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 |
Bibliography | 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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additive model African Americans analysis anova approach approximation coef coefficients compute confidence interval consider correlation cpergore dataset degrees of freedom Df Deviance diagnostics Dispersion parameter distribution Error t value Estimate Std example exponential family F-statistic F-test factor femsmoke fitted values fixed effects Gaussian half-normal income independent Intercept interpretation least squares likelihood ratio test linear model linear regression link function lmer lmod log-likelihood logit logLik math maximum likelihood mean method mmod model fit modl multinomial nonparametric normal Null deviance observed outliers overdispersion ozone p-value package panel of Figure perAA plot Poisson Poisson regression predict probability proportion Quantiles R-Squared random effects regression model REML Residual deviance Residual standard error response sample score shown significant smoothing splines standard error summary temp transformations tree undercount value Pr(>|t variables variance function wafer Wald test weights xtabs zero
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