Contents
Accessing the Supplementary Content
Chapter 1 Introducing Partial Least Squares
Partial Least Squares in Today’s World
Transforming, and Centering and Scaling Data
Chapter 2 A Review of Multiple Linear Regression
Underfitting and Overfitting: A Simulation
The Effect of Correlation among Predictors: A Simulation
Chapter 3 Principal Components Analysis: A Brief Visit
Centering and Scaling: An Example
The Importance of Exploratory Data Analysis in Multivariate Studies
Dimensionality Reduction via PCA
Chapter 4 A Deeper Understanding of PLS
PLS as a Multivariate Technique
An Example Exploring Prediction
Choosing the Number of Factors
A Simulation of K-Fold Cross Validation
Validation in the PLS Platform
The NIPALS and SIMPLS Algorithms
Useful Things to Remember About PLS
Chapter 5 Predicting Biological Activity
The Partial Least Squares Report
Performance on Data from Second Study
Comparing Predicted Values for the Second Study to Actual Values
Comparing Residuals for Both Studies
Chapter 6 Predicting the Octane Rating of Gasoline
Creating a Test Set Indicator Column
Constructing Plots of the Individual Spectra
Model Assessment Using Test Set
Chapter 7 Equation Chapter 1 Section 1Water Quality in the Savannah River Basin
Conclusions from Visual Analysis and Implications
A First PLS Model for the Savannah River Basin
The Partial Least Squares Report
A Pruned PLS Model for the Savannah River Basin
Saving the Prediction Formulas
Comparing Actual Values to Predicted Values for the Test Set
A First PLS Model for the Blue Ridge Ecoregion
A Pruned PLS Model for the Blue Ridge Ecoregion
Comparing Actual Values to Predicted Values for the Test Set
Chapter 8 Baking Bread That People Like
Visual Exploration of Overall Liking and Consumer Xs
The Plan for the First Stage Model
Comparing the Stage One Models
Visual Exploration of Ys and Xs
The Combined Model for Overall Liking
Constructing the Prediction Formula
The Singular Value Decomposition of a Matrix
Relationship to Spectral Decomposition
Principal Components Regression
The Idea behind PLS Algorithms
Properties of the NIPALS Algorithm
Implications for the Algorithm
Determining the Number of Factors
Cross Validation: How JMP Does It
Appendix 2: Simulation Studies
The Bias-Variance Tradeoff in PLS
Using PLS for Variable Selection