Dear all,
when you only have two indicators for a factor, normally one would have to set the variance of the factor to 1 and the loadings equal to have an identified model.
However, I now have such a factor as part of a larger model, and I noticed that then I do not need to constrain the loadings to be equal: the model also runs when I don't do this.
But is this correct? Do I need to constrain the loadings to be equal anyway to get the 'correct' results? The model fit and correlations between the specific factor and other factors can change considerably when I do or do not set them equal, so it does matter for the results...
Help would be very much appreciated!
Kind regards,
Dirk pelt
Philippe is right. Ideally, a model should be locally and globally identified. However, you will find that it is common practice across many research fields that obtaining overall model identification is perfectly acceptable. This is certainly true for many publications in Business & Management as well as the Social Sciences. Some authors would also (inappropriately) report alpha values for such two-item factors, but I would not recommend this as this does not make good sense.
Thank you for your answers! I am a bit amazed that this issue, as Philippe points out, is rarely being discussed when models are reported.
I guess reviewers would accept it when you constrain the loadings and report "In order to have the model locally and globally identified, constraints were imposed... etc". However, I do not think I have read this before in any paper..
Hi Sui,
let's say you have a latent factor with two indicators V1 and V2, normally for identification one of them would be fixed to 1, and the other free. So in your output the standardized loading for V1 on the latent factor will be for example .7 and for V2 it could be 0.6. By "setting loadings equal" I mean contraining them to have the same loading/value. I don't know which software you use but usually in Mplus or R for example this is achieved by using the same labels for the loadings (e.g., Factor1 = label_a * V1 + label_a * V2). In your output you will see that the standardized loadings are the same, so for example both 0.6. Hope this helps! Dirk
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