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E-raamat: Multivariate Generalized Linear Mixed Models Using R

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, (Lancaster University, UK)
  • Formaat: 304 pages
  • Ilmumisaeg: 25-Apr-2011
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439813270
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Multivariate Generalized Linear Mixed Models Using RSuurem pilt
  • Formaat: 304 pages
  • Ilmumisaeg: 25-Apr-2011
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439813270
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Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.

A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model estimation, and endogenous variables, along with SabreR commands and examples.

Improve Your Longitudinal StudyIn medical and social science research, MGLMMs help disentangle state dependence from incidental parameters. Focusing on these sophisticated data analysis techniques, this book explains the statistical theory and modeling involved in longitudinal studies. Many examples throughout the text illustrate the analysis of real-world data sets. Exercises, solutions, and other material are available on a supporting website.

Arvustused

I think this is a very well organised and written book and therefore I highly recommend it not only to professionals and students but also to applied researchers from many research areas such as education, psychology and economics working on complex and large data sets. Sebnem Er, Journal of Applied Statistics, 2012

List of Figures xi
List of Tables xiii
List of Applications xv
List of Datasets xvii
Preface xix
Acknowledgments xxiii
1 Introduction 1(8)
2 Generalized linear models for continuous/interval scale data 9(12)
2.1 Introduction
9(1)
2.2 Continuous/interval scale data
10(1)
2.3 Simple and multiple linear regression models
11(1)
2.4 Checking assumptions in linear regression models
12(1)
2.5 Likelihood: multiple linear regression
13(1)
2.6 Comparing model likelihoods
14(1)
2.7 Application of a multiple linear regression model
15(2)
2.8 Exercises on linear models
17(4)
3 Generalized linear models for other types of data 21(22)
3.1 Binary data
21(5)
3.1.1 Introduction
21(1)
3.1.2 Logistic regression
22(1)
3.1.3 Logit and probit transformations
23(1)
3.1.4 General logistic regression
24(1)
3.1.5 Likelihood
24(1)
3.1.6 Example with binary data
24(2)
3.2 Ordinal data
26(6)
3.2.1 Introduction
26(1)
3.2.2 The ordered logit model
27(2)
3.2.3 Dichotomization of ordered categories
29(1)
3.2.4 Likelihood
29(1)
3.2.5 Example with ordered data
30(2)
3.3 Count data
32(5)
3.3.1 Introduction
32(1)
3.3.2 Poisson regression models
33(1)
3.3.3 Likelihood
34(1)
3.3.4 Example with count data
34(3)
3.4 Exercises
37(6)
4 Family of generalized linear models 43(6)
4.1 Introduction
43(1)
4.2 The linear model
44(1)
4.3 The binary response model
44(2)
4.4 The Poisson model
46(1)
4.5 Likelihood
46(3)
5 Mixed models for continuous/interval scale data 49(26)
5.1 Introduction
49(1)
5.2 Linear mixed model
49(2)
5.3 The intraclass correlation coefficient
51(2)
5.4 Parameter estimation by maximum likelihood
53(1)
5.5 Regression with level-two effects
54(1)
5.6 Two-level random intercept models
55(1)
5.7 General two-level models including random intercepts
56(2)
5.8 Likelihood
58(1)
5.9 Residuals
58(1)
5.10 Checking assumptions in mixed models
59(1)
5.11 Comparing model likelihoods
60(1)
5.12 Application of a two-level linear model
61(5)
5.13 Two-level growth models
66(1)
5.13.1 A two-level repeated measures model
66(1)
5.13.2 A linear growth model
66(1)
5.13.3 A quadratic growth model
67(1)
5.14 Likelihood
67(1)
5.15 Example using linear growth models
68(1)
5.16 Exercises using mixed models for continuous/interval scale data
69(6)
6 Mixed models for binary data 75(10)
6.1 Introduction
75(1)
6.2 The two-level logistic model
75(2)
6.3 General two-level logistic models
77(1)
6.4 Intraclass correlation coefficient
77(1)
6.5 Likelihood
78(1)
6.6 Example using binary data
78(3)
6.7 Exercises using mixed models for binary data
81(4)
7 Mixed models for ordinal data 85(8)
7.1 Introduction
85(1)
7.2 The two-level ordered logit model
85(1)
7.3 Likelihood
86(1)
7.4 Example using mixed models for ordered data
87(3)
7.5 Exercises using mixed models for ordinal data
90(3)
8 Mixed models for count data 93(6)
8.1 Introduction
93(1)
8.2 The two-level Poisson model
93(1)
8.3 Likelihood
94(1)
8.4 Example using mixed models for count data
95(2)
8.5 Exercises using mixed models for count data
97(2)
9 Family of two-level generalized linear models 99(6)
9.1 Introduction
99(1)
9.2 The mixed linear model
100(1)
9.3 The mixed binary response model
100(2)
9.4 The mixed Poisson model
102(1)
9.5 Likelihood
102(3)
10 Three-level generalized linear models 105(10)
10.1 Introduction
105(1)
10.2 Three-level random intercept models
105(1)
10.3 Three-level generalized linear models
106(1)
10.4 Linear models
107(1)
10.5 Binary response models
108(1)
10.6 Likelihood
108(1)
10.7 Example using three-level generalized linear models
109(3)
10.8 Exercises using three-level generalized linear mixed models
112(3)
11 Models for multivariate data 115(20)
11.1 Introduction
115(1)
11.2 Multivariate two-level generalized linear model
116(1)
11.3 Bivariate Poisson model: example
117(4)
11.4 Bivariate ordered response model: example
121(5)
11.5 Bivariate linear-probit model: example
126(5)
11.6 Multivariate two-level generalized linear model likelihood
131(1)
11.7 Exercises using multivariate generalized linear mixed models
131(4)
12 Models for duration and event history data 135(22)
12.1 Introduction
135(2)
12.1.1 Left censoring
135(1)
12.1.2 Right censoring
135(1)
12.1.3 Time-varying explanatory variables
136(1)
12.1.4 Competing risks
136(1)
12.2 Duration data in discrete time
137(6)
12.2.1 Single-level models for duration data
137(2)
12.2.2 Two-level models for duration data
139(1)
12.2.3 Three-level models for duration data
140(3)
12.3 Renewal data
143(4)
12.3.1 Introduction
143(2)
12.3.2 Example: renewal models
145(2)
12.4 Competing risk data
147(6)
12.4.1 Introduction
147(1)
12.4.2 Likelihood
148(2)
12.4.3 Example: competing risk data
150(3)
12.5 Exercises using renewal and competing risks models
153(4)
13 Stayers, non-susceptibles and endpoints 157(12)
13.1 Introduction
157(1)
13.2 Mover-stayer model
157(3)
13.3 Likelihood incorporating the mover-stayer model
160(1)
13.4 Example 1: stayers within count data
161(3)
13.5 Example 2: stayers within binary data
164(2)
13.6 Exercises: stayers
166(3)
14 Handling initial conditions/state dependence in binary data 169(26)
14.1 Introduction to key issues: heterogeneity, state dependence and non-stationarity
169(1)
14.2 Example
170(1)
14.3 Random effects models
171(1)
14.4 Initial conditions problem
172(1)
14.5 Initial treatment
173(1)
14.6 Example: depression data
174(1)
14.7 Classical conditional analysis
174(1)
14.8 Classical conditional model: example
175(1)
14.9 Conditioning on initial response but allowing random effect uol to be dependent on z3
176(1)
14.10 Wooldridge conditional model: example
177(1)
14.11 Modelling the initial conditions
178(1)
14.12 Same random effect in the initial response and subsequent response models with a common scale parameter
179(1)
14.13 Joint analysis with a common random effect: example
180(1)
14.14 Same random effect in models of the initial response and subsequent responses but with different scale parameters
181(1)
14.15 Joint analysis with a common random effect (different scale parameters): example
182(1)
14.16 Different random effects in models of the initial response and subsequent responses
183(1)
14.17 Different random effects: example
184(1)
14.18 Embedding the Wooldridge approach in joint models for the initial response and subsequent responses
185(2)
14.19 Joint model incorporating the Wooldridge approach: example
187(1)
14.20 Other link functions
187(1)
14.21 Exercises using models incorporating initial conditions/state dependence in binary data
188(7)
15 Incidental parameters: an empirical comparison of fixed effects and random effects models 195(20)
15.1 Introduction
195(2)
15.2 Fixed effects treatment of the two-level linear model
197(2)
15.3 Dummy variable specification of the fixed effects model
199(1)
15.4 Empirical comparison of two-level fixed effects and random effects estimators
200(4)
15.5 Implicit fixed effects estimator
204(1)
15.6 Random effects models
204(4)
15.7 Comparing two-level fixed effects and random effects models
208(1)
15.8 Fixed effects treatment of the three-level linear model
208(1)
15.9 Exercises comparing fixed effects and random effects
209(6)
A SabreR installation, SabreR commands, quadrature, estimation, endogenous effects 215(14)
A.1 SabreR installation
215(1)
A.2 SabreR commands
215(3)
A.2.1 The arguments of the SabreR object
215(1)
A.2.2 The anatomy of a SabreR command file
216(2)
A.3 Quadrature
218(5)
A.3.1 Standard Gaussian quadrature
218(1)
A.3.2 Performance of Gaussian quadrature
219(2)
A.3.3 Adaptive quadrature
221(2)
A.4 Estimation
223(2)
A.4.1 Maximizing the log likelihood of random effects models
223(2)
A.5 Fixed effects linear models
225(1)
A.6 Endogenous and exogenous variables
226(3)
B Introduction to R for Sabre 229(20)
B.1 Getting started with R
229(11)
B.1.1 Preliminaries
229(3)
B.1.1.1 Working with R in interactive mode
229(2)
B.1.1.2 Basic functions
231(1)
B.1.1.3 Getting help
232(1)
B.1.1.4 Stopping R
232(1)
B.1.2 Creating and manipulating data
232(5)
B.1.2.1 Vectors and lists
232(1)
B.1.2.2 Vectors
233(1)
B.1.2.3 Vector operations
234(1)
B.1.2.4 Lists
235(1)
B.1.2.5 Data frames
236(1)
B.1.3 Session management
237(2)
B.1.3.1 Managing objects
237(1)
B.1.3.2 Attaching and detaching objects
237(1)
B.1.3.3 Serialization
238(1)
B.1.3.4 R scripts
238(1)
B.1.3.5 Batch processing
239(1)
B.1.4 R packages
239(1)
B.1.4.1 Loading a package into R
239(1)
B.1.4.2 Installing a package for use in R
239(1)
B.1.4.3 R and Statistics
240(1)
B.2 Data preparation for SabreR
240(9)
B.2.1 Creation of dummy variables
240(3)
B.2.2 Missing values
243(2)
B.2.3 Creating lagged response covariate data
245(4)
References 249(10)
Author Index 259(4)
Subject Index 263
Damon M. Berridge is a senior lecturer in the Department of Mathematics and Statistics at Lancaster University. Dr. Berridge has nearly 20 years of experience as a statistical consultant. His research focuses on the modeling of binary and ordinal recurrent events through random effects models, with application in medical and social statistics.

Robert Crouchley is a professor of applied statistics and director of the Centre for e-Science at Lancaster University. His research interests involve the development of statistical methods and software for causal inference in nonexperimental data. These methods include models for errors in variables, missing data, heterogeneity, state dependence, nonstationarity, event history data, and selection effects.
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