Generalized, Linear, and Mixed Models

Name: Generalized, Linear, and Mixed Models
Availability: OutOfStock
ISBN: 9780471654049

ISBN-10: 0471654043

ISBN-13: 9780471654049

Edition: 2001

Authors: Charles E. McCulloch, Shayle R. Searle

List price: $143.50

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Description:

Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.

Book details

List price: $143.50
Copyright year: 2001
Publisher: John Wiley & Sons, Incorporated
Publication date: 3/22/2004
Binding: E-Book
Pages: 358
Language: English



Preface


Preface to the First Edition



Introduction



Models



Linear models (LM) and linear mixed models (LMM)



Generalized models (GLMs and GLMMs)



Factors, Levels, Cells, Effects and Data



Fixed Effects Models



Example 1: Placebo and a drug



Example 2: Comprehension of humor



Example 3: Four dose levels of a drug



Random Effects Models



Example 4: Clinics



Notation



Example 5: Ball bearings and calipers



Linear Mixed Models (LMMs)



Example 6: Medications and clinics



Example 7: Drying methods and fabrics



Example 8: Potomac River Fever



Regression models



Longitudinal data



Example 9: Osteoarthritis Initiative



Model equations



Fixed or Random?



Example 10: Clinical trials



Making a decision



Inference



Estimation



Testing



Prediction



Computer Software



Exercises



One-Way Classifications



Normality and Fixed Effects



Model



Estimation by ML



Generalized likelihood ratio test



Confidence intervals



Hypothesis tests



Normality, Random Effects and MLE



Model



Balanced data



Unbalanced data



Bias



Sampling variances



Normality, Random Effects and Reml



Balanced data



Unbalanced data



More on Random Effects and Normality



Tests and confidence intervals



Predicting random effects



Binary Data: Fixed Effects



Model equation



Likelihood



ML equations and their solutions



Likelihood ratio test



The usual chi-square test



Large-sample tests and confidence intervals



Exact tests and confidence intervals



Example: Snake strike data



Binary Data: Random Effects



Model equation



Beta-binomial model



Logit-normal model



Probit-normal model



Computing



Exercises



Single-Predictor Regression



Introduction



Normality: Simple Linear Regression



Model



Likelihood



Maximum likelihood estimators



Distributions of MLEs



Tests and confidence intervals



Illustration



Normality: A Nonlinear Model



Model



Likelihood



Maximum likelihood estimators



Distributions of MLEs



Transforming Versus Linking



Transforming



Linking



Comparisons



Random Intercepts: Balanced Data



The model



Estimating [mu] and [beta]



Estimating variances



Tests of hypotheses - using LRT



Illustration



Predicting the random intercepts



Random Intercepts: Unbalanced Data



The model



Estimating [mu] and [beta] when variances are known



Bernoulli - Logistic Regression



Logistic regression model



Likelihood



ML equations



Large-sample tests and confidence intervals



Bernoulli - Logistic with Random Intercepts



Model



Likelihood



Large-sample tests and confidence intervals



Prediction



Conditional Inference



Exercises



Linear Models (LMs)



A General Model



A Linear Model for Fixed Effects



Mle Under Normality



Sufficient Statistics



Many Apparent Estimators



General result



Mean and variance



Invariance properties



Distributions



Estimable Functions



Introduction



Definition



Properties



Estimation



A Numerical Example



Estimating Residual Variance



Estimation



Distribution of estimators



The One- and Two-Way Classifications



The one-way classification



The two-way classification



Testing Linear Hypotheses



Likelihood ratio test



Wald test



t-Tests and Confidence Intervals



Unique Estimation Using Restrictions



Exercises



Generalized Linear Models (GLMs)



Introduction



Structure of the Model



Distribution of y



Link function



Predictors



Linear models



Transforming Versus Linking



Estimation by Maximum Likelihood



Likelihood



Some useful identities



Likelihood equations



Large-sample variances



Solving the ML equations



Example: Potato flour dilutions



Tests of Hypotheses



Likelihood ratio tests



Wald tests



Illustration of tests



Confidence intervals



Illustration of confidence intervals



Maximum Quasi-Likelihood



Introduction



Definition



Exercises



Linear Mixed Models (LMMs)



A General Model



Introduction



Basic properties



Attributing Structure to Var(y)



Example



Taking covariances between factors as zero



The traditional variance components model



An LMM for longitudinal data



Estimating Fixed Effects for V Known



Estimating Fixed Effects for V Unknown



Estimation



Sampling variance



Bias in the variance



Approximate F-statistics



Predicting Random Effects for V Known



Predicting Random Effects for V Unknown



Estimation



Sampling variance



Bias in the variance



Anova Estimation of Variance Components



Balanced data



Unbalanced data



Maximum Likelihood (ML) Estimation



Estimators



Information matrix



Asymptotic sampling variances



Restricted Maximum Likelihood (REML)



Estimation



Sampling variances



Notes and Extensions



ML or REML?



Other methods for estimating variances



Appendix for Chapter 6



Differentiating a log likelihood



Differentiating a generalized inverse



Differentiation for the variance components model



Exercises



Generalized Linear Mixed Models



Introduction



Structure of the Model



Conditional distribution of y



Consequences of Having Random Effects



Marginal versus conditional distribution



Mean of y



Variances



Covariances and correlations



Estimation by Maximum Likelihood



Likelihood



Likelihood equations



Other Methods of Estimation



Penalized quasi-likelihood



Conditional likelihood



Simpler models



Tests of Hypotheses



Likelihood ratio tests



Asymptotic variances



Wald tests



Score tests



Illustration: Chestnut Leaf Blight



A random effects probit model



Exercises



Models for Longitudinal Data



Introduction



A Model for Balanced Data



Prescription



Estimating the mean



Estimating V[subscript 0]



A Mixed Model Approach



Fixed and random effects



Variances



Random Intercept and Slope Models



Variances



Within-subject correlations



Predicting Random Effects



Uncorrelated subjects



Uncorrelated between, and within, subjects



Uncorrelated between, and autocorrelated within



Random intercepts and slopes



Estimating Parameters



The general case



Uncorrelated subjects



Uncorrelated between, and autocorrelated within, subjects



Unbalanced Data



Example and model



Uncorrelated subjects



Models for Non-Normal Responses



Covariances and correlations



Estimation



Prediction of random effects



Binary responses, random intercepts and slopes



A Summary of Results



Balanced data



Unbalanced data



Appendix



For Section 8.4a



For Section 8.4b



Exercises



Marginal Models



Introduction



Examples of Marginal Regression Models



Generalized Estimating Equations



Models with marginal and conditional interpretations



Contrasting Marginal and Conditional Models



Exercises



Multivariate Models



Introduction



Multivariate Normal Outcomes



Non-Normally Distributed Outcomes



A multivariate binary model



A binary/normal example



A Poisson/Normal Example



Correlated Random Effects



Likelihood-Based Analysis



Example: Osteoarthritis Initiative



Notes and Extensions



Missing data



Efficiency



Exercises



Nonlinear Models



Introduction



Example: Corn Photosynthesis



Pharmacokinetic Models



Computations for Nonlinear Mixed Models



Exercises



Departures from Assumptions



Introduction



Incorrect Model for Response



Omitted covariates



Misspecified link functions



Misclassified binary outcomes



Informative cluster sizes



Incorrect Random Effects Distribution



Incorrect distributional family



Correlation of covariates and random effects



Covariate-dependent random effects variance



Diagnosing Misspecification



Conditional likelihood methods



Between/within cluster covariate decompositions



Specification tests



Nonparametric maximum likelihood



A Summary of Results



Exercises



Prediction



Introduction



Best Prediction (BP)



The best predictor



Mean and variance properties



A correlation property



Maximizing a mean



Normality



Best Linear Prediction (BLP)



BLP(u)



Example



Derivation



Ranking



Linear Mixed Model Prediction (BLUP)



BLUE(X[beta])



BLUP(t'X[beta] + s'u)



Two variances



Other derivations



Required Assumptions



Estimated Best Prediction



Henderson's Mixed Model Equations



Origin



Solutions



Use in ML estimation of variance components



Appendix



Verification of (13.5)



Verification of (13.7) and (13.8)



Exercises



Computing



Introduction



Computing ML Estimates for LMMs



The EM algorithm



Using E[uy]



Newton-Raphson method



Computing ML Estimates for GLMMs



Numerical quadrature



EM algorithm



Markov chain Monte Carlo algorithms



Stochastic approximation algorithms



Simulated maximum likelihood



Penalized Quasi-Likelihood and Laplace



Iterative Bootstrap Bias Correction



Exercises



Some Matrix Results



Vectors and Matrices of Ones



Kronecker (or Direct) Products



A Matrix Notation in Terms of Elements



Generalized Inverses



Definition



Generalized inverses of X'X



Two results involving X(X'V[superscript -1]X)[superscript -]X'V[superscript -1]



Solving linear equations



Rank results



Vectors orthogonal to columns of X



A theorem for K' with K'X being null



Differential Calculus



Definition



Scalars



Vectors



Inner products



Quadratic forms



Inverse matrices



Determinants



Some Statistical Results



Moments



Conditional moments



Mean of a quadratic form



Moment generating function



Normal Distributions



Univariate



Multivariate



Quadratic forms in normal variables



Exponential Families



Maximum Likelihood



The likelihood function



Maximum likelihood estimation



Asymptotic variance-covariance matrix



Asymptotic distribution of MLEs



Likelihood Ratio Tests



MLE Under Normality



Estimation of [beta]



Estimation of variance components



Asymptotic variance-covariance matrix



Restricted maximum likelihood (REML)


References


Index