PLS Path Modeling with R Gaston Sanchez www.gastonsanchez.com This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License (CC BY-NC-SA 3.0) http://creativecommons.org/licenses/by-nc-sa/3.0/ In short: Gaston Sanchez retains the Copyright but you are free to reproduce, reblog, remix and modify the content only under the same license to this one. You may not use this work for commercial purposes but permission to use this material in nonprofit teaching is still granted, provided the authorship and licensing information here is displayed. Citation Sanchez, G. (2013) PLS Path Modeling with R Trowchez Editions. Berkeley, 2013. http://www.gastonsanchez.com/PLS Path Modeling with R.pdf i To Jessica for her manifest love, her latent support, her outer energy, and her inner strength. I wish my college teachers would have taught many more things than the ones they did. Preferably, I would have liked to be taught more computational courses and programming classes. They taught me the basics but they missed one key lesson that I learned years later with a blend of great disillusionment and enriching experience: the important modeling should take place in the mind of the analyst, not in the computer. Computers and software are indispensable but they can't make sense of data; only people who have developed the necessary data analysis skills can. Whether it is PLS Path Modeling or any other type of modeling, always remember this little-big advice. Optimism Luck Dedication Work Achievement Patience Sacrifice My Model Contents Preface......................................... vii 1 Introduction.................................... 3 1.1 PLS Path Modeling................................ 3 1.2 R package plspm ................................. 5 1.2.1 Why R?.................................. 5 1.3 About Partial Least Squares........................... 6 1.3.1 Short tale of PLS............................. 7 1.3.2 Regressionists and Path-modelists.................... 7 1.4 Structure of the book............................... 8 1.5 R and plspm .................................... 9 1.5.1 Installing plspm .............................. 11 1.5.2 Some Extra Details............................ 12 1.6 Reading List.................................... 13 2 Getting Started with PLS-PM ......................... 15 2.1 Case Study: Index of Success .......................... 15 2.1.1 Of latent and manifest variables..................... 16 2.1.2 Measuring Success, Attack and Defense................. 20 2.1.3 Path Model................................ 21 2.1.4 Inner and Outer models ......................... 22 2.2 Applying PLS-PM with the R package plspm . 23 2.2.1 Preparing the ingredients for plspm() . 24 2.2.2 Running plspm() ............................. 26 2.2.3 Plotting results.............................. 29 2.3 Reading List.................................... 31 3 Setting the PLS-PM Framework........................ 33 3.1 PLS-PM Frame of Mind ............................. 33 3.2 PLS Path Modeling Specs ............................ 35 3.3 Formal Model: What we want .......................... 35 3.3.1 The Structural Model........................... 36 3.3.2 The Measurement Model......................... 37 v 3.3.3 The Weight Relations........................... 38 3.4 Operative Model: How to get what we want . 39 3.4.1 Stage 1: Iterative Process ........................ 41 3.4.2 Stage 2: Path Coefficients ........................ 46 3.4.3 Stage 3: Loadings............................. 46 3.4.4 Wrapping up ............................... 46 3.5 Reading List.................................... 47 4 Interpreting PLS-PM Results.......................... 49 4.1 Reminder of Our Success Index Model ..................... 50 4.1.1 PLS-PM with plspm ........................... 50 4.1.2 The function plspm() .......................... 51 4.2 Handling PLS-PM results ............................ 54 4.3 Measurement Model Assessment: Reflective Indicators ............................... 55 4.3.1 All for one and one for all ........................ 55 4.3.2 Unidimensionality of indicators ..................... 56 4.3.3 Loadings and Communalities ...................... 62 4.3.4 Cross-loadings............................... 64 4.4 Measurement Model Assessment: Formative Indicators............................... 67 4.5 Structural Model Assessment .......................... 67 4.5.1 Coefficients of determination R2 ..................... 68 4.5.2 Redundancy................................ 68 4.5.3 GoF .................................... 69 4.6 Validation..................................... 70 4.6.1 Bootstrapping............................... 70 4.7 Reading List.................................... 72 5 Running a PLS-PM Analysis.......................... 75 5.1 Modeling Customer Satisfaction......................... 75 5.1.1 ECSI Model................................ 76 5.1.2 Case Study: Satisfaction in Education ................. 77 5.2 Preliminary Exploration ............................. 81 5.2.1 Looking at the data............................ 82 5.2.2 Seeing the forest, not just the trees................... 84 5.3 PLS-PM Round 1................................. 86 5.4 PLS-PM Round 2................................. 90 5.5 PLS-PM Round 3................................. 94 5.5.1 Checking unidimensionality ....................... 94 5.5.2 Loadings and Communalities ...................... 95 5.5.3 Path Coefficients ............................. 97 5.5.4 Structural Regressions .......................... 99 5.5.5 Effects................................... 100 5.5.6 Inner Model Summary.......................... 103 5.5.7 GoF .................................... 104 5.5.8 Bootstrap Validation........................... 105 5.5.9 Inspecting scores of latent variables................... 108 5.6 Guidelines for a PLS-PM analysis........................ 111 5.7 Reading List.................................... 113 6 Comparing Groups ................................117 6.1 The million dollar question............................ 117 6.2 Group Comparison Approaches ......................... 119 6.2.1 Bootstrap t-test.............................. 120 6.2.2 Permutation Procedure.......................... 121 6.2.3 Case Study: College GPA ........................ 122 6.2.4 PLS-PM Analysis: GPA Model ..................... 125 6.2.5 Female and Male Student Models.................... 128 6.3 Comparing Groups: Bootstrap t-test ...................... 129 6.4 Comparing Groups: Permutation test...................... 131 6.5 Reading List.................................... 133 7 Moderating Effects ................................135 7.1 Moderator Variables ............................... 135 7.2 Moderating effects in PLS-PM.......................... 136 7.2.1 Moderator variables as constructs.................... 137 7.2.2 Case Study: Simplified Customer Satisfaction . 137 7.3 Product Indicator Approach........................... 138 7.3.1 Example.................................. 139 7.4 Two-Stage Path Modeling Approach ...................... 143 7.4.1 Example.................................. 144 7.5 Two-Stage Regression Approach......................... 147 7.5.1 Example.................................. 148 7.6 Categorical Variable Approach.......................... 151 7.6.1 Example.................................. 152 7.7 Reading List.................................... 155 8 PLS Path Models with Higher-Order Constructs . 157 8.1 Constructify-it: How to model higher-order constructs? .................................... 158 8.1.1 Two types of higher-order constructs .................. 159 8.1.2 Modeling higher-order constructs in PLS-PM . 160 8.1.3 Case Study: NFL data.......................... 161 viii 8.2 Repeated Indicators: The Poor Man's Approach . 164 8.2.1 Repeated Indicators example ...................... 165 8.3 Two-Step Option: The Patch Approach . 167 8.3.1 Two-Step example ............................ 167 8.4 Hybrid Option: The Give Away Approach . 172 8.4.1 Hybrid Approach example........................ 172 8.5 Wrapping Up ................................... 173 8.6 Reading List.................................... 175 9 Detecting Classes with REBUS-PLS......................177 9.1 Diversity in Data................................. 177 9.1.1 Unobserved Classes............................ 178 9.2 What is REBUS?................................. 179 9.2.1 The REBUS Approach.......................... 179 9.2.2 Case Study: Success Index Model.................... 181 9.2.3 Global PLS Path Model ......................... 182 9.3 Applying REBUS................................. 188 9.3.1 Local Models ............................... 193 9.3.2 Quality of REBUS models........................ 198 9.3.3 Final Comments ............................. 201 9.4 Reading List.................................... 201 A Historical Overview of PLS-PM ........................205 1 Preliminaries ................................... 205 2 Herman Wold................................... 208 2.1 The Econometrician ........................... 209 2.2 The Least Squares Affair......................... 210 2.3 The Philosopher of Science........................ 213 3 Pre-PLS Era.................................... 214 4 Soft Modeling................................... 217 5 PLS-PM Related Timeline............................ 218 6 Reading List.................................... 221 CC BY-NC-SA 3.0 Gaston Sanchez PLS Path Modeling with R Preface On a sunny September morning