Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models / Edition 1

Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models / Edition 1

by Julian J. Faraway
     
 

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ISBN-10: 158488424X

ISBN-13: 9781584884248

Pub. Date: 03/15/2006

Publisher: Taylor & Francis

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

Overview

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.

Product Details

ISBN-13:
9781584884248
Publisher:
Taylor & Francis
Publication date:
03/15/2006
Series:
Chapman & Hall/CRC Texts in Statistical Science Series , #66
Edition description:
Older Edition
Pages:
312
Sales rank:
1,146,513
Product dimensions:
6.10(w) x 9.40(h) x 0.90(d)

Related Subjects

Table of Contents

INTRODUCTION

BINOMIAL DATA
Challenger Disaster Example
Binomial Regression Model
Inference
Tolerance Distribution
Interpreting Odds
Prospective and Retrospective Sampling
Choice of Link Function
Estimation Problems
Goodness of Fit
Prediction and Effective Doses
Overdispersion
Matched Case-Control Studies

COUNT REGRESSION
Poisson Regression
Rate Models
Negative Binomial

CONTINGENCY TABLES
Two-by-Two Tables
Larger Two-Way Tables
Matched Pairs
Three-Way Contingency Tables
Ordinal Variables

MULTINOMIAL DATA
Multinomial Logit Model
Hierarchical or Nested Responses
Ordinal Multinomial Responses

GENERALIZED LINEAR MODELS
GLM Definition
Fitting a GLM
Hypothesis Tests
GLM Diagnostics

OTHER GLMS
Gamma GLM
Inverse Gaussian GLM
Joint Modeling of the Mean and Dispersion
Quasi-Likelihood

RANDOM EFFECTS
Estimation
Inference
Predicting Random Effects
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

MIXED EFFECT MODELS FOR NONNORMAL RESPONSES
Generalized Linear Mixed Models
Generalized Estimating Equations

NONPARAMETRIC REGRESSION
Kernel Estimators
Splines
Local Polynomials
Wavelets
Other Methods
Comparison of Methods
Multivariate Predictors

ADDITIVE MODELS
Additive Models Using the gam Package
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
Classification Trees

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

APPENDICES
Likelihood Theory
R Information
Bibliography
Index

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