Introduction to general and generalized linear models:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2011
|
| Schriftenreihe: | Texts in statistical science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 302 S. graph. Darst. |
| ISBN: | 9781420091557 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to general and generalized linear models |c Henrik Madsen ; Poul Thyregod |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XIII, 302 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts in statistical science | |
| 650 | 4 | |a Linear models (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804139369225781248 |
|---|---|
| adam_text | Contents
Preface
xi
Notation............................... xiii
1
Introduction
1
1.1
Examples of types of data
................... 2
1.2
Motivating examples
...................... 3
1.3
A first view on the models
.................. 5
2
The likelihood principle
9
2.1
Introduction
.......................... 9
2.2
Point estimation theory
.................... 10
2.3
The likelihood function
.................... 14
2.4
The score function
....................... 17
2.5
The information matrix
.................... 18
2.6
Alternative parameterizations of the likelihood
....... 20
2.7
The maximum likelihood estimate (MLE)
.......... 21
2.8
Distribution of the ML estimator
............... 22
2.9
Generalized loss-function and deviance
............ 23
2.10
Quadratic approximation of the log-likelihood
....... 23
2.11
Likelihood ratio tests
..................... 25
2.12
Successive testing in hypothesis chains
............ 27
2.13
Dealing with nuisance parameters
.............. 33
2.14
Problems
............................ 38
3
General linear models
41
3.1
Introduction
.......................... 41
3.2
The multivariate normal distribution
............. 42
3.3
General linear models
..................... 44
3.4
Estimation of parameters
................... 48
3.5
Likelihood ratio tests
..................... 53
3.6
Tests for model reduction
................... 58
3.7
Collinearity
........................... 64
3.8
Inference on parameters in parameterized models
...... 70
3.9
Model diagnostics: residuals and influence
.......... 73
viii
Contents
3.10
Analysis of residuals
...................... 77
3.11
Representation of linear models
................ 78
3.12
General linear models in
R
.................. 81
3.13
Problems
............................ 83
Generalized linear models
87
4.1
Types of response variables
.................. 89
4.2
Exponential families of distributions
............. 90
4.3
Generalized linear models
................... 99
4.4
Maximum likelihood estimation
............... 102
4.5
Likelihood ratio tests
.....................
Ill
4.6
Test for model reduction
................... 115
4.7
Inference on individual parameters
.............. 116
4.8
Examples
............................ 117
4.9
Generalized linear models in
R
................ 152
4.10
Problems
............................ 153
Mixed effects models
157
5.1
Gaussian mixed effects model
................ 159
5.2
One-way random effects model
................ 160
5.3
More examples of hierarchical variation
........... 174
5.4
General linear mixed effects models
............. 179
5.5
Bayesian interpretations
.................... 185
5.6
Posterior distributions
..................... 191
5.7
Random effects for multivariate measurements
....... 192
5.8
Hierarchical models in metrology
............... 197
5.9
General mixed effects models
................. 199
5.10
Laplace approximation
.................... 201
5.11
Mixed effects models in
R
................... 218
5.12
Problems
............................ 219
Hierarchical models
225
6.1
Introduction, approaches to modeling of overdispersion
. . 225
6.2
Hierarchical
Poisson
Gamma model
............. 226
6.3
Conjugate prior distributions
................. 233
6.4
Examples of one-way random effects models
......... 237
6.5
Hierarchical generalized linear models
............ 242
6.6
Problems
............................ 243
Real life inspired problems
245
7.1 Dioxin
emission
........................ 246
7.2
Depreciation of used cars
................... 249
7.3
Young fish in the North Sea
.................. 250
7.4
Traffic accidents
........................ 251
7.5
Mortality of snails
....................... 252
Contents
ix
A Supplement on the law of error propagation
255
A.I Function of one random variable
............... 255
A.
2
Function of several random variables
............. 255
В
Some probability distributions
257
B.I The binomial distribution model
............... 259
B.2 The
Poisson
distribution model
................ 262
B.3 The negative binomial distribution model
.......... 264
B.4 The exponential distribution model
............. 266
B.5 The gamma distribution model
................ 268
B.6 The inverse Gaussian distribution model
.......... 275
B.7 Distributions derived from the normal distribution
..... 280
B.8 The Gamma-function
..................... 284
С
List of symbols
285
Bibliography
287
Index
293
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| isbn | 9781420091557 |
| language | English |
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| physical | XIII, 302 S. graph. Darst. |
| publishDate | 2011 |
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| publisher | CRC Press |
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| series2 | Texts in statistical science |
| spelling | Madsen, Henrik 1955- Verfasser (DE-588)101522623X aut Introduction to general and generalized linear models Henrik Madsen ; Poul Thyregod Boca Raton [u.a.] CRC Press 2011 XIII, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Verallgemeinertes lineares Modell (DE-588)4124382-1 s DE-604 Thyregod, Poul Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017727045&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Madsen, Henrik 1955- Thyregod, Poul Introduction to general and generalized linear models Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| subject_GND | (DE-588)4124382-1 (DE-588)4151278-9 |
| title | Introduction to general and generalized linear models |
| title_auth | Introduction to general and generalized linear models |
| title_exact_search | Introduction to general and generalized linear models |
| title_full | Introduction to general and generalized linear models Henrik Madsen ; Poul Thyregod |
| title_fullStr | Introduction to general and generalized linear models Henrik Madsen ; Poul Thyregod |
| title_full_unstemmed | Introduction to general and generalized linear models Henrik Madsen ; Poul Thyregod |
| title_short | Introduction to general and generalized linear models |
| title_sort | introduction to general and generalized linear models |
| topic | Linear models (Statistics) Verallgemeinertes lineares Modell (DE-588)4124382-1 gnd |
| topic_facet | Linear models (Statistics) Verallgemeinertes lineares Modell Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017727045&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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