Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models
Linear 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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Generalized Linear Models
Repeated Measures and Longitudinal Data
Mixed Effect Models for Nonnormal Responses
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additive model African Americans analysis approach approximation coefficients compute confidence interval consider correlation dataset degrees of freedom Df Deviance diagnostics Dispersion parameter distribution Error t value Estimate Std example exponential family F-statistic factor fitted values fixed effects freedom Multiple R-Squared freedom Residual deviance gamma GLM income independent Intercept interpretation least squares likelihood ratio test linear model linear regression link function log-likelihood 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 Poisson regression predicted probability proportion quantiles R-Squared random effects regression model REML Residual standard error response sample score shown significant smoothing splines standard error Table temp transformations tree undercount value Pr(>|t variables variance function wafer Wald test wavelet weights zero
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