## Generalized, Linear, and Mixed ModelsWiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models |

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### Contents

1 INTRODUCTION | 1 |

2 ONEWAY CLASSIFICATIONS | 28 |

3 SINGLEPREDICTOR REGRESSION | 71 |

4 LINEAR MODELS LMs | 113 |

5 GENERALIZED LINEAR MODELS GLMs | 135 |

6 LINEAR MIXED MODELS LMMs | 156 |

7 LONGITUDINAL DATA | 187 |

8 GLMMs | 220 |

### Other editions - View all

Generalized, Linear, and Mixed Models Charles E. McCulloch,Shayle R. Searle No preview available - 2004 |

### Common terms and phrases

algorithm analysis of variance ANOVA Applied approximation assume assumption asymptotic balanced data Bernoulli distribution best predictor beta-binomial model calculated Chapter clinics computing conditional distribution conﬁdence interval consider correlation covariance deﬁned deﬁnition degrees of freedom denote density derived elements example expected value ﬁnd ﬁrst ﬁxed effects function given gives GLMMs GLMs homoscedastic hypothesis indep Inference inverse iterative least squares levels likelihood function likelihood ratio test linear mixed models linear model LMMs log likelihood maximize maximum likelihood estimators mean methods ML equations ML estimators model equation Multivariate nonlinear normally distributed notation observations p-value parameters prediction probability probit quasi—likelihood random effects random effects model random factors random variables reject H0 REML estimators replaced scalar Searle Second Edition Section simpliﬁes solutions speciﬁcation Stochastic Suppose unbalanced unbiased estimator var(y variance components variance-covariance matrix vector Wald test Xﬁ zero