How to check for measurement invariance?

[Green]

Hi,

I am conducting PLS MGA and therefore i have to check for measurement invariance. There are some approaches in schoarly but i dont know how to use them in SmartPLS3. For example there articles about using "constrained models", but i think Smart PLS is not able to compute them.

Can anyone give me a hint what to do?


Thanks

[Hengkov]

Hi,

See literature that can help you here

viewtopic.php?f=7&t=21&start=210

Best regards,

[Green]

I have read the article by Henseler (2015) : Testing Measurement Invariance of Composites Using Partial Least Squares

The problem with their approach is that it is made for formative models, but my model ist reflective.

Is there no simple way to check for measurement variance in PLS-SEM.... for example like in AMOS.

Best regards

[Hengkov]

Hi,

Why do you not use SmartPLS v. 3.2.2?
MICOM test for measurement invariance already has been added there. So, you can test this very easily.

Best regards,

[Green]

Thank you very much for this information. I didn't know there is an update for SmartPLS.... as the "Check for Update"-function didn't work. Seems like it was on october 1st.

[Green]

I got those Results:

Step1

screen1.JPG (44.92 KiB) Viewed 15280 times

The null hypothesis cannot be established for some of the factors, which means that compositional invariance cannot be estbalished.
But what does it mean, if there is no p-value for some of the factors in Step 2?

Step2

screen 2.JPG (89.96 KiB) Viewed 15280 times

BR

[jmbecker]

Please increase the decimal points. It seems that all your correlations are very close to 1. If there is no variation (all correlations are the same between permutations) the Permutation P-Value will be 0 (if you hide zero values, they are not shown).
The zero value in this very special case might be misleading as you actually have perfect measurement equivalence (in Step 2).

It usually happen for single item constructs and all other cases where the weights don't change that measurement equivalence (in Step 2) is perfect.

[Green]

Thanks, you are right. I was hiding the zero values.

But now i am confused. Some p-values are above 0,05 and therefore measurement invariance (metric invariance) is not eastablished, isn't it?

[boraokur44]

......

[jmbecker]

From the MICOM paper:

"6. We test the null hypothesis that c equals one. If c is smaller than the 5%-quantile of the empirical
distribution of cu, we must reject the hypothesis of compositional invariance, because the derivation from
one is unlikely to stem from sampling variation."

Hence, if you Original Correlation is smaller than the 5% quantil you have significant difference from 1 and measurement invariance is not eastablished.
The same applies if your Permutation P-Value is lower than 5%.

HOWEVER: There is a small problem in the calculation of Permutation P-Values for Single-Items at the moment. If many (all) permutation values are equal to the original correlation, than the Permutation P-Value is misleading. This is the case with single-items as they always have a weight of 1. Hence, Compositional Invariance is always given between groups for Single-Items and thus the MICOM Step 2 does not make any sense in this case.

[Green]

Thanks, you helped me a lot!

[jmbecker]

I would also add, that I think that it is questionable to test measurement invariance for interaction terms. They are not "real" latent variables, but only mathematical constructions to calculate the moderated regression analysis. Hence, I would advice only to check measurement invariance for each of the two constructs that are used for the construction of the interaction term, but not the interaction term itself.

[Green]

Thanks for this information.

There is another question upcoming: Is it allowed to compare mean values between groups if measurement invariance in step 3 is established? I am asking, as in the MICOM-Paper it is simply mentionend that pooling of the data is allowed, but nothing about comparing mean values.