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. |
Contents
Introduction | 1 |
Binomial Data | 25 |
Count Regression | 55 |
Contingency Tables | 69 |
Multinomial Data | 95 |
Generalized Linear Models | 113 |
Other GLMs | 133 |
Random Effects | 151 |
Nonparametric Regression | 209 |
Additive Models | 229 |
Trees | 251 |
Neural Networks | 267 |
Likelihood Theory | 277 |
R Information | 285 |
| 287 | |
Back Cover | 295 |
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Extending the Linear Model with R: Generalized Linear, Mixed Effects and ... Julian J. Faraway No preview available - 2005 |
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analysis applied approach appropriate approximation binomial called choice coefficients combinations components compute consider correlation corresponding counties dataset degrees of freedom described determine deviance dispersion distribution error estimate Estimate Std example expect factor Figure fixed effects function Gaussian given gives income increase independent indicates individual interaction Intercept interest interpretation interval larger likelihood linear model look mean measure method normal Notice null observed obtained p-value package panel of Figure parameter plot points Poisson possible predicted predictors probability problem proportion random effects ratio regression relationship relative represent residuals response sample scale score seen selection shown significant simply smoothing squares standard statistic Suppose Table transformations tree variables variance weights zero
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