Generalized Additive Models: An Introduction With R 2nd Edition by Simon Wood ISBN 1498728375 9781498728379

Generalized Additive Models: An Introduction With R 2nd Edition BY Simon N. Wood – Ebook PDF Instant Download/Delivery: 1498728375, 978-1498728379
Full download Generalized Additive Models: An Introduction With R 2nd Edition after payment

Product details:

ISBN 10:      1498728375
ISBN 13: 978-1498728379
Author:      Simon N. Wood

Generalized Additive Models: An Introduction With R 2nd Table of contents:

1. Linear Models

1.1 A Simple Linear Model

• Simple least squares estimation
  1.1.1 Sampling properties of β
  1.1.2 So how old is the universe?
  1.1.3 Adding a distributional assumption
• Testing hypotheses about β
• Confidence intervals

1.2 Linear Models in General

1.3 The Theory of Linear Models

• Least squares estimation of β
• The distribution of β​
• F-ratio results I
• F-ratio results II
• The influence matrix
• The residuals ϵepsilonϵ and fitted values μmuμ
• Results in terms of X
• The Gauss Markov Theorem: What’s special about least squares?

1.4 The Geometry of Linear Modelling

• Least squares
• Fitting by orthogonal decompositions
• Comparison of nested models

1.5 Practical Linear Modelling

• Model fitting and model checking
• Model summary
• Model selection
• Another model selection example (A follow-up)
• Confidence intervals
• Prediction
• Co-linearity, confounding, and causation

1.6 Practical Modelling with Factors

• Identifiability
• Multiple factors
• ‘Interactions’ of factors
• Using factor variables in R

1.7 General Linear Model Specification in R

1.8 Further Linear Modelling Theory

• Constraints I: General linear constraints
• Constraints II: ‘Contrasts’ and factor variables
• Likelihood
• Non-independent data with variable variance
• Simple AR correlation models
• AIC and Mallows’ statistic
• The wrong model
• Non-linear least squares
• Further reading

1.9 Exercises

---

2. Linear Mixed Models

2.1 Mixed Models for Balanced Data

• A motivating example
  • The wrong approach: A fixed effects linear model
  • The right approach: A mixed effects model
    2.1.2 General principles
    2.1.3 A single random factor
    2.1.4 A model with two factors
    2.1.5 Discussion

2.2 Maximum Likelihood Estimation

• Numerical likelihood maximization

2.3 Linear Mixed Models in General

2.4 Linear Mixed Model Maximum Likelihood Estimation

• The distribution of b∣y,βb | y, betab∣y,β given θthetaθ
• The distribution of βbetaβ given θthetaθ
• The distribution of θthetaθ
• Maximizing the profile likelihood
• REML
• Effective degrees of freedom
• The EM algorithm
• Model selection

2.5 Linear Mixed Models in R

• Package nlme
• Tree growth: An example using lme
• Several levels of nesting
• Package lme4
• Package mgcv

2.6 Exercises

---

3. Generalized Linear Models (GLMs)

3.1 GLM Theory

• The exponential family of distributions
• Fitting generalized linear models
• Large sample distribution of βbetaβ
• Comparing models
  • Deviance
  • Model comparison with unknown ϕphiϕ
  • AIC
• Estimating ϕphiϕ, Pearson’s statistic, and Fletcher’s estimator
• Canonical link functions
• Residuals: Pearson residuals, Deviance residuals
• Quasi-likelihood
• Tweedie and negative binomial distributions
• The Cox proportional hazards model for survival data: Cumulative hazard and survival functions

3.2 Geometry of GLMs

• The geometry of IRLS
• Geometry and IRLS convergence

3.3 GLMs with R

• Binomial models and heart disease
• A Poisson regression epidemic model
• Cox proportional hazards modelling of survival data
• Log-linear models for categorical data
• Sole eggs in the Bristol Channel

3.4 Generalized Linear Mixed Models

• Penalized IRLS
• The PQL method
• Distributional results

3.5 GLMMs with R

• glmmPQL
• gam
• glmer

3.6 Exercises

---

4. Introducing GAMs

4.1 Introduction

4.2 Univariate Smoothing

• Representing a function with basis expansions
  • A very simple basis: Polynomials
  • The problem with polynomials
  • The piecewise linear basis
  • Using the piecewise linear basis
• Controlling smoothness by penalizing wiggliness
• Choosing the smoothing parameter, A, by cross-validation
• The Bayesian/mixed model alternative

4.3 Additive Models

• Penalized piecewise regression representation of an additive model
• Fitting additive models by penalized least squares

4.4 Generalized Additive Models

4.5 Summary

4.6 Introducing Package mgcv

• Finer control of gam
• Smooths of several variables
• Parametric model terms
• The mgcv help pages

4.7 Exercises

---

5. Smoothers

5.1 Smoothing Splines

• Natural cubic splines are smoothest interpolators
• Cubic smoothing splines

5.2 Penalized Regression Splines

5.3 Some One-Dimensional Smoothers

• Cubic regression splines
• A cyclic cubic regression spline
• P-splines
• P-splines with derivative-based penalties
• Adaptive smoothing
• SCOP-splines

5.4 Some Useful Smoother Theory

• Identifiability constraints
• ‘Natural’ parameterization, effective degrees of freedom, and smoothing bias
• Null space penalties

5.5 Isotropic Smoothing

• Thin plate regression splines
  • Thin plate splines
  • Properties of thin plate regression splines
  • Knot-based approximation
• Duchon splines
• Splines on the sphere
• Soap film smoothing over finite domains

5.6 Tensor Product Smooth Interactions

• Tensor product bases
• Tensor product penalties
• ANOVA decompositions of smooths
• Numerical identifiability constraints for nested terms
• Tensor product smooths under shape constraints
• An alternative tensor product construction: What is being penalized?

5.7 Isotropy versus Scale Invariance

5.8 Smooths, Random Fields, and Random Effects

• Gaussian Markov random fields
• Gaussian process regression smoothers

5.9 Choosing the Basis Dimension

5.10 Generalized Smoothing Splines

5.11 Exercises

---

6. GAM Theory

6.1 Setting up the Model

• Estimating βbetaβ given λlambdaλ
• Degrees of freedom and scale parameter estimation
• Stable least squares with negative weights

6.2 Smoothness Selection Criteria

• Known scale parameter: UBRE
• Unknown scale parameter: Cross-validation
  • Leave-several-out cross-validation
  • Problems with ordinary cross-validation
• Generalized cross-validation
• Double cross-validation
• Prediction error criteria for the generalized case
• Marginal likelihood and REML
• The problem with log |Sλlambdaλ|+
• Prediction error criteria vs marginal likelihood
• Unpenalized coefficient bias

6.3 Computing the Smoothing Parameter Estimates

6.4 The Generalized Fellner-Schall Method

• General regular likelihoods

6.5 Direct Gaussian Case and Performance Iteration (PQL)

• Newton optimization of the GCV score
• REML, log |Sλlambdaλ|+ and its derivatives

6.6 Direct Nested Iteration Methods

• Prediction error criteria
• Example: Cox proportional hazards model

6.7 Initial Smoothing Parameter Guesses

6.8 GAMM Methods

• GAMM inference with mixed model estimation

6.9 Bigger Data Methods

6.10 Posterior Distribution and Confidence Intervals

• Nychka’s coverage probability argument
• Interval limitations and simulations
• Whole function intervals
• Posterior simulation in general

6.11 AIC and Smoothing Parameter Uncertainty

• Smoothing parameter uncertainty
• A corrected AIC

6.12 Hypothesis Testing and p-values

• Approximate p-values for smooth terms
• Approximate p-values for random effect terms
• Testing a parametric term against a smooth alternative
• Approximate generalized likelihood ratio tests

6.13 Other Model Selection Approaches

6.14 Further GAM Theory

• The geometry of penalized regression
• Backfitting GAMs

6.15 Exercises

---

7. GAMs in Practice: mgcv

7.1 Specifying Smooths

• How smooth specification works

7.2 Brain Imaging Example

• Preliminary modelling
• Would an additive structure be better?
• Isotropic or tensor product smooths?
• Detecting symmetry (with by variables)
• Comparing two surfaces
• Prediction with predict.gam
• Variances of non-linear functions of the fitted model

7.3 A Smooth ANOVA Model for Diabetic Retinopathy

7.4 Air Pollution in Chicago

• A single index model for pollution-related deaths
• A distributed lag model for pollution-related deaths

7.5 Mackerel Egg Survey Example

• Model development
• Model predictions
• Alternative spatial smooths and geographic regression

7.6 Spatial Smoothing of Portuguese Larks Data

7.7 Generalized Additive Mixed Models with R

• A space-time GAMM for sole eggs
  • Soap film improvement of boundary behavior
• The temperature in Cairo
• Fully Bayesian stochastic simulation: jagam
• Random wiggly curves

7.8 Primary Biliary Cirrhosis Survival Analysis

• Time dependent covariates

7.9 Location-Scale Modelling

• Extreme rainfall in Switzerland

7.10 Fuel Efficiency of Cars: Multivariate Additive Models

7.11 Functional Data Analysis

• Scalar on function regression: Prostate cancer screening
• A multinomial prostate screening model
• Function on scalar regression: Canadian weather

7.12 Other Packages

7.13 Exercises

 

People also search for Generalized Additive Models: An Introduction With R 2nd :

simon wood generalized additive models
when to use generalized additive models
hierarchical generalized additive models
practical variable selection for generalized additive models
introduction to generalized additive models

Tags:

Simon Wood,Generalized,Additive,Models:,Introduction 2nd