I aim to validate a formative construct (GPers) and I put it in a model with two reflective constructs (CI and Willing) to do so.
AMOS gives me estimates in the output, but they don't appear in the AMOS graphic depiction. AMOS states that iteration limit is reached and results are therefore incorrect.
I should mention that the manifest variables capturing GPerso are sum scores, summing together multiple items (though I think that should not change anything in AMOS).
Does anyone know what might be the problem and how to fix it?
Thanks in advance.
You have an identification problem due to the "formative" specification. The "formative" G_Pers factor is identifiable only because it has two reflective indicators (CI and Willing), which means it is not really a "formative" factor; that is, G_Pers is really a second-order (reflective) factor with the CI and Willing first-order factors as (reflective) indicators. To identify the model, both second-order factor loadings (paths from G_Pers to CI and Willing) need to be fixed to 1 because there are only those two (reflective) indicators for G_Pers.
The "formative" indicators do not contribute to the identification of G_Pers. This factor derives its identification and meaning only from the CI and Willing factors, which is why I find the entire concept of "formative measurement" to be dubious. G_Pers accounts for the covariance between CI and Willing (and that covariance is what identifies the variance of G_Pers). The G_Pers factor is not defined by its "formative indicators." I would see the "formative indicators" merely as predictors of the second-order factor G_Pers.
Hello Christian, thanks for your answe!
Thanks also for your recommendation; the model was estimable when I set the two paths emitting from G_Pers to the reflective Variables to 1.
Can you elaborate on why that is so? Following Diamantopoulos and Winklhofer (2001) or Jarvis et al., 2003, when adding two reflective constructs (or two reflective indicators), the model should be identified without having to constrain the paths leading to these constructs, i.e. also the paths should be estimable.
Also, in the context of the full model (after validating G_Pers and other formative constructs that are part of the model), I will actually need the paths coming out of those constructs to be estimated (as we're testing their influence in a mediating variable), so setting them to 1 will not be an option.
I understand your apprehension regarding formative constructs. As they come with some estimation and identification issues, they are much less frequently used. Yet, our construct is theoretically not explainable as a formative one.
Thanks in advance, I really appreciate it,
Charlotte
The G_Pers factor may be identifiable without fixing both paths (to CI and Willing) if at least one of the "formative indicators" of G_Pers is substantially correlated with the G_Pers factor (i.e., if at least one of the paths from the "formative indicators" is substantially different from 0). However, one of the reflective paths (to either CI or Willing) will still have to be fixed as far as I can tell. Otherwise, the G_Pers factor with a freely estimated residual variance (variance of e40 in your picture) will not be identified.
This is why I would think of the G_Pers factor as being a reflective (second-order) factor rather than a "formative" variable. Its identification and meaning is based on the reflective indicators (CI and Willing) rather than the "formative indicators." The "formative indicators" are merely observed predictor variables (covariates) of a second-order reflective factor.
The problem is not so much estimation/identification as it is interpretation. In my opinion, only reflective measurement can be considered "measurement" in a classical sense. That being said, you might consider using composites, which are clearly defined. See, for example, work by Joerg Henseler, Florian Schuberth, and colleagues on confirmatory composite analysis:
https://scholar.google.com/scholar?hl=de&as_sdt=0%2C49&q=confirmatory+composite+analysis&oq=confirmatory+composi
Thanks Christian Geiser for introducing CCA to me. This might be appropriate for our purpose.
Thanks again for taking the time to reply.
All the best, Charlotte
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