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Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models

Provides readers with an up-to-date, well-stocked toolbox of statistical methodologies
Includes numerous real examples that illustrate the use of R for data analysis
Covers GLM diagnostics, generalized linear mixed models, trees, and the use of neural networks in statistics
Reviews linear models as well as the basics of using R
Offers the datasets and other material on the author’s website

Series: Chapman & Hall/CRC Texts in Statistical Science

By: Julian J Faraway (Author)

399 pages, 115 b/w illustrations, 6 tables

Productivity Press

Hardback | May 2016 | Edition: 2 | #230536 | ISBN-13: 9781498720960
Availability: Usually dispatched within 48 hours
NHBS Price: £63.99 $81/€75 approx

About this book

Start Analyzing a Wide Range of Problems
Since the publication of the bestselling, highly recommended first edition, R has considerably expanded both in popularity and in the number of packages available. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models, Second Edition takes advantage of the greater functionality now available in R and substantially revises and adds several topics.

New to the Second Edition:
- Expanded coverage of binary and binomial responses, including proportion responses, quasibinomial and beta regression, and applied considerations regarding these models
- New sections on Poisson models with dispersion, zero inflated count models, linear discriminant analysis, and sandwich and robust estimation for generalized linear models (GLMs)
- Revised chapters on random effects and repeated measures that reflect changes in the lme4 package and show how to perform hypothesis testing for the models using other methods
- New chapter on the Bayesian analysis of mixed effect models that illustrates the use of STAN and presents the approximation method of INLA
- Revised chapter on generalized linear mixed models to reflect the much richer choice of fitting software now available
- Updated coverage of splines and confidence bands in the chapter on nonparametric regression
- New material on random forests for regression and classification
- Revamped R code throughout, particularly the many plots using the ggplot2 package
- Revised and expanded exercises with solutions now included

Demonstrates the Interplay of Theory and Practice
This textbook continues to cover a range of techniques that grow from the linear regression model. It presents three extensions to the linear framework: GLMs, mixed effect models, and nonparametric regression models. The book explains data analysis using real examples and includes all the R commands necessary to reproduce the analyses.

Reviews of the first edition:

" [...] well-written and the discussions are easy to follow [...] very useful as a reference book for applied statisticians and would also serve well as a textbook for students graduating in statistics."
Computational Statistics, April 2009, Vol. 24

"The text is well organized and carefully written [...] provides an overview of many modern statistical methodologies and their applications to real data using software. This makes it a useful text for practitioners and graduate students alike."
Journal of the American Statistical Association, December 2007, Vol. 102, No. 480

"I enjoyed this text as much as [Faraway's Linear Models with R]. The book is recommended as a textbook for a computational statistical and data mining course including GLMs and non-parametric regression, and will also be of great value to the applied statistician whose statistical programming environment of choice is R."
Journal of Applied Statistics, July 2007, Vol. 34, No. 5

"This is a very pleasant book to read. It clearly demonstrates the different methods available and in which situations each one applies. It covers almost all of the standard topics beyond linear models that a graduate student in statistics should know. It also includes discussion of topics such as model diagnostics, rarely addressed in books of this type. The presentation incorporates an abundance of well-chosen examples [...] this book is highly recommended [...] "
Biometrics, December 2006


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Contents

Introduction

Binary Response
Heart Disease Example
Logistic Regression
Inference
Diagnostics
Model Selection
Goodness of Fit
Estimation Problems

Binomial and Proportion Responses
Binomial Regression Model
Inference
Pearson’s χ2 Statistic
Overdispersion
Quasi-Binomial
Beta Regression

Variations on Logistic Regression
Latent Variables
Link Functions
Prospective and Retrospective Sampling
Prediction and Effective Doses
Matched Case-Control Studies

Count Regression
Poisson Regression
Dispersed Poisson Model
Rate Models
Negative Binomial
Zero Inflated Count Models

Contingency Tables
Two-by-Two Tables
Larger Two-Way Tables
Correspondence Analysis
Matched Pairs
Three-Way Contingency Tables
Ordinal Variables

Multinomial Data
Multinomial Logit Model
Linear Discriminant Analysis
Hierarchical or Nested Responses
Ordinal Multinomial Responses

Generalized Linear Models
GLM Definition
Fitting a GLM
Hypothesis Tests
GLM Diagnostics
Sandwich Estimation
Robust Estimation

Other GLMs
Gamma GLM
Inverse Gaussian GLM
Joint Modeling of the Mean and Dispersion
Quasi-Likelihood GLM
Tweedie GLM

Random Effects
Estimation
Inference
Estimating Random Effects
Prediction
Diagnostics
Blocks as Random Effects
Split Plots
Nested Effects
Crossed Effects
Multilevel Models

Repeated Measures and Longitudinal Data
Longitudinal Data
Repeated Measures
Multiple Response Multilevel Models

Bayesian Mixed Effect Models
STAN
INLA
Discussion

Mixed Effect Models for Nonnormal Responses
Generalized Linear Mixed Models
Inference
Binary Response
Count Response
Generalized Estimating Equations

Nonparametric Regression
Kernel Estimators
Splines
Local Polynomials
Confidence Bands
Wavelets
Discussion of Methods
Multivariate Predictors

Additive Models
Modeling Ozone Concentration
Additive Models Using mgcv
Generalized Additive Models
Alternating Conditional Expectations
Additivity and Variance Stabilization
Generalized Additive Mixed Models
Multivariate Adaptive Regression Splines

Trees
Regression Trees
Tree Pruning
Random Forests
Classification Trees
Classification Using Forests

Neural Networks
Statistical Models as NNs
Feed-Forward Neural Network with One Hidden Layer
NN Application
Conclusion

Appendix A: Likelihood Theory
Appendix B: About R

Bibliography
Index


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Biography

Julian J. Faraway is a professor of statistics in the Department of Mathematical Sciences at the University of Bath. His research focuses on the analysis of functional and shape data with particular application to the modeling of human motion. He earned a PhD in statistics from the University of California, Berkeley.

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