| Preface |
| Preface to the First Edition |
| Introduction / 1： |
| Models / 1.1： |
| Linear models (LM) and linear mixed models (LMM) / a： |
| Generalized models (GLMs and GLMMs) / b： |
| Factors, Levels, Cells, Effects and Data / 1.2： |
| Fixed Effects Models / 1.3： |
| Example 1: Placebo and a drug |
| Example 2: Comprehension of humor |
| Example 3: Four dose levels of a drug / c： |
| Random Effects Models / 1.4： |
| Example 4: Clinics |
| Notation |
| Example 5: Ball bearings and calipers |
| Linear Mixed Models (LMMs) / 1.5： |
| Example 6: Medications and clinics |
| Example 7: Drying methods and fabrics |
| Example 8: Potomac River Fever |
| Regression models / d： |
| Longitudinal data / e： |
| Example 9: Osteoarthritis Initiative / f： |
| Model equations / g： |
| Fixed or Random? / 1.6： |
| Example 10: Clinical trials |
| Making a decision |
| Inference / 1.7： |
| Estimation |
| Testing |
| Prediction |
| Computer Software / 1.8： |
| Exercises / 1.9： |
| One-Way Classifications / 2： |
| Normality and Fixed Effects / 2.1： |
| Model |
| Estimation by ML |
| Generalized likelihood ratio test |
| Confidence intervals |
| Hypothesis tests |
| Normality, Random Effects and MLE / 2.2： |
| Balanced data |
| Unbalanced data |
| Bias |
| Sampling variances |
| Normality, Random Effects and Reml / 2.3： |
| More on Random Effects and Normality / 2.4： |
| Tests and confidence intervals |
| Predicting random effects |
| Binary Data: Fixed Effects / 2.5： |
| 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 / h： |
| Binary Data: Random Effects / 2.6： |
| Beta-binomial model |
| Logit-normal model |
| Probit-normal model |
| Computing / 2.7： |
| Single-Predictor Regression / 2.8： |
| Normality: Simple Linear Regression / 3.1： |
| Maximum likelihood estimators |
| Distributions of MLEs |
| Illustration |
| Normality: A Nonlinear Model / 3.3： |
| Transforming Versus Linking / 3.4： |
| Transforming |
| Linking |
| Comparisons |
| Random Intercepts: Balanced Data / 3.5： |
| The model |
| Estimating [mu] and [beta] |
| Estimating variances |
| Tests of hypotheses - using LRT |
| Predicting the random intercepts |
| Random Intercepts: Unbalanced Data / 3.6： |
| Estimating [mu] and [beta] when variances are known |
| Bernoulli - Logistic Regression / 3.7： |
| Logistic regression model |
| ML equations |
| Bernoulli - Logistic with Random Intercepts / 3.8： |
| Conditional Inference |
| Linear Models (LMs) / 3.9： |
| A General Model / 4.1： |
| A Linear Model for Fixed Effects / 4.2： |
| Mle Under Normality / 4.3： |
| Sufficient Statistics / 4.4： |
| Many Apparent Estimators / 4.5： |
| General result |
| Mean and variance |
| Invariance properties |
| Distributions |
| Estimable Functions / 4.6： |
| Definition |
| Properties |
| A Numerical Example / 4.7： |
| Estimating Residual Variance / 4.8： |
| Distribution of estimators |
| The One- and Two-Way Classifications / 4.9： |
| The one-way classification |
| The two-way classification |
| Testing Linear Hypotheses / 4.10： |
| Wald test |
| t-Tests and Confidence Intervals / 4.11： |
| Unique Estimation Using Restrictions / 4.12： |
| Generalized Linear Models (GLMs) / 4.13： |
| Structure of the Model / 5.1： |
| Distribution of y |
| Link function |
| Predictors |
| Linear models |
| Estimation by Maximum Likelihood / 5.3： |
| Some useful identities |
| Likelihood equations |
| Large-sample variances |
| Solving the ML equations |
| Example: Potato flour dilutions |
| Tests of Hypotheses / 5.5： |
| Likelihood ratio tests |
| Wald tests |
| Illustration of tests |
| Illustration of confidence intervals |
| Maximum Quasi-Likelihood / 5.6： |
| Basic properties / 5.7： |
| Attributing Structure to Var(y) / 6.2： |
| Example |
| Taking covariances between factors as zero |
| The traditional variance components model |
| An LMM for longitudinal data |
| Estimating Fixed Effects for V Known / 6.3： |
| Estimating Fixed Effects for V Unknown / 6.4： |
| Sampling variance |
| Bias in the variance |
| Approximate F-statistics |
| Predicting Random Effects for V Known / 6.5： |
| Predicting Random Effects for V Unknown / 6.6： |
| Anova Estimation of Variance Components / 6.7： |
| Maximum Likelihood (ML) Estimation / 6.8： |
| Estimators |
| Information matrix |
| Asymptotic sampling variances |
| Restricted Maximum Likelihood (REML) / 6.9： |
| Notes and Extensions / 6.10： |
| ML or REML? |
| Other methods for estimating variances |
| Appendix for Chapter 6 / 6.11： |
| Differentiating a log likelihood |
| Differentiating a generalized inverse |
| Differentiation for the variance components model |
| Generalized Linear Mixed Models / 6.12： |
| Conditional distribution of y / 7.1： |
| Consequences of Having Random Effects / 7.3： |
| Marginal versus conditional distribution |
| Mean of y |
| Variances |
| Covariances and correlations |
| Other Methods of Estimation / 7.4： |
| Penalized quasi-likelihood |
| Conditional likelihood |
| Simpler models |
| Asymptotic variances / 7.6： |
| Score tests |
| Illustration: Chestnut Leaf Blight / 7.7： |
| A random effects probit model |
| Models for Longitudinal Data / 7.8： |
| A Model for Balanced Data / 8.1： |
| Prescription |
| Estimating the mean |
| Estimating V[subscript 0] |
| A Mixed Model Approach / 8.3： |
| Fixed and random effects |
| Random Intercept and Slope Models / 8.4： |
| Within-subject correlations |
| Predicting Random Effects / 8.5： |
| Uncorrelated subjects |
| Uncorrelated between, and within, subjects |
| Uncorrelated between, and autocorrelated within |
| Random intercepts and slopes |
| Estimating Parameters / 8.6： |
| The general case |
| Uncorrelated between, and autocorrelated within, subjects |
| Unbalanced Data / 8.7： |
| Example and model |
| Models for Non-Normal Responses / 8.8： |
| Prediction of random effects |
| Binary responses, random intercepts and slopes |
| A Summary of Results / 8.9： |
| Appendix / 8.10： |
| For Section 8.4a |
| For Section 8.4b |
| Marginal Models / 8.11： |
| Examples of Marginal Regression Models / 9.1： |
| Generalized Estimating Equations / 9.3： |
| Models with marginal and conditional interpretations |
| Contrasting Marginal and Conditional Models / 9.4： |
| Multivariate Models / 9.5： |
| Multivariate Normal Outcomes / 10.1： |
| Non-Normally Distributed Outcomes / 10.3： |
| A multivariate binary model |
| A binary/normal example |
| A Poisson/Normal Example |
| Correlated Random Effects / 10.4： |
| Likelihood-Based Analysis / 10.5： |
| Example: Osteoarthritis Initiative / 10.6： |
| Missing data / 10.7： |
| Efficiency |
| Nonlinear Models / 10.8： |
| Example: Corn Photosynthesis / 11.1： |
| Pharmacokinetic Models / 11.3： |
| Computations for Nonlinear Mixed Models / 11.4： |
| Departures from Assumptions / 11.5： |
| Incorrect Model for Response / 12.1： |
| Omitted covariates |
| Misspecified link functions |
| Misclassified binary outcomes |
| Informative cluster sizes |
| Incorrect Random Effects Distribution / 12.3： |
| Incorrect distributional family |
| Correlation of covariates and random effects |
| Covariate-dependent random effects variance |
| Diagnosing Misspecification / 12.4： |
| Conditional likelihood methods |
| Between/within cluster covariate decompositions |
| Specification tests |
| Nonparametric maximum likelihood |
| Best Prediction (BP) / 12.5： |
| The best predictor |
| Mean and variance properties |
| A correlation property |
| Maximizing a mean |
| Normality |
| Best Linear Prediction (BLP) / 13.3： |
| BLP(u) |
| Derivation |
| Ranking |
| Linear Mixed Model Prediction (BLUP) / 13.4： |
| BLUE(X[beta]) |
| BLUP(t'X[beta] + s'u) |
| Two variances |
| Other derivations |
| Required Assumptions / 13.5： |
| Estimated Best Prediction / 13.6： |
| Henderson's Mixed Model Equations / 13.7： |
| Origin |
| Solutions |
| Use in ML estimation of variance components |
| Verification of (13.5) / 13.8： |
| Verification of (13.7) and (13.8) |
| Computing ML Estimates for LMMs / 13.9： |
| The EM algorithm |
| Using E[u|y] |
| Newton-Raphson method |
| Computing ML Estimates for GLMMs / 14.3： |
| Numerical quadrature |
| EM algorithm |
| Markov chain Monte Carlo algorithms |
| Stochastic approximation algorithms |
| Simulated maximum likelihood |
| Penalized Quasi-Likelihood and Laplace / 14.4： |
| Iterative Bootstrap Bias Correction / 14.5： |
| Some Matrix Results / 14.6： |
| Vectors and Matrices of Ones / M.1： |
| Kronecker (or Direct) Products / M.2： |
| A Matrix Notation in Terms of Elements / M.3： |
| Generalized Inverses / M.4： |
| 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 / M.5： |
| Scalars |
| Vectors |
| Inner products |
| Quadratic forms |
| Inverse matrices |
| Determinants |
| Some Statistical Results / Appendix S： |
| Moments / S.1： |
| Conditional moments |
| Mean of a quadratic form |
| Moment generating function |
| Normal Distributions / S.2： |
| Univariate |
| Multivariate |
| Quadratic forms in normal variables |
| Exponential Families / S.3： |
| Maximum Likelihood / S.4： |
| The likelihood function |
| Maximum likelihood estimation |
| Asymptotic variance-covariance matrix |
| Asymptotic distribution of MLEs |
| Likelihood Ratio Tests / S.5： |
| MLE Under Normality / S.6： |
| Estimation of [beta] |
| Estimation of variance components |
| Restricted maximum likelihood (REML) |
| References |
| Index |
| Longitudinal Data |
| GLMMs |
ＥＢ
