Checking discriminant validity between higher-order latent constructs
Juliette van Acker
I want to check if my higher-order constructs "A_v" and "R_v" are discriminant (see my second-order factor model in the attachment). How can I do this?
As far as I understand, the following options are not possible:
- The Fornell-Larcker criterion is only used to ensure that the dimensions within a construct are distinct and measure separate underlying concepts. It's not designed to assess the distinctiveness between different constructs. The latter is what I'm interested in.
- Comparing the model fit of different models, such as a model where the higher order constructs are correlated versus a model where they are not, is also not possible, since I have the same degrees of freedom for both models if the only difference between the models is an added correlation between "A_v" and "R_v".
- I used DWLS as the estimator because my indicators are dichotomous. I understand that checking the AIC and BIC is not possible with DWLS.
What other options do I have?
Rönkkö, Mikko
Hi,
Fornell-Larcker criterion is not very useful. You can do a nested model comparison* or you can inspect the confidence interval of the correlation between the factors. See
https://journals.sagepub.com/doi/full/10.1177/1094428120968614
*As for the comment about df begin the same: That should not be the case. If you add a correlation, you should lose one degree of freedom. If you find that df does not change, it means that you have also changed the model somehow to gain one df to compensate. I suggest comparing the parameter vectors “coef(fit)” to see what you are estimating and how the models differ.
Mikko
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