Generalized Additive Models
Preface
Part I: Concepts
Introduction
Beyond the General Linear Model I
General Linear Model
Generalized Linear Model
Generalized Additive Model
Beyond the General Linear Model II
Fitting the Standard Linear Model
Polynomial Regression
Scatterplot Smoothing
Generalized Additive Models
Summary
The case for GAMs
Why not just use standard methods?
Heteroscedasticity, non-normality etc.
Polynomial Regression
A more complex relationship
Building up to GAMs
Piecewise polynomial
What is a GAM?
Polynomial spline
Part II: Praxis
Application Using R
Initial Examination
Single Feature
Linear Fit
GAM
Visualization
Model Comparison
Multiple Features
Linear Fit
GAM
Visualization
Model Comparison
Issues
Estimation
Shrinkage & Variable Selection
Choice of Smoothing Function
Diagnostics
Concurvity
Prediction
Model Comparison Revisited
Big Data
Other Approaches
Other Nonlinear Modeling Approaches
Known Functional Form
Response Transformation
The Black Box
Bayesian Estimation
Extensions
Other GAMs
Reproducing Kernel Hilbert Space
Gaussian Processes
Concluding remarks
Part III: Addendum
Technical details
GAM
Penalized regression
Effective degrees of freedom again
A detailed example
Preview of other bases
The number of knots and where to put them
Interpreting output for smooth terms
Effective degrees of freedom
Deviance explained
Visual depiction
Examining first derivatives
Appendix
R packages
A comparison to mixed models
Time and Space
Time
Space
References
Generalized Additive Models
Generalized Additive Models
Michael Clark
m-clark.github.io