## Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression ModelsLinear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway's critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author's treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the data described in the book is available at http://people.bath.ac.uk/jjf23/ELM/ Statisticians need to be familiar with a broad range of ideas and techniques. This book provides a well-stocked toolbox of methodologies, and with its unique presentation of these very modern statistical techniques, holds the potential to break new ground in the way graduate-level courses in this area are taught. |

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### Contents

1 | |

2 Binomial Data | 28 |

3 Count Regression | 61 |

4 Contingency Tables | 76 |

5 Multinomial Data | 106 |

6 Generalized Linear Models | 126 |

7 Other GLMs | 149 |

8 Random Effects | 169 |

11 Nonparametric Regression | 232 |

12 Additive Models | 254 |

13 Trees | 278 |

14 Neural Networks | 296 |

Appendix A | 307 |

Appendix B | 316 |

318 | |

324 | |

9 Repeated Measures and Longitudinal Data | 203 |

10 Mixed Effect Models for Nonnormal Responses | 221 |

### Common terms and phrases

additive model African Americans analysis approach approximation coefficients compute confidence interval consider correlation cross-validation dataset degrees of freedom Df Deviance diagnostics Dispersion parameter distribution Error t value Estimate Std example exponential family F-statistic factor family taken family=poisson fitted values fixed effects freedom Multiple R-Squared freedom Residual deviance gamma GLM Gaussian income independence Intercept interpretation least squares likelihood ratio likelihood ratio test linear model link function lmod log-likelihood log-odds logit maximum likelihood mean method missing values model fit multinomial nonparametric normal Null deviance null model observed outliers output overdispersion p-value package panel of Figure perAA plot Poisson regression predicted probability proportion R-Squared random effects regression model REML Residual standard error response sample saturated model scores selection shown significant smoothing splines standard error Table transformations tree undercount value Pr(>|t variables variance function wafer Wald test weights zero