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El. knyga: Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood, Second Edition

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(Imperial College, London, UK), (Karolinska Institute, Stockholm, Sweden), (Seoul National University, South Korea)
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This is the second edition of a monograph on generalized linear models with random effects that extends the classic work of McCullagh and Nelder. It has been thoroughly updated, with around 80 pages added, including new material on the extended likelihood approach that strengthens the theoretical basis of the methodology, new developments in variable selection and multiple testing, and new examples and applications. It includes an R package for all the methods and examples that supplement the book.

Recenzijos

"Generalized Linear Models with Random Effects is a comprehensive book on likelihood methods in generalized linear models (GLMs) including linear models with normally distributed errors. The book is suitable for those with graduate training in mathematical statistics. The level of mathematical detail is similar to that of McCullagh and Nelder (1989), with the focus shifted towards likelihood methods. All chapters contain examples with a fair amount of detail. The book is very broad and offers a comprehensive overview of likelihood methods." Christiana Drake, in ISCB News, December 2018

Praise for the first edition:

" This book provides a comprehensive summary of [ the authors' past work]. However, it is much more than that, and even statisticians who do not agree with their approach to inference will find much here of interest. some instructors might find this to be a useful text for a course on generalized linear models. there are many ideas that will be useful for students to mull over " A. Agresti (University of Florida), Short Book Reviews

"The book is well written and replete with examples and discussions. With over 500 references, the authors have amassed an enormous amount of information in a single source." James W. Hardin, University of South Carolina, in Journal of the American Statistical Association, June 2009, Vol. 104, No. 486

"The books material is valuable . . . There are numerous examples and applications, illustrated on the accompanying Genstat CD." Hassan S. Bakouch, Tanta University, in Journal of Applied Statistics, September 2007, Vol. 34, No. 7

List of notations
xv
Preface to first edition xvii
Preface xix
Introduction 1(4)
1 Classical likelihood theory
5(34)
1.1 Definition
5(5)
1.2 Quantities derived from the likelihood
10(4)
1.3 Profile likelihood
14(2)
1.4 Distribution of the likelihood ratio statistic
16(4)
1.5 Distribution of the MLE and the Wald statistic
20(4)
1.6 Model selection
24(1)
1.7 Marginal and conditional likelihoods
25(5)
1.8 Higher-order approximations
30(2)
1.9 Adjusted profile likelihood
32(2)
1.10 Bayesian and likelihood methods
34(2)
1.11 Confidence distribution
36(3)
2 Generalized linear models
39(28)
2.1 Linear models
39(5)
2.2 Generalized linear models
44(7)
2.3 Model checking
51(4)
2.4 Examples
55(12)
3 Quasi-likelihood
67(32)
3.1 Examples
70(4)
3.2 Iterative weighted least squares
74(1)
3.3 Asymptotic inference
75(4)
3.4 Dispersion models
79(3)
3.5 Extended quasi--likelihood
82(5)
3.6 Joint GLM of mean and dispersion
87(5)
3.7 Joint GLMs for quality improvement
92(7)
4 Extended likelihood inferences
99(32)
4.1 Two kinds of likelihoods
100(6)
4.2 Wallet game and extended likelihood
106(2)
4.3 Inference about the fixed parameters
108(2)
4.4 Inference about the random parameters
110(1)
4.5 Canonical scale, h-likelihood and joint inference
111(7)
4.6 Prediction of random parameters
118(3)
4.7 Prediction of future outcome
121(1)
4.8 Finite sample adjustment
122(4)
4.9 Is marginal likelihood enough for inference about fixed parameters?
126(1)
4.10 Summary: likelihoods in extended framework
126(5)
5 Normal linear mixed models
131(36)
5.1 Developments of normal mixed linear models
134(3)
5.2 Likelihood estimation of fixed parameters
137(5)
5.3 Classical estimation of random effects
142(9)
5.4 H-likelihood approach
151(8)
5.5 Example
159(3)
5.6 Invariance and likelihood inference
162(5)
6 Hierarchical GLMS
167(30)
6.1 HGLMs
167(2)
6.2 H-likelihood
169(8)
6.3 Inferential procedures using h-likelihood
177(6)
6.4 Penalized quasi-likelihood
183(4)
6.5 Deviances in HGLMs
187(1)
6.6 Examples
188(5)
6.7 Choice of random effect scale
193(4)
7 HGLMs with structured dispersion
197(26)
7.1 Description of model
197(2)
7.2 Quasi-HGLMs
199(8)
7.3 Examples
207(16)
8 Correlated random effects for HGLMs
223(36)
8.1 HGLMs with correlated random effects
223(2)
8.2 Random effects described by fixed L matrices
225(2)
8.3 Random effects described by a covariance matrix
227(1)
8.4 Random effects described by a precision matrix
228(1)
8.5 Fitting and model checking
229(1)
8.6 Examples
229(15)
8.7 Twin and family data
244(13)
8.8 Ascertainment problem
257(2)
9 Smoothing
259(30)
9.1 Spline models
260(4)
9.2 Mixed model framework
264(6)
9.3 Automatic smoothing
270(3)
9.4 Smoothing via a model with singular precision matrix
273(5)
9.5 Non-Gaussian smoothing
278(11)
10 Double HGLMs
289(24)
10.1 Model description
289(4)
10.2 Models for finance data
293(1)
10.3 Joint splines
294(1)
10.4 H-likelihood procedure for fitting DHGLMs
295(4)
10.5 Random effects in the A component
299(1)
10.6 Examples
300(13)
11 Variable selection and sparsity models
313(28)
11.1 Penalized least squares
314(2)
11.2 Random effect variable selection
316(2)
11.3 Implied penalty functions
318(2)
11.4 Scalar β case
320(3)
11.5 Estimating the dispersion and tuning parameters
323(1)
11.6 Example: diabetes data
324(1)
11.7 Numerical studies
325(3)
11.8 Asymptotic property of HL method
328(1)
11.9 Sparse multivariate methods
329(3)
11.10 Structured variable selection
332(3)
11.11 Interaction and hierarchy constraints
335(6)
12 Multivariate and missing data analysis
341(26)
12.1 Multivariate models
342(7)
12.2 Missing data problems
349(6)
12.3 Missing data in longitudinal studies
355(6)
12.4 Denoising signals by imputation
361(6)
13 Multiple testing
367(14)
13.1 Single hypothesis testing
367(3)
13.2 Multiple testing
370(2)
13.3 Multiple testing with two states
372(2)
13.4 Multiple testing with three states
374(3)
13.5 Examples
377(4)
14 Random effect models for survival data
381(26)
14.1 Proportional-hazard model
381(2)
14.2 Frailty models and the associated h-likelihood
383(12)
14.3 Mixed linear models with censoring
395(6)
14.4 Extensions
401(2)
14.5 Proofs
403(4)
References 407(20)
Data Index 427(2)
Author Index 429(6)
Subject Index 435
Youngjo Lee is Professor at Seoul National University, South Korea.
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