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
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
Preface
A Word to the Practitioner
Welcome to Discovering Partial Least Squares with JMP. This book introduces you to the exciting area of partial least squares. Partial least squares is a multivariate modeling technique based on the idea of projection—the inspiration for the book’s cover design. You will obtain background understanding and see the technique applied in a number of examples. The book is built around the intuitive and powerful JMP statistical software, which will help you understand and internalize this new topic in a way that just reading simply cannot.
Since our goal is to help you apply partial least squares in your own setting, the textual material exists only to build your understanding and confidence as you progress through the worked examples. Although we endeavor to provide the salient details, the area of partial least squares is very broad and this book is necessarily incomplete. To the extent that we cannot cover certain topics fully, we provide references for your further study.
The Organization of the Book
We open with a number of introductory chapters that describe the concepts behind partial least squares and help position it in the wider world of statistical methodology and application. The meat of the book is found in Chapters 5 through 8, which contain four examples. Working through these examples using JMP prepares you to apply partial least squares to your own data. The book also contains two appendixes that provide further statistical details and the results of some simulation studies. Depending on your level and area of interest, you might find these useful.
Required Software
Although a user of standard JMP 11 or later will find this book useful, many examples require JMP Pro 11 or later. Compared to the standard version of JMP, the Pro version is intended for those who require deeper analytical capabilities. In JMP Pro, the implementation of partial least squares is quite complete.
The
