Statistical modelling in R:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Edition: | 1. publ. |
| Series: | Oxford statistical science series
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 576 S. graph. Darst. |
| ISBN: | 9780199219148 9780199219131 |
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MARC
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| 245 | 1 | 0 | |a Statistical modelling in R |c Murray Aitkin ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XII, 576 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford statistical science series |v 35 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a R (Computer program language) | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematical statistics |x Data processing | |
| 650 | 4 | |a R (Computer program language) | |
| 650 | 0 | 7 | |a R |g Programm |0 (DE-588)4705956-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Aitkin, Murray |e Sonstige |4 oth | |
| 830 | 0 | |a Oxford statistical science series |v 35 |w (DE-604)BV001908661 |9 35 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016608963 | ||
Record in the Search Index
| _version_ | 1804137821783457792 |
|---|---|
| adam_text | Contents
1
Introducing R
1
1.1
Statistical packages and statistical modelling
1
1.2
Getting started in
R
1
1.3
Reading data into
R
3
1.4
Assignment and data generation
6
1.5
Displaying data
8
1.6
Data structures and the workspace
9
1.7
Transformations and data modification
11
1.8
Functions and suffixing
12
.8.1
Structure functions
13
.8.2
Mathematical functions
13
.8.3
Logical operators
14
.8.4
Control functions
14
.8.5
Statistical functions
14
.8.6
Random numbers
15
.8.7
Suffixes in expressions
16
1.8.8
Extracting subsets of data
17
1.8.9
Recoding
variâtes
and factors into new factors
17
.9
Graphical facilities
18
.10
Text functions
21
. 11
Writing your own functions
22
.12
Sorting and tabulation
23
.13
Editing
R
code
26
.14
Installing and using packages
27
2
Statistical modelling and inference
28
2.1
Statistical models
28
2.2
Types of variables
30
2.3
Population models
31
2.4
Random sampling
44
2.5
The likelihood function
44
viii CONTENTS
2.6
Inference for single parameter models
46
2.6.1
Comparing two simple hypotheses
47
2.6.2
Information about a single parameter
49
2.6.3
Comparing a simple null hypothesis and a composite
alternative
54
2.7
Inference with nuisance parameters
58
2.7.1
Profile likelihoods
59
2.7.2
Marginal likelihood for the variance
63
2.7.3
Likelihood normalizing transformations
66
2.7.4
Alternative test procedures
68
2.7.5
Bayes
inference
71
2.7.6
Binomial model
74
2.7.7
Hypergeometric sampling from finite populations
80
2.8
The effect of the sample design on inference
81
2.9
The exponential family
82
2.9.1
Mean and variance
83
2.9.2
Generalized linear models
83
2.9.3
Maximum likelihood fitting of the GLM
84
2.9.4
Model comparisons through maximized likelihoods
87
2.10
Likelihood inference without models
89
2.10.1
Likelihoods for percentiles
89
2.10.2
Empirical likelihood
92
3
Regression and analysis of variance
97
3.1
An example
97
3.2
Strategies for model simplification
107
3.3
Stratified, weighted and clustered samples 111
3.4
Model criticism
114
3.4.1
Mis-specification of the probability distribution
116
3.4.2
Mis-specification of the link function
119
3.4.3
The occurrence of aberrant and influential observations
119
3.4.4
Mis-specification of the systematic part of the model
123
3.5
The
Box
-Сох
transformation family
123
3.6
Modelling and background information
126
3.7
Link functions and transformations
136
3.8
Regression models for prediction
138
3.9
Model choice and mean square prediction error
140
3.10
Model selection through cross-validation
141
3.11
Reduction of complex regression models
144
3.12
Sensitivity of the
Box
-Сох
transformation
153
3.13
The use of regression models for calibration
156
CONTENTS ix
3.14
Measurement error in the explanatory variables
159
3.15
Factorial designs
161
3.16
Unbalanced cross-classifications
168
3.16.1
The Bennett hostility data
168
3.16.2
ANO VA
of the cross-classification
170
3.16.3
Regression analysis of the cross-classification
174
3.16.4
Statistical package treatments of cross-classifications
176
3.17
Missing data
178
3.18
Approximate methods for missing data
180
3.19
Modelling of variance heterogeneity
180
3.19.1
Poison example
184
3.19.2
Tree example
191
4
Binary response data
195
4.1
Binary responses
195
4.2
Transformations and link functions
197
4.2.1
Profile likelihoods for functions of parameters
202
4.3
Model criticism
207
4.3.1
Mis-specification of the probability distribution
207
4.3.2
Mis-specification of the link function
207
4.3.3
The occurrence of aberrant and influential observations
207
4.4
Binary data with continuous covariates
208
4.5
Contingency table construction from binary data
223
4.6
The prediction of binary outcomes
235
4.7
Profile and conditional likelihoods in
2
χ
2
tables
242
4.8
Three-dimensional contingency tables with a binary response
246
4.8.1
Prenatal care and infant mortality
246
4.8.2
Coronary heart disease
248
4.9
Multidimensional contingency tables with a binary response
255
5
Multinomial and
Poisson
response data
269
5.1
The
Poisson
distribution
269
5.2
Cross-classified counts
271
5.3
Multicategory responses
279
5.4
Multinomial logit model
285
5.5
The Poisson-multinomial relation
287
5.6
Fitting the multinomial logit model
293
5.7
Ordered response categories
298
5.7.1
Common slopes for the regressions
299
5.7.2
Linear trend over response categories
301
x
CONTENTS
5.7.3 Proportional
slopes
304
5.7.4
The continuation ratio model
304
5.7.5
Other models
308
5.8
An Example
310
5.8.1
Multinomial logit model
ЗІЗ
5.8.2
Continuation ratio model
320
5.9
Structured multinomial responses
330
5.9.1
Independent outcomes
331
5.9.2
Correlated outcomes
339
6
Survival data
347
6.1
Introduction
347
6.2
The exponential distribution
347
6.3
Fitting the exponential distribution
349
6.4
Model criticism
354
6.5
Comparison with the normal family
361
6.6
Censoring
364
6.7
Likelihood function for censored observations
365
6.8
Probability plotting with censored data: the Kaplan-Meier
estimator
368
6.9
The gamma distribution
377
6.9.1
Maximum likelihood with uncensored data
379
6.9.2
Maximum likelihood with censored data
382
6.9.3
Double modelling
384
6.10
The Weibull distribution
388
6.11
Maximum likelihood fitting of the Weibull distribution
390
6.12
The extreme value distribution
394
6.13
The reversed extreme value distribution
397
6.14
Survivor function plotting for the Weibull and extreme value
distributions
398
6.15
The Cox proportional hazards model and the piecewise
exponential distribution
400
6.16
Maximum likelihood fitting of the piecewise exponential
distribution
403
6.17
Examples
404
6.18
The logistic and log-logistic distributions
407
6.19
The normal and
lognormal
distributions
411
6.20
Evaluating the proportional hazard assumption
414
6.21
Competing risks
420
6.22
Time-dependent explanatory variables
427
6.23
Discrete time models
427
7.1
Introduction
7.2
Example
-
girl birthweights
7.3
Finite
mixtures of distributions
7.4
Maximum likelihood in finite mixtures
7.5
Standard errors
7.6
Testing for the number of components
7.6.1
Example
7.7
Likelihood spikes
7.8
Galaxy data
7.9
Kernel density estimates
CONTENTS
xi
7
Finite mixture models
433
433
434
434
435
437
440
443
448
450
458
8
Random effect models
461
8.1
Overdispersion
461
8.1.1
Testing for overdispersion
464
8.2
Conjugate random effects
466
8.2.1
Normal kernel: the/-distribution
466
8.2.2
Poisson
kernel: the negative binomial distribution
472
8.2.3
Binomial kernel: beta-binomial distribution
477
8.2.4
Gamma kernel
478
8.2.5
Difficulties with the conjugate approach
478
8.3
Normal random effects
479
8.3.1
Predicting from the normal random effect model
481
8.4
Gaussian quadrature examples
481
8.4.1
Overdispersion model fitting
481
8.4.2
Poisson
-
the fabric fault data
482
8.4.3
Binomial
-
the toxoplasmosis data
484
8.5
Other specified random effect distributions
487
8.6
Arbitrary random effects
487
8.7
Examples
489
8.7.1
The fabric fault data
489
8.7.2
The toxoplasmosis data
492
8.7.3
Leukaemia remission data
493
8.7.4
The Brownlee stack-loss data
493
8.8
Random coefficient regression models
496
8.8.1
Example
-
the fabric fault data
498
8.9
Algorithms for mixture fitting
499
8.9.1
The trypanosome data
499
8.10
Modelling the mixing probabilities
503
8.11
Mixtures of mixtures
504
xii CONTENTS
9
Variance component models
508
9.1
Models with shared random effects
508
9.2
The normal/normal model
508
9.3
Exponential family two-level models
511
9.4
Other approaches
513
9.5
NPML estimation of the masses and mass-points
514
9.6
Random coefficient models
514
9.7
Variance component model fitting
515
9.7.1
Children s height development
516
9.7.2
Multi-centre trial of beta-blockers
524
9.7.3
Longitudinal study of obesity
530
9.8
Autoregressive
random effect models
537
9.9
Latent variable models
543
9.9.1
The normal factor model
543
9.10
IRT
models
544
9.10.1
The
Rasch
model
544
9.10.2
The two-parameter model
545
9.10.3
The three-parameter logit (3PL) model
547
9.10.4
Example-The Law School Aptitude Test (LSAT)
547
9.11
Spatial dependence
551
9.12
Multivariate correlated responses
552
9.13
Discreteness of the NPML estimate
552
Bibliography
554
R
function and constant index
567
Dataset
index
570
Subject index
571
|
| adam_txt |
Contents
1
Introducing R
1
1.1
Statistical packages and statistical modelling
1
1.2
Getting started in
R
1
1.3
Reading data into
R
3
1.4
Assignment and data generation
6
1.5
Displaying data
8
1.6
Data structures and the workspace
9
1.7
Transformations and data modification
11
1.8
Functions and suffixing
12
.8.1
Structure functions
13
.8.2
Mathematical functions
13
.8.3
Logical operators
14
.8.4
Control functions
14
.8.5
Statistical functions
14
.8.6
Random numbers
15
.8.7
Suffixes in expressions
16
1.8.8
Extracting subsets of data
17
1.8.9
Recoding
variâtes
and factors into new factors
17
.9
Graphical facilities
18
.10
Text functions
21
. 11
Writing your own functions
22
.12
Sorting and tabulation
23
.13
Editing
R
code
26
.14
Installing and using packages
27
2
Statistical modelling and inference
28
2.1
Statistical models
28
2.2
Types of variables
30
2.3
Population models
31
2.4
Random sampling
44
2.5
The likelihood function
44
viii CONTENTS
2.6
Inference for single parameter models
46
2.6.1
Comparing two simple hypotheses
47
2.6.2
Information about a single parameter
49
2.6.3
Comparing a simple null hypothesis and a composite
alternative
54
2.7
Inference with nuisance parameters
58
2.7.1
Profile likelihoods
59
2.7.2
Marginal likelihood for the variance
63
2.7.3
Likelihood normalizing transformations
66
2.7.4
Alternative test procedures
68
2.7.5
Bayes
inference
71
2.7.6
Binomial model
74
2.7.7
Hypergeometric sampling from finite populations
80
2.8
The effect of the sample design on inference
81
2.9
The exponential family
82
2.9.1
Mean and variance
83
2.9.2
Generalized linear models
83
2.9.3
Maximum likelihood fitting of the GLM
84
2.9.4
Model comparisons through maximized likelihoods
87
2.10
Likelihood inference without models
89
2.10.1
Likelihoods for percentiles
89
2.10.2
Empirical likelihood
92
3
Regression and analysis of variance
97
3.1
An example
97
3.2
Strategies for model simplification
107
3.3
Stratified, weighted and clustered samples 111
3.4
Model criticism
114
3.4.1
Mis-specification of the probability distribution
116
3.4.2
Mis-specification of the link function
119
3.4.3
The occurrence of aberrant and influential observations
119
3.4.4
Mis-specification of the systematic part of the model
123
3.5
The
Box
-Сох
transformation family
123
3.6
Modelling and background information
126
3.7
Link functions and transformations
136
3.8
Regression models for prediction
138
3.9
Model choice and mean square prediction error
140
3.10
Model selection through cross-validation
141
3.11
Reduction of complex regression models
144
3.12
Sensitivity of the
Box
-Сох
transformation
153
3.13
The use of regression models for calibration
156
CONTENTS ix
3.14
Measurement error in the explanatory variables
159
3.15
Factorial designs
161
3.16
Unbalanced cross-classifications
168
3.16.1
The Bennett hostility data
168
3.16.2
ANO VA
of the cross-classification
170
3.16.3
Regression analysis of the cross-classification
174
3.16.4
Statistical package treatments of cross-classifications
176
3.17
Missing data
178
3.18
Approximate methods for missing data
180
3.19
Modelling of variance heterogeneity
180
3.19.1
Poison example
184
3.19.2
Tree example
191
4
Binary response data
195
4.1
Binary responses
195
4.2
Transformations and link functions
197
4.2.1
Profile likelihoods for functions of parameters
202
4.3
Model criticism
207
4.3.1
Mis-specification of the probability distribution
207
4.3.2
Mis-specification of the link function
207
4.3.3
The occurrence of aberrant and influential observations
207
4.4
Binary data with continuous covariates
208
4.5
Contingency table construction from binary data
223
4.6
The prediction of binary outcomes
235
4.7
Profile and conditional likelihoods in
2
χ
2
tables
242
4.8
Three-dimensional contingency tables with a binary response
246
4.8.1
Prenatal care and infant mortality
246
4.8.2
Coronary heart disease
248
4.9
Multidimensional contingency tables with a binary response
255
5
Multinomial and
Poisson
response data
269
5.1
The
Poisson
distribution
269
5.2
Cross-classified counts
271
5.3
Multicategory responses
279
5.4
Multinomial logit model
285
5.5
The Poisson-multinomial relation
287
5.6
Fitting the multinomial logit model
293
5.7
Ordered response categories
298
5.7.1
Common slopes for the regressions
299
5.7.2
Linear trend over response categories
301
x
CONTENTS
5.7.3 Proportional
slopes
304
5.7.4
The continuation ratio model
304
5.7.5
Other models
308
5.8
An Example
310
5.8.1
Multinomial logit model
ЗІЗ
5.8.2
Continuation ratio model
320
5.9
Structured multinomial responses
330
5.9.1
Independent outcomes
331
5.9.2
Correlated outcomes
339
6
Survival data
347
6.1
Introduction
347
6.2
The exponential distribution
347
6.3
Fitting the exponential distribution
349
6.4
Model criticism
354
6.5
Comparison with the normal family
361
6.6
Censoring
364
6.7
Likelihood function for censored observations
365
6.8
Probability plotting with censored data: the Kaplan-Meier
estimator
368
6.9
The gamma distribution
377
6.9.1
Maximum likelihood with uncensored data
379
6.9.2
Maximum likelihood with censored data
382
6.9.3
Double modelling
384
6.10
The Weibull distribution
388
6.11
Maximum likelihood fitting of the Weibull distribution
390
6.12
The extreme value distribution
394
6.13
The reversed extreme value distribution
397
6.14
Survivor function plotting for the Weibull and extreme value
distributions
398
6.15
The Cox proportional hazards model and the piecewise
exponential distribution
400
6.16
Maximum likelihood fitting of the piecewise exponential
distribution
403
6.17
Examples
404
6.18
The logistic and log-logistic distributions
407
6.19
The normal and
lognormal
distributions
411
6.20
Evaluating the proportional hazard assumption
414
6.21
Competing risks
420
6.22
Time-dependent explanatory variables
427
6.23
Discrete time models
427
7.1
Introduction
7.2
Example
-
girl birthweights
7.3
Finite
mixtures of distributions
7.4
Maximum likelihood in finite mixtures
7.5
Standard errors
7.6
Testing for the number of components
7.6.1
Example
7.7
Likelihood 'spikes'
7.8
Galaxy data
7.9
Kernel density estimates
CONTENTS
xi
7
Finite mixture models
433
433
434
434
435
437
440
443
448
450
458
8
Random effect models
461
8.1
Overdispersion
461
8.1.1
Testing for overdispersion
464
8.2
Conjugate random effects
466
8.2.1
Normal kernel: the/-distribution
466
8.2.2
Poisson
kernel: the negative binomial distribution
472
8.2.3
Binomial kernel: beta-binomial distribution
477
8.2.4
Gamma kernel
478
8.2.5
Difficulties with the conjugate approach
478
8.3
Normal random effects
479
8.3.1
Predicting from the normal random effect model
481
8.4
Gaussian quadrature examples
481
8.4.1
Overdispersion model fitting
481
8.4.2
Poisson
-
the fabric fault data
482
8.4.3
Binomial
-
the toxoplasmosis data
484
8.5
Other specified random effect distributions
487
8.6
Arbitrary random effects
487
8.7
Examples
489
8.7.1
The fabric fault data
489
8.7.2
The toxoplasmosis data
492
8.7.3
Leukaemia remission data
493
8.7.4
The Brownlee stack-loss data
493
8.8
Random coefficient regression models
496
8.8.1
Example
-
the fabric fault data
498
8.9
Algorithms for mixture fitting
499
8.9.1
The trypanosome data
499
8.10
Modelling the mixing probabilities
503
8.11
Mixtures of mixtures
504
xii CONTENTS
9
Variance component models
508
9.1
Models with shared random effects
508
9.2
The normal/normal model
508
9.3
Exponential family two-level models
511
9.4
Other approaches
513
9.5
NPML estimation of the masses and mass-points
514
9.6
Random coefficient models
514
9.7
Variance component model fitting
515
9.7.1
Children's height development
516
9.7.2
Multi-centre trial of beta-blockers
524
9.7.3
Longitudinal study of obesity
530
9.8
Autoregressive
random effect models
537
9.9
Latent variable models
543
9.9.1
The normal factor model
543
9.10
IRT
models
544
9.10.1
The
Rasch
model
544
9.10.2
The two-parameter model
545
9.10.3
The three-parameter logit (3PL) model
547
9.10.4
Example-The Law School Aptitude Test (LSAT)
547
9.11
Spatial dependence
551
9.12
Multivariate correlated responses
552
9.13
Discreteness of the NPML estimate
552
Bibliography
554
R
function and constant index
567
Dataset
index
570
Subject index
571 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| building | Verbundindex |
| bvnumber | BV023426614 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.45.R3 |
| callnumber-search | QA276.45.R3 |
| callnumber-sort | QA 3276.45 R3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 850 ST 250 ST 601 |
| ctrlnum | (OCoLC)235032224 (DE-599)BVBBV023426614 |
| dewey-full | 519.50285/5133 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.50285/5133 |
| dewey-search | 519.50285/5133 |
| dewey-sort | 3519.50285 45133 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV023426614 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:33:03Z |
| indexdate | 2024-07-09T21:18:23Z |
| institution | BVB |
| isbn | 9780199219148 9780199219131 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016608963 |
| oclc_num | 235032224 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-945 DE-578 DE-824 |
| owner_facet | DE-703 DE-29T DE-945 DE-578 DE-824 |
| physical | XII, 576 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford statistical science series |
| series2 | Oxford statistical science series |
| spelling | Statistical modelling in R Murray Aitkin ... 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XII, 576 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford statistical science series 35 Hier auch später erschienene, unveränderte Nachdrucke Linear models (Statistics) R (Computer program language) Datenverarbeitung Mathematical statistics Data processing R Programm (DE-588)4705956-4 gnd rswk-swf R Programm (DE-588)4705956-4 s DE-604 Aitkin, Murray Sonstige oth Oxford statistical science series 35 (DE-604)BV001908661 35 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Statistical modelling in R Oxford statistical science series Linear models (Statistics) R (Computer program language) Datenverarbeitung Mathematical statistics Data processing R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4705956-4 |
| title | Statistical modelling in R |
| title_auth | Statistical modelling in R |
| title_exact_search | Statistical modelling in R |
| title_exact_search_txtP | Statistical modelling in R |
| title_full | Statistical modelling in R Murray Aitkin ... |
| title_fullStr | Statistical modelling in R Murray Aitkin ... |
| title_full_unstemmed | Statistical modelling in R Murray Aitkin ... |
| title_short | Statistical modelling in R |
| title_sort | statistical modelling in r |
| topic | Linear models (Statistics) R (Computer program language) Datenverarbeitung Mathematical statistics Data processing R Programm (DE-588)4705956-4 gnd |
| topic_facet | Linear models (Statistics) R (Computer program language) Datenverarbeitung Mathematical statistics Data processing R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001908661 |
| work_keys_str_mv | AT aitkinmurray statisticalmodellinginr |