Mixed Models : Theory and Applications with R.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Demidenko, Eugene
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Wiley, 2013.
Colección:Wiley series in probability and statistics ; 893.
Temas:
Analysis of variance.
Analyse de variance.
Analysis of variance
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Dedication
  • Contents
  • Preface
  • Preface to the Second Edition
  • R Software and Functions
  • Data Sets
  • Open Problems in Mixed Models
  • 1 Introduction: Why Mixed Models?
  • 1.1 Mixed effects for clustered data
  • 1.2 ANOVA, variance components, and the mixed model
  • 1.3 Other special cases of the mixed effects model
  • 1.4 Compromise between Bayesian and frequentist approaches
  • 1.5 Penalized likelihood and mixed effects
  • 1.6 Healthy Akaike information criterion
  • 1.7 Penalized smoothing
  • 1.8 Penalized polynomial fitting
  • 1.9 Restraining parameters, or what to eat
  • 1.10 Ill-posed problems, Tikhonov regularization, and mixed effects
  • 1.11 Computerized tomography and linear image reconstruction
  • 1.12 GLMM for PET
  • 1.13 Maple leaf shape analysis
  • 1.14 DNA Western blot analysis
  • 1.15 Where does the wind blow?
  • 1.16 Software and books
  • 1.17 Summary points
  • 2 MLE for the LME Model
  • 2.1 Example: weight versus height
  • 2.1.1 The first R script
  • 2.2 The model and log-likelihood functions
  • 2.2.1 The model
  • 2.2.2 Log-likelihood functions
  • 2.2.3 Dimension-reduction formulas
  • 2.2.4 Profile log-likelihood functions
  • 2.2.5 Dimension-reduction GLS estimate
  • 2.2.6 Restricted maximum likelihood
  • 2.2.7 Weight versus height (continued)
  • 2.3 Balanced random-coefficient model
  • 2.4 LME model with random intercepts
  • 2.4.1 Balanced random-intercept model
  • 2.4.2 How random effect affects the variance of MLE
  • 2.5 Criterion for MLE existence
  • 2.6 Criterion for the positive definiteness of matrix D
  • 2.6.1 Example of an invalid LME model
  • 2.7 Pre-estimation bounds for variance parameters
  • 2.8 Maximization algorithms
  • 2.9 Derivatives of the log-likelihood function
  • 2.10 Newton-Raphson algorithm
  • 2.11 Fisher scoring algorithm
  • 2.11.1 Simplified FS algorithm
  • 2.11.2 Empirical FS algorithm
  • 2.11.3 Variance-profile FS algorithm
  • 2.12 EM algorithm
  • 2.12.1 Fixed-point algorithm
  • 2.13 Starting point
  • 2.13.1 FS starting point
  • 2.13.2 FP starting point
  • 2.14 Algorithms for restricted MLE
  • 2.14.1 Fisher scoring algorithm
  • 2.14.2 EM algorithm
  • 2.15 Optimization on nonnegative definite matrices
  • 2.15.1 How often can one hit the boundary?
  • 2.15.2 Allow matrix D to be not nonnegative definite
  • 2.15.3 Force matrix D to stay nonnegative definite
  • 2.15.4 Matrix D reparameterization
  • 2.15.5 Criteria for convergence
  • 2.16 lmeFS and lme in R
  • 2.17 Appendix: proof of the existence of MLE
  • 2.18 Summary points
  • 3 Statistical Properties of the LME Model
  • 3.1 Introduction
  • 3.2 Identifiability of the LME model
  • 3.2.1 Linear regression with random coefficients
  • 3.3 Information matrix for variance parameters
  • 3.3.1 Efficiency of variance parameters for balanced data
  • 3.4 Profile-likelihood confidence intervals
  • 3.5 Statistical testing of the presence of random effects

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