Hello Tomasz,

if you want to specify second order factor you either need 3 primary factors or two primaries + correlations with other factors (primary or secondary). It seems at first glance, that your model fulfils the second case. Hence, I guess that your second-order-factors don't correlate rendering each of the two factor models unidentified.

Whether you should specify a (secondary) factor model for the PVQ values is a more theoretical question. In this thread, Alex Gaut had a model with the Schwartz values and we discussed a bit about the theory. This could be interesting for you:

https://www.researchgate.net/post/In_SEM_how_to_interpret_standardised_regression_weights_and_their_significance

Best,

Holger

Dear Holger Steinmetz - Thank you for your answer.

As for the shape of the model, it is also a theoretical adventure for me, because I would like to know if models with master factors or rather master latent variables make sense in SEM. And how to properly specify them. In Alex's topic, I saw that the model just turned low-order latents into observables (computes their raw score) and works on them. But I want to avoid this and make a model that has a horizontal structure with levels of latent variables. Let's say that the theory for the model does not matter to me at the moment. I just want to properly specify the model and calculate its coefficients.

I've tried as you suggest, make three second-order latents, one higher-order latent, and add two observable variables. Also this model does not starts. (The model is probably unidentified. In order to achieve identifiability, it will probably be necessary to impose 1 additional constraint. AMOS says). Model looks similar to this: http://davidakenny.net/cm/mvar.htm

What im doing wrong? Can You explain to me for example, by drawing in Paint what is missing from my model? :)

Hello Tomasz,

first, my recommendation to read Alex' thread was rather the discussion about the appropriateness of common factors (primary or secondary) for the constructs in Schwartz' theory and hence, as a structural theory that explains a) the emergence of item responses and b) their interrelationships (e.g., the necessity of somewhat homogeneous correlation patterns among items that measure the same factor).

Second, I am quite puzzled that you say that the theory does not matter while at the same time having the goal to "properly specify the model and calculate its coefficients". For this goal, theory is essential and by adopting any modeling stile, actually you implicitly or explicitly apply SOME theory. Your model that specifies a second order factor IS a (structural) theory. And that's fine. My point in Alex' point was simply that this thinking does not represent Schwartz' theory. Just be clear about this fact that you apply your theory (and not "no theory").

Third, I don't understand what you mean with "master latent".

Here's a further thread on the meaning with second order factors:

https://www.researchgate.net/post/Scales_Subscales_in_Confirmatory_Factor_Analysis-how_do_you_analyse_them#view=5fd0852ede0d8552fe4a3716

(BTW: The reason why I refer to my own posting is not that I think I am almighty but simply don't want to write the same stuff again and again.

Fourth, the identification issues probably are due to your omission of a fixed-to-1-effect of C_SD on one of the primary factors. Any latent has to be scaled to assign a metric to it. This is done by fixing one effect which assigns the metric of the primary factor on the second order factor. The scale of the primary factor, in turn is assigned from its observed variable so all of them have the metric of this one (marker) item.

Fifth, you added age and gender as dependent variables, right? This will ad "identification-relevant information" if the effects are significant. If not you end up with a second-order-factor model with three primaries which is just-identified and cannot misfit.

We see that later :)

HTH

Holger

Tomazs, refering to Holger's critique concerning identification: If you have two first-order factors both loading onto a second-order factor, then it is necessary to either fix both second-order loadings to one and estimate the variance of the second-order factor freely, or to fix the latent variance of the second-order factor to one and to impose an equality constraint on both second-oder factor loadings.

This is the same problem that you generally have with first-order factors: If you only have two indicators, then both first-order factor loadings should be fixed to one because the measurement model with only two indicators is not identified.

The same applies to the second-order factor: With only two first-order factors as indicators, the higher-order measurement model is not identified.

HTH, Karin

Dear Karin Schermelleh-Engel and Holger Steinmetz - perhaps it was not clear, but my question is not about theory, but about the practical implementation of the model in AMOS (or other software). It is completely understandable for me that the SEM model requires a theory and only in relation to it one can interpret the model indicators. But this model is an example of a problem that I can't solve - and I don't look for changing theoretical approach, but the question is why some model that works in the tutorials won't be computable in SPSS AMOS. Even if the theory for this questionnaire is questionable - there are certainly some that consider a similar structure.

Specific variables (age, gender) are of secondary importance to me, I can put anything there that will have a greater empirical sense. At this moment all observable variables (questionnaire items) correlate with each other at the level

Tomasz,

if you have fixed the loadings to 1 for both latent variables, and the model is unidentified then both latent variables don't correlate (an isolated 2-indicator-latent factor model is unidentified). It is (empirically) identified if the latent in question correlates with other variables (manifest or latent) as these correlations add to the "knowns" in the equation system. In this situation, the proposal by Karin is the only way. But this does not provide a test of the model.

Fixing the loading to 0 makes no sense at all. BTW: You constantly change your model which makes the discussion a bit tedious.

All the best,

--Holger

It took a while, I did a lot of rehearsal and managed to fix some points.

• First of all - I did not fully understand it, but in AMOS, in order to establish a model with second-ordert latent factors, it is almost always necessary to set their impact regression weights exactly at 1. I marked it in the figure below, so that it is clear where they are supposed to appear. Then the AMOS makes it possible to calculate model estimates and model fit altogether. Thanks for the tips Holger Steinmetz and Karin Schermelleh-Engel
• The reasons for setting these regression weights to 1 are here: https://stats.stackexchange.com/questions/58999/why-set-weights-to-1-in-confirmatory-factor-analysis I trust that this will help the next person with a similar problem in understanding this aproach
• Since AMOS may incorrectly compute standardized regression weights, there are several ways to force AMOS to make "better" coefficients: https://www.youtube.com/watch?v=Vx24KFf-rAo There may be some doubts as to whether these calculations are correct, but at least the results make sense and can be interpreted somehow.
• From model like this, one can create further modifications, insert new variables, or simply add the rest of the model that is needed by the researcher and AMOS will allow you to calculate the whole thing.

It is worth returning to the point that such a model maybe does not have reasonable theoretical background composition - for example, if we assume a superior variable and correlations between lower-order components, it would be appropriate at least to somehow confirm first that they are separable, not a one latent variable... but that's not consideration of my topic.

Good luck everyone!

Hi Tomasz,

you need to fix one loading in a common factor model to 1 (regardless of whether the factor is primary or secondary) to identify the model and set the scale of the latent. You had to fix both loadings because your model is unidentified by having only to primary factors. This may work but you cannot test whether the second-order factor model is valid. Factor models (as any SEM) are not only nice descriptions of the data, they make ontological and causal claims. There is this strange tradition especially in psychology to have these "factor-only" models and articles. Import some supposed causes and/or consequences of the second-order to see whether it passes the essential reality check (that is, whether it is the second-order factor and not the primary factor that is the causal agent). Such a model has the essential implication that the correlation between a cause/consequent and both primary factor is zero once the second-order factor is controlled.

With regard to the Gaskin Video: Yes you can tinker a lot to let the model look good but it doesn't fix the problem which in this case will be either a misspec of the model or an underidentification.

All the best,

--Holger

@Tomasz you need to put regression weights on the paths from zero order latent factors to second order latent factors viz. C_SD and C_PO. Kindly put regression weights on both the paths as AMOS won't run the model when regression weights are not put when there are two zero order latent factors (two paths) preceding second order latent factor.