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Contents

Preface

A Word to the Practitioner

The Organization of the Book

Required Software

Accessing the Supplementary Content

Chapter 1 Introducing Partial Least Squares

Modeling in General

Partial Least Squares in Today’s World

Transforming, and Centering and Scaling Data

An Example of a PLS Analysis

The Data and the Goal

The Analysis

Testing the Model

Chapter 2 A Review of Multiple Linear Regression

The Cars Example

Estimating the Coefficients

Underfitting and Overfitting: A Simulation

The Effect of Correlation among Predictors: A Simulation

Chapter 3 Principal Components Analysis: A Brief Visit

Principal Components Analysis

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

Centering and Scaling in PLS

PLS as a Multivariate Technique

Why Use PLS?

How Does PLS Work?

PLS versus PCA

PLS Scores and Loadings

Some Technical Background

An Example Exploring Prediction

One-Factor NIPALS Model

Two-Factor NIPALS Model

Variable Selection

SIMPLS Fits

Choosing the Number of Factors

Cross Validation

Types of Cross Validation

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

Background

The Data

Data Table Description

Initial Data Visualization

A First PLS Model

Our Plan

Performing the Analysis

The Partial Least Squares Report

The SIMPLS Fit Report

Other Options

A Pruned PLS Model

Model Fit

Diagnostics

Performance on Data from Second Study

Comparing Predicted Values for the Second Study to Actual Values

Comparing Residuals for Both Studies

Obtaining Additional Insight

Conclusion

Chapter 6 Predicting the Octane Rating of Gasoline

Background

The Data

Data Table Description

Creating a Test Set Indicator Column

Viewing the Data

Octane and the Test Set

Creating a Stacked Data Table

Constructing Plots of the Individual Spectra

Individual Spectra

Combined Spectra

A First PLS Model

Excluding the Test Set

Fitting the Model

The Initial Report

A Second PLS Model

Fitting the Model

High-Level Overview

Diagnostics

Score Scatterplot Matrices

Loading Plots

VIPs

Model Assessment Using Test Set

A Pruned Model

Chapter 7 Equation Chapter 1 Section 1Water Quality in the Savannah River Basin

Background

The Data

Data Table Description

Initial Data Visualization

Missing Response Values

Impute Missing Data

Distributions

Transforming AGPT

Differences by Ecoregion

Conclusions from Visual Analysis and Implications

A First PLS Model for the Savannah River Basin

Our Plan

Performing the Analysis

The Partial Least Squares Report

The NIPALS Fit Report

Defining a Pruned Model

A Pruned PLS Model for the Savannah River Basin

Model Fit

Diagnostics

Saving the Prediction Formulas

Comparing Actual Values to Predicted Values for the Test Set

A First PLS Model for the Blue Ridge Ecoregion

Making the Subset

Reviewing the Data

Performing the Analysis

The NIPALS Fit Report

A Pruned PLS Model for the Blue Ridge Ecoregion

Model Fit

Comparing Actual Values to Predicted Values for the Test Set

Conclusion

Chapter 8 Baking Bread That People Like

Background

The Data

Data Table Description

Missing Data Check

The First Stage Model

Visual Exploration of Overall Liking and Consumer Xs

The Plan for the First Stage Model

Stage One PLS Model

Stage One Pruned PLS Model

Stage One MLR Model

Comparing the Stage One Models

Visual Exploration of Ys and Xs

Stage Two PLS Model

Stage Two MLR Model

The Combined Model for Overall Liking

Constructing the Prediction Formula

Viewing the Profiler

Conclusion

Appendix 1: Technical Details

Ground Rules

The Singular Value Decomposition of a Matrix

Definition

Relationship to Spectral Decomposition

Other Useful Facts

Principal Components Regression

The Idea behind PLS Algorithms

NIPALS

The NIPALS Algorithm

Computational Results

Properties of the NIPALS Algorithm

SIMPLS

Optimization Criterion

Implications for the Algorithm

The SIMPLS Algorithm

More on VIPs

The Standardize X Option

Determining the Number of Factors

Cross Validation: How JMP Does It

Appendix 2: Simulation Studies

Introduction

The Bias-Variance Tradeoff in PLS

Introduction

Two Simple Examples

Motivation

The Simulation Study

Results and Discussion

Conclusion

Using PLS for Variable Selection

Introduction

Structure of the Study

The Simulation

Computation of Result Measures

Results

Conclusion

References

Index

Discovering Partial Least Squares with JMP

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