.1
Introduction
187
10.2
Survivor functions and hazard functions
189
10.3
Empirical survivor function
193
10.4
Estimation
195
10.5
Inference
198
10.6
Model checking
199
10.7
Example: Remission times
201
10.8
Exercises
202
11
Clustered and Longitudinal Data
207
11.1
Introduction
207
11.2
Example: Recovery from stroke
209
11.3
Repeated measures models for Normal data
213
11.4
Repeated measures models for non-Normal data
218
11.5
Multilevel models
219
11.6
Stroke example continued
222
11.7
Comments
224
11.8
Exercises
225
12
Bayesian Analysis
229
12.1
Frequentisi
and Bayesian paradigms
229
12.2
Priors
233
12.3
Distributions and hierarchies in Bayesian analysis
238
12.4
WinBUGS software for Bayesian analysis
238
12.5
Exercises
241
13
Markov Chain Monte Carlo Methods
243
13.1
Why standard inference fails
243
13.2
Monte Carlo integration
243
13.3
Markov chains
245
13.4
Bayesian inference
255
13.5
Diagnostics of chain convergence
256
13.6
Bayesian model fit: the DIC
260
13.7
Exercises
262
14
Example Bayesian Analyses
267
14.1
Introduction
267
14.2
Binary variables and logistic regression
267
14.3
Nominal logistic regression
271
14.4
Latent variable model
272
14.5
Survival analysis
275
14.6
Random effects
277
14.7
Longitudinal data analysis
279
14.8
Some practical tips for WinBUGS
286
14.9
Exercises
288
Appendix
291
Software
293
References
295
Index
303
|
| adam_txt |
Contents
Preface
1
Introduction
1
1.1
Background
1
1.2
Scope
1
1.3
Notation
5
1.4
Distributions related to the Normal distribution
7
1.5
Quadratic forms
11
1.6
Estimation
12
1.7
Exercises
15
2
Model Fitting
19
2.1
Introduction
19
2.2
Examples
19
2.3
Some principles of statistical modelling
32
2.4
Notation and coding for explanatory variables
37
2.5
Exercises
40
3
Exponential Family and Generalized Linear Models
45
3.1
Introduction
45
3.2
Exponential family of distributions
46
3.3
Properties of distributions in the exponential family
48
3.4
Generalized linear models
51
3.5
Examples
52
3.6
Exercises
55
4
Estimation
59
4.1
Introduction
59
4.2
Example: Failure times for pressure vessels
59
4.3
Maximum likelihood estimation
64
4.4
Poisson
regression example
66
4.5
Exercises
69
5
Inference
73
5.1
Introduction
73
5.2
Sampling distribution for score statistics
74
5.3 Taylor
series
approximations
76
5.4
Sampling
distribution for
MLEs
77
5.5
Log-likelihood ratio statistic
79
5.6
Sampling distribution for the deviance
80
5.7
Hypothesis testing
85
5.8
Exercises
87
Normal Linear Models
89
6.1
Introduction
89
6.2
Basic results
89
6.3
Multiple linear regression
95
6.4
Analysis of variance
102
6.5
Analysis of covariance
114
6.6
General linear models
117
6.7
Exercises
118
Binary Variables and Logistic Regression
123
7.1
Probability distributions
123
7.2
Generalized linear models
124
7.3
Dose response models
124
7.4
General logistic regression model
131
7.5
Goodness of fit statistics
135
7.6
Residuals
138
7.7
Other diagnostics
139
7.8
Example: Senility and WAIS
140
7.9
Exercises
143
Nominal and Ordinal Logistic Regression
149
8.1
Introduction
149
8.2
Multinomial distribution
149
8.3
Nominal logistic regression
151
8.4
Ordinal logistic regression
157
8.5
General comments
162
8.6
Exercises
163
Poisson
Regression and Log-Linear Models
165
9.1
Introduction
165
9.2
Poisson
regression
166
9.3
Examples of contingency tables
171
9.4
Probability models for contingency tables
175
9.5
Log-linear models
177
9.6
Inference for log-linear models
178
9.7
Numerical examples
179
9.8
Remarks
183
9.9
Exercises
183
10
Survival
Analysis
187
10.1
Introduction
187
10.2
Survivor functions and hazard functions
189
10.3
Empirical survivor function
193
10.4
Estimation
195
10.5
Inference
198
10.6
Model checking
199
10.7
Example: Remission times
201
10.8
Exercises
202
11
Clustered and Longitudinal Data
207
11.1
Introduction
207
11.2
Example: Recovery from stroke
209
11.3
Repeated measures models for Normal data
213
11.4
Repeated measures models for non-Normal data
218
11.5
Multilevel models
219
11.6
Stroke example continued
222
11.7
Comments
224
11.8
Exercises
225
12
Bayesian Analysis
229
12.1
Frequentisi
and Bayesian paradigms
229
12.2
Priors
233
12.3
Distributions and hierarchies in Bayesian analysis
238
12.4
WinBUGS software for Bayesian analysis
238
12.5
Exercises
241
13
Markov Chain Monte Carlo Methods
243
13.1
Why standard inference fails
243
13.2
Monte Carlo integration
243
13.3
Markov chains
245
13.4
Bayesian inference
255
13.5
Diagnostics of chain convergence
256
13.6
Bayesian model fit: the DIC
260
13.7
Exercises
262
14
Example Bayesian Analyses
267
14.1
Introduction
267
14.2
Binary variables and logistic regression
267
14.3
Nominal logistic regression
271
14.4
Latent variable model
272
14.5
Survival analysis
275
14.6
Random effects
277
14.7
Longitudinal data analysis
279
14.8
Some practical tips for WinBUGS
286
14.9
Exercises
288
Appendix
291
Software
293
References
295
Index
303 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Dobson, Annette J. 1945- Barnett, Adrian G. |
| author_GND | (DE-588)14077954X (DE-588)136168019 |
| author_facet | Dobson, Annette J. 1945- Barnett, Adrian G. |
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| author_sort | Dobson, Annette J. 1945- |
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| building | Verbundindex |
| bvnumber | BV035146373 |
| callnumber-first | Q - Science |
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| classification_tum | MAT 622f |
| ctrlnum | (OCoLC)315676440 (DE-599)HBZHT015652701 |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV035146373 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:28:58Z |
| indexdate | 2024-07-09T21:23:21Z |
| institution | BVB |
| isbn | 9781584889502 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016813675 |
| oclc_num | 315676440 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-20 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-M347 DE-578 DE-188 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-20 DE-473 DE-BY-UBG DE-19 DE-BY-UBM DE-M347 DE-578 DE-188 DE-11 |
| physical | 307 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall/CRC Texts in statistical science series |
| series2 | Chapman & Hall/CRC Texts in statistical science series |
| spelling | Dobson, Annette J. 1945- Verfasser (DE-588)14077954X aut An introduction to generalized linear models Annette J. Dobson ; Adrian G. Barnett 3. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2008 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC Texts in statistical science series [77] Lineares Modell (DE-588)4134827-8 gnd rswk-swf Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Modelltheorie (DE-588)4114617-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Verallgemeinertes lineares Modell (DE-588)4124382-1 s Statistik (DE-588)4056995-0 s Modellierung (DE-588)4170297-9 s 1\p DE-604 Lineares Modell (DE-588)4134827-8 s 2\p DE-604 Modelltheorie (DE-588)4114617-7 s 3\p DE-604 Barnett, Adrian G. Verfasser (DE-588)136168019 aut Frühere Ausg. u.d.T. Dobson, Annette J. Introduction to statistical modelling Chapman & Hall/CRC Texts in statistical science series [77] (DE-604)BV022819715 77 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dobson, Annette J. 1945- Barnett, Adrian G. An introduction to generalized linear models Chapman & Hall/CRC Texts in statistical science series Lineares Modell (DE-588)4134827-8 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Modellierung (DE-588)4170297-9 gnd Modelltheorie (DE-588)4114617-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4134827-8 (DE-588)4124382-1 (DE-588)4170297-9 (DE-588)4114617-7 (DE-588)4056995-0 (DE-588)4151278-9 |
| title | An introduction to generalized linear models |
| title_auth | An introduction to generalized linear models |
| title_exact_search | An introduction to generalized linear models |
| title_exact_search_txtP | An introduction to generalized linear models |
| title_full | An introduction to generalized linear models Annette J. Dobson ; Adrian G. Barnett |
| title_fullStr | An introduction to generalized linear models Annette J. Dobson ; Adrian G. Barnett |
| title_full_unstemmed | An introduction to generalized linear models Annette J. Dobson ; Adrian G. Barnett |
| title_old | Dobson, Annette J. Introduction to statistical modelling |
| title_short | An introduction to generalized linear models |
| title_sort | an introduction to generalized linear models |
| topic | Lineares Modell (DE-588)4134827-8 gnd Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd Modellierung (DE-588)4170297-9 gnd Modelltheorie (DE-588)4114617-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Lineares Modell Verallgemeinertes lineares Modell Modellierung Modelltheorie Statistik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016813675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022819715 |
| work_keys_str_mv | AT dobsonannettej anintroductiontogeneralizedlinearmodels AT barnettadriang anintroductiontogeneralizedlinearmodels |