Preface... xi. A Word to the Practitioner... xi The Organization of the Book... xi Required Software... xii Accessing the Supplementary Content...

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1 Contents Preface... xi A Word to the Practitioner... xi The Organization of the Book... xi Required Software... xii Accessing the Supplementary Content... xii Chapter 1 Introducing Partial Least Squares... 1 Modeling in General... 1 Partial Least Squares in Today s World... 2 Transforming, and Centering and Scaling Data... 3 An Example of a PLS Analysis... 4 The Data and the Goal... 4 The Analysis... 5 Testing the Model... 9 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... 25

2 vi 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... 93

3 vii 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

4 viii 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

5 ix 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

6 x 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

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