Longitudinal data with serial correlation: a state-space approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Chapman & Hall
1993
|
| Edition: | 1. ed. |
| Series: | Monographs on statistics and applied probability
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 225 S. graph. Darst. |
| ISBN: | 0412406500 |
Staff View
MARC
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| 264 | 1 | |a London u.a. |b Chapman & Hall |c 1993 | |
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Record in the Search Index
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| adam_text | Contents
Preface x
1 Introduction 1
1.1 A simple example 1
1.2 Repeated measures experiments 4
1.3 Longitudinal data 5
1.4 An example 7
1.5 Balanced compound symmetry 11
1.5.1 Maximum likelihood estimation 11
1.6 Missing observations 21
1.7 Exercises 24
2 A General Linear Mixed Model 26
2.1 The Laird Ware Model 26
2.2 The likelihood function 32
2.2.1 Numerical evaluation 33
2.3 Variance heterogeneity 37
2.4 Residuals 38
2.5 Restricted maximum likelihood 39
2.6 The EM algorithm 10
2.7 Predictions 42
2.7.1 Population mean curves 43
2.7.2 Individual predictions 43
2.8 Model selection 44
2.9 Testing contrasts 47
2.10 An example 50
2.11 Exercises 51
vii
viii
3 First Order Autoregressive Errors 52
3.1 Introduction 52
3.2 Equally spaced observations 53
3.3 Unequally spaced observations 56
3.4 Some simulated error structures 60
3.5 Other possible error structures 65
3.6 Circadian rhythms 67
3.7 Exercises 74
4 State Space Representations 77
4.1 A tracking example 78
4.2 The Kalman recursion 86
4.2.1 Missing observations 89
4.3 AR(1) process with observational error 90
4.3.1 Equally spaced data 90
4.3.2 Arbitrarily spaced data 92
4.4 Derivation of the Kalman recursion 94
4.5 Numerical considerations 96
4.6 Exercises 98
5 The Laird Ware Model in State Space Form 100
5.1 Fixed effects 100
5.1.1 The algorithm 103
5.1.2 Estimating an unknown mean 107
5.2 Random effects in the state 111
5.2.1 An example 113
5.3 Predictions 115
5.4 Shrinkage estimates 116
5.5 Data analysis 117
5.6 Exercises 118
6 Autoregressive Moving Average Errors 120
6.1 Equally spaced observations 120
6.1.1 The initial state covariance matrix 123
6.1.2 Reparameterizing for stability 127
6.2 Unequally spaced observations 128
6.2.1 The state space method 131
6.3 An exercise 138
ix
7 Nonlinear Models 139
7.1 Fitting nonlinear models 139
7.2 Nonlinear random effects 142
7.2.1 The Michaelis Menten equation 142
7.2.2 Simulated data 147
7.2.3 A general nonlinear equation 151
7.3 A four parameter logistic model 154
8 Multivariate Models 156
8.1 Multivariate AR(1) errors 161
8.2 Multivariate mixed models 166
8.3 The multivariate algorithm 167
8.3.1 Model fitting strategy 170
8.4 A bivariate example 171
8.4.1 Predictions 177
8.5 Doubly labeled water 181
8.6 Exercise 183
Appendix 186
A FORTRAN subroutines 186
A.I Matrix factorization 186
A.2 Equally spaced ARMA processes 189
A.3 Unequally spaced ARMA processes 197
A.4 A multivariate subroutine 205
References 218
Index 224
|
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| id | DE-604.BV009593265 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:37:40Z |
| institution | BVB |
| isbn | 0412406500 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006341280 |
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| physical | XI, 225 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Jones, R. H. 1934- Verfasser (DE-588)1029366004 aut Longitudinal data with serial correlation a state-space approach R. H. Jones 1. ed. London u.a. Chapman & Hall 1993 XI, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 47 Longitudinaal onderzoek gtt Multivariate analyse gtt Longitudinal Studies methods Longitudinal method Multivariate Analysis methods Multivariate analysis Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s DE-604 Monographs on statistics and applied probability 47 (DE-604)BV002494005 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006341280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jones, R. H. 1934- Longitudinal data with serial correlation a state-space approach Monographs on statistics and applied probability Longitudinaal onderzoek gtt Multivariate analyse gtt Longitudinal Studies methods Longitudinal method Multivariate Analysis methods Multivariate analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4067486-1 |
| title | Longitudinal data with serial correlation a state-space approach |
| title_auth | Longitudinal data with serial correlation a state-space approach |
| title_exact_search | Longitudinal data with serial correlation a state-space approach |
| title_full | Longitudinal data with serial correlation a state-space approach R. H. Jones |
| title_fullStr | Longitudinal data with serial correlation a state-space approach R. H. Jones |
| title_full_unstemmed | Longitudinal data with serial correlation a state-space approach R. H. Jones |
| title_short | Longitudinal data with serial correlation |
| title_sort | longitudinal data with serial correlation a state space approach |
| title_sub | a state-space approach |
| topic | Longitudinaal onderzoek gtt Multivariate analyse gtt Longitudinal Studies methods Longitudinal method Multivariate Analysis methods Multivariate analysis Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Longitudinaal onderzoek Multivariate analyse Longitudinal Studies methods Longitudinal method Multivariate Analysis methods Multivariate analysis Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006341280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT jonesrh longitudinaldatawithserialcorrelationastatespaceapproach |