This document summarizes the process of operationalizing prediction using partial least squares path modeling (PLS-PM). It outlines how PLS-PM is used to (1) estimate the measurement and structural models on training data, (2) form exogenous latent variable scores to predict endogenous variables, (3) estimate outcome variables, and (4) evaluate predictions on holdout data using various metrics like RMSE and cross-validation. Open issues like incorporating mediation and alternative PLS estimators are also discussed. Implementations of these prediction procedures in R packages are noted.

1. PLOWING THROUGH THE PLS PATH MODEL:
OPERATIONALIZING PREDICTION
FROM MEASUREMENT AND STRUCTURE
Institute of Service Science
National Tsing Hua University
Taiwan, R.O.C.
Soumya Ray
Associate Professor
Nicholas Danks
Phd Student
Galit Shmueli
Distinguished Professor

2. A Simple PLS Model
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λ12
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y12
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Exogenous Factors Endogenous Factors
Structural model (Inner model)
Measurement Model (Outer Model)
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3. Overview of Prediction Process
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Holdout Data (~30%)
Evaluation
Data Split
Training
Prediction

4. Training: Estimation of PLS Model
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Structural Model
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structural paths

5. Prediction: Forming Exogenous Scores
2. Predict 𝑿. 𝒊
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1. Create standardized holdout data 𝒙𝒊𝒋𝒌
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6. Prediction: Structural Latent
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7. Prediction: Outcome Items
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Evaluation: Prediction Metrics
2. Item-level RMSE1. Factor-level RMSE
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b. Estimate out-of-sample Y scores
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9. Evaluation: Cross-Validation
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4. Estimate k-fold 𝑹𝑴𝑺𝑬 𝒚) 𝒊𝒋
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1. Create 10 combinations of:
90% training
10% holdout
2. Estimate Training Models
3. Predict holdout outcomes

10. Evaluation: Prediction Intervals
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1. Bootstrap Training Datasets (B=1000)
Bootstrapping
4. Predict B holdout outcomes
Single Holdout Dataset
2. Estimate B
training models
3. Predict B training outcomes
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5. Compute Training
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6. Add randomly selected
error to each prediction
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11. Evaluation: Visualizing Predictions
Sort cases by:
1. Actuals
2. Predicted values
Case-wise prediction interval
Average-case prediction interval
Case-specific prediction
Actual case value

12. Likert Scale Prediction Intervals
Cases, sorted
Actuals,Predictions,Intervals
Simulated Likert Scale Data Model

13. Open Issues
Y1 Y2
β
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y21
y22
λ
λ
λ
X1
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x11
x12
w
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λ λ
X2
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x21
x22
λ
λ
λ
β
β
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λ λ
Mediated Models
Alternative PLS Estimation
Consistent PLS WarpPLS

14. Implementations
https://github.com/ISS-Analytics/pls-predict
https://github.com/ISS-Analytics/seminr
predictions,
intervals
modeling,
mediation
visualizations,
reports
Summer 2017 Fall 2017 Winter 2017
PLSpredict v0.1
SEMinR v0.1
PLSpredict v0.2
SEMinR v0.2
PLSpredict v1.0
SEMinR v1.0
library(seminr)
sec = read.csv("security_data.csv")
# Measurement Model
sec_mm <- measure(
reflect("TRUST", multi_items("TRST", 1:4)),
reflect("SEC", multi_items("PSEC", 1:4)),
form("REP", multi_items("PREP", 1:4)),
reflect("INV", multi_items("PINV", 1:3)),
reflect("POL", multi_items("PPSS", 1:3)),
reflect("FAML", single_item("FAML1"))
)
sec_intxn <- interact(
interaction_ortho("REP", "POL")
)
print_paths(sec_pls)
SEC TRUST
R^2 0.44 0.37
REP 0.30 .
INV 0.17 .
POL 0.32 .
FAML 0.01 .
REP.POL -0.11 .
SEC . 0.61