PLS Group Comparison:A Proposal for Relaxing Measurement

Invariance Assumptions

Lucian VisinescuUniversity of North Texas, Denton, USA

Presentation Agenda

• Framing the Question

• The Simulation

• Conclusions

Framing the Question

• Understanding and generalizing phenomena involves comparison of frameworks or models in different settings

• Multi-group analysis studies require adequate equivalence of the instruments used to assess the theoretical constructs under investigation

• The study of the equivalence of instruments in cross-national/multiple-group studies is known as the problem of measurement invariance

SEM Measurement Invariance

• “Whether or not, under different conditions of observing and studying phenomena, measurement operations yield measures of the same attribute” (Horn and McArdle 1992, p. 117)

• Measurement invariance hypotheses verify: - configural variance - construct-level metric invariance - item-level metric invariance - residual variance invariance - intercept invariance - equivalence of construct variance - equivalence of construct covariance - equivalence of latent means (Cheung & Rensvold, 2002).

SEM Measurement Invariance

• “hypothesis HΛ,Φ(jj) states that the variance of constructs (i.e., latent variables) are invariant across groups…whereas hypothesis HΛ,ν,Κ posits that the latent means are invariant across groups.” (Cheung & Rensvold , 2002 p.238)

• There have been calls and discussions for measurement invariance relaxation, known as partial measurement invariance (Byrne, Shavelson, & Muthen, 1989; Cheung and Rensvold, 2002).

PLS Measurement Invariance Group Comparison

Construct measures are invariant among groups

Moderator variable effect is restricted to the path coefficient

Sarstedt et al. (2011)

Imaginary Model

LV1X1

X3

X2LV2

Y1

Y3

Y2

m

Framework From Sarstedt et al. (2011)

Group 1

LV11

X1

X3

X2LV2

1

Y1

Y3

Y2

LV12

X1

X3

X2LV2

2

Y1

Y3

Y2

Group 2

Latent Variable Means

LV11,2 LV2

1

LV22

When latent variables are not significantly different Sarstedt et al. (2011), path coefficients can be directly compared using Chin (2000)

Latent Variable Means Easy Scenario

Latent Variable Means Scenario

LV11,2 LV2

1

LV22

Latent Variable Means Scenario

LV11 LV1

2 LV21 LV2

2

If Latent Variable Means are different…

What to do?

How might we approach this?

Latent Variable Means

LV11,2 LV2

1

LV22

Latent Variable Means

L11,2 L2

1

L22

The Simulation

The Simulation

Conclusion

Before comparing path coefficients in multi-group analysis, checking the latent variable means may remove a potential for bias from our analysis.

If latent variable means are different, one might adopt the suggested approach in a similar situation.

Questions and suggestions, please.