Question about model fit

[bwardmusic]

I am analyzing the fit of the following model:

UWES Second Order.JPG (40.05 KiB) Viewed 5670 times

I get this output for the Forner Lacker Criterion

Forner Lacker Criterion UWES Second Order Model.JPG (17.99 KiB) Viewed 5670 times

It is my understanding that the values at the intersection of each variable should be higher than the values below it. Although my model fit indices are adequate (GFI, NFI, CFI etcetera) the discrimminant validty above doesn't appear to exist with this metric.

Further, I am also not getting the cross loadings report that will show how the factors load on each construct. There is no option given for it in the report. Why?

Here is what my HTMT output looks like:

HTMT Output.JPG (10 KiB) Viewed 5668 times

...continued in an additional post below.

[bwardmusic]

Here are my model fit indices:

UWES Second ORder Model Fit Indices.JPG (40.16 KiB) Viewed 5666 times

Why is there no cross loading report, and how would you interpret this model? Must I throw out using this measurement model to do my structural equations later, and am I unable to conclude anything about the dimensionality of the Engagement Construct?

[jmbecker]

First, you seem to have a second-order construct. Engagement does not have any indicators directly attached. Thus, there is no reliability measures reported because they are usually based on the loadings of the indicators. As second-order construct is a theoretical lens, it is impossible for the software to understand that you now want to interpret some of the structural path coefficients as loadings. Therefore, you have to calculate these measures yourself.
We have some guidelines on this for PLS models in the following article:
Sarstedt, M., Hair, J. F., Cheah, J.-H., Becker, J.-M., & Ringle, C. M. (2019). How to Specify, Estimate, and Validate Higher-Order Constructs in PLS-SEM. Australasian Marketing Journal, 27(3), 197-211. https://doi.org/10.1016/j.ausmj.2019.05.003

But assessing discriminant validity from the higher-order construct to the lower-order constructs also does not make much sense. In your model, they reflect Engagement and thus they are part of the construct. Talking about being distinct or not does not make much sense.

Second, the CB-SEM method does not automatically provide cross-loadings. If you do not specify cross-loading in the model, they are assumed to be zero in the model estimation. However, if you specify a cross-loading then also the estimation changes. Thus, this is usually not a common evaluation instrument for CB-SEM models.