What I will Show You Today (in 10 Minutes!) PLS has no advantage at - - PowerPoint PPT Presentation

What I will Show You Today

(in 10 Minutes!)

• PLS has no advantage at small sample size

– Not for accuracy; not for statistical power

• PLS does not correct for measurement error, affecting

its accuracy

– Neither does regression, but CB-SEM does

• PLS has excessive false positives when multicollinearity

combines with measurement error

– Regression does too, but less so; CB-SEM --no problem here

• Many of PLS’s touted strengths are really weaknesses!

μ

KSI1 KSI2 KSI3 KSI4

X10 X11 X12 X7 X8 X9 X4 X5 X6 .70 .76 .82 X1 X2 X3

.70 .76 .82

.70 .76 .82 .70 .76 .82

Gamma 2 (.000) Gamma 3

(.292)

Gamma 4 (.510) Gamma 1 (.292)

ETA1

Y1 Y2 Y3 .70 .76 .82

0.0

0.0 0.0

General Model for the Monte Carlo Simulation

We can modify: effect size, sample size, reliability of the indicators, amount of correlation between independent constructs

• 0.250
• 0.200
• 0.150
• 0.100
• 0.050

0.000 0.050 20 40 90 150 200

Sample Size

LISREL Regression PLS

• 0.25
• 0.20
• 0.15
• 0.10
• 0.05

0.00 0.05 20 40 90 150 200

Sample Size

LISREL Regression PLS 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 20 40 90 150 200

Sample Size

LISREL Regression PLS 0.000 0.200 0.400 0.600 0.800 1.000 1.200 20 40 90 150 200

Sample Size

LISREL Regression PLS 0.00 0.20 0.40 0.60 0.80 1.00 1.20 20 40 90 150 200

Sample Size

LISREL Regression PLS 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 20 40 90 150 200

Sample Size

LISREL Regression PLS

Strong Effect Size Accuracy (Bias) Standard Deviations Power Medium Effect Size

Accuracy and Power for PLS, LISREL and Regression at Different Sample Sizes

Accuracy (Bias) Effect Size = L, M, S; = .74, .84, .91

(Averaging Across N = 90, 150, 200 Sample Sizes)

LISREL is quite accurate throughout. Accuracy for PLS and regression depends on reliability. When corrected for measurement error, PLS and regression are quite accurate

• 0.30
• 0.20
• 0.10

0.00 0.10 0.20 0.30 L Effect, a=.74 L Effect, a=.84 L Effect, a=.91 M Effect, a=.74 M Effect, a=.84 M Effect, a=.91 S Effect, a=.74 S Effect, a=.84 S Effect, a=.91 Bias

Unadjusted Results

LISREL Regression PLS

• 0.30
• 0.20
• 0.10

0.00 0.10 0.20 0.30 L Effect, a=.74 L Effect, a=.84 L Effect, a=.91 M Effect, a=.74 M Effect, a=.84 M Effect, a=.91 S Effect, a=.74 S Effect, a=.84 S Effect, a=.91 Bias

Adjusting for Measurement Attenuation (Nunnally & Bernstein)

LISREL Reg-Adj PLS-Adj

False Positives From Measurement Error and Multi-collinearity, = .80

(Based on 500 Samples, 95% confidence interval around 5% is 3.1% to 6.9%)

0% 5% 10% 15% 20% 25% 30% 0.0 0.4 0.6 0.8 0.9 LISREL Regression PLS 0% 5% 10% 15% 20% 25% 30% 0.0 0.4 0.6 0.8 0.9 LISREL Regression PLS

N = 100 N = 300

Correlation between independent constructs Correlation between independent constructs

Touted Strengths of PLS

• Better at small sample size
• No distribution requirements
• Consistency and Consistency at Large
• Exploratory versus Theory Testing
• Testing with pseudo-F statistics