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# What is Predictive About Partial Least Squares?

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Presentation by Galit Shmueli at the Sixth Symposium on Statistical Challenges in eCommerce Research (SCECR), Austin TX, 2010

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• All reflective
• Formative on left; reflective on right
• ### Transcript of "What is Predictive About Partial Least Squares?"

1. 1. What is PredictiveAbout Partial Least Squares?Galit Shmueli Otto KoppiusUMD Erasmus
2. 2. Barclay, Higgins & Thompson Technology Studies, 1995
3. 3. Explanatory PLS: test causal hypothesesPath coefficientsloadingsweightsInitialize: = avg(y1,…,yq)= f(x1,…xp)= avg( 1x1,…, pxp)yi = f( )Last: = f( )iterate
4. 4. Biased coefficients(Dijkstra , J Econ 1983; Chin et al., ISR 2003)Under-estimatedpath coefficientsOver-estimatedloadingsweights
5. 5. PLS path modeling is “causal-predictive”Jöreskog & Wold, 1982Fornell & Bookstein, 1982Barclay, Higgins & Thompson, 1995
6. 6. PLS RegressionPLS Path Models
7. 7. Explanatorystatistical model:Theory-based,empirical testing ofcausal hypothesesExplanatory power:Strength ofrelationship instatistical modelPredictive model:Empirical methodfor predicting newobservationsPredictive power:Ability toaccurately predictnew observations
8. 8. Measuring Predictive PowerHoldout data setPrediction errorsniii yynRMSE12ˆ1 ni iiiyyynMAPE1%100ˆ1
9. 9. Predictive Aspects of PLS?Not in PLS softwareNot in published research
10. 10. Note: Cross-validation(blindfolding)Explanatory context• Validate measurementmodel, structural model• Estimate communality,redundancy
11. 11. How to predict holdout datawith PLS?
12. 12. Example: TAMGefen & Straub, CAIS 2005PUPEOUUSE
13. 13. TAM: Predictive Power?Training: n=70 Holdout: n=30RMSE = 2.1MAPE = 38%
14. 14. Can we do better with aPredictive Model?
15. 15. Iterative estimationNode-level errorsNeural NetworkHackl & Westlund TQM 2000 ; Hsu, Chen & Hsieh TQM 2006
16. 16. PLS Neural NetHypothesis testing Purely predictiveCausal theory No causal theoryLatent nodes importantPath coefficients matterHidden layers – utilityWeights – for predictionLinear relationships Nonlinear relationshipsRestricted paths All possible pathsbetween layers
17. 17. Predictive Performance(on holdout)Method RMSEPLS (reflective) 2.10Neural Net 1.94Linear Regression 1.84PLS (formative) 2.18Predicts “3”Lots of data?