Hello Osama,

your question is not quite clear. If you mean whether you can incorporate the second-order factor in a structure of antecedents, then yes of course. Your factor is statistically identified. Whether is a reasonable and correct representation of the data is a different question. What's the model chi-square? I would have some doubts about the primary factor model as you incorporated two quite substantial error covariances. In addition, giving a latent variable a name that includes a plural (e.g., skillS) potentially signals a problematic theoretical underpinning of the factor as a factor is a single entity and your set of indicators looks quite heterogeneous.

HTH

--Holger

Holger Steinmetz

Hello,

Dear. Prof. Holger,

This diagram is just an example. The model of my study consists of 4 latent factors = skills, knowledge, attitude, awareness. Theoretically, these dimensions estimate one common factor called intercultural competence (developed by Fantini). For me, it is easy to build second-order CFA (4 latent factors in the first level and one general factor in the second level). Therefore, the model will look like as in the picture (Higher-order CFA). The next step is to make SEM.

What I want to know is: to build an SEM model (which is built through second-order CFA + path diagram = SEM). Is it possible? in other words, to consider the common or general factor (intercultural competence ) as the dependent variable and its dimensions as an independent variable in SEM.

Best regards

@Osama Yes second order latent factor(s) can be taken into a SEM model to predict endogenous variable(s). But, here, I see a problem in your CFA model. You have drawn reflective path from Medical Knowledge (latent variable) to OCSE Hearing Test (an observed variable from other latent factor. And similarly for other latent factors as well, you've done the same. This might be the reason for low factor loadings and cause poor fit indices. You should fix this before going for SEM.

Hello Osama,

as I said, technically, you can embed the second-order factor in any structure you propose. However, you said a strange thing:

"in other words, to consider the common or general factor (intercultural competence ) as the dependent variable and its dimensions as an independent variable in SEM"

The dimensions of a second-order factor (SOF) are *consequences* of the SOF--not independent variables. Or do you mean that there are one or several variables (not yet in your path diagram) on which the primary factors (e.g., "procedural skills") are supposed to have an effect? It is hard to belief how this variable (let's call it Y) would be dependent on the primary factors and a cause of the second-order factor....In such a case, Y would be a mediator by which the primary factor(s) cause the SOF which runs against the main premise of the whole SOF structure (and would imply a loop which cannot be estimated without either longitudinal data or instrumental variables).

Hence, such a model would not be reasonable and technically not possible.

But perhaps I have misunderstood. We could spare some time if you draw exactly the model that you have in mind. A great tool is dagitty.net in which you can draw a path diagram and "publish it" (what means that you simply get a link that you can include here.

Holger

Holger Steinmetz

Dear Prof. Holger,

I have drawn the model as shown in pictures. one for second-order CFA and the next one for SEM. This is my inquiry. I did not see SEM having a general factor like that. However, I want to know if it is possible technically.

Best Regards

Imran Anwar

Dear Imran,

This picture is just an example. You are right. I avoided that in the model of my study. Thank you for the answer.

Best Regards,

Hi again,

the intercultural competence factor can only be identified by its common causes on the four primary factors (PF). Hence, this not the case in your second graph.

Apart from that, this graph represents a completely different causal structure compared to your SOF model. Here I created a different arrangement of your second graph which indicates the problem more clearly

http://dagitty.net/mlvP97w

As you see, this model would propose that skills, knowledge, and attitude have no causal relationship at all with intercultural competence nor with awareness and awareness has an effect on intercultural competence which is a completely different claim than the one inherent in your first graph (where intercultural competence is the cause of awareness).

HTH

Holger

Holger Steinmetz

Dear Prof. Holger,

So, just to be sure completely, in your diagram, you did not draw the items or observed variables. But, as I understand and imagine, skills, knowledge, attitude, and awareness have observed variables except for the general factor (no items) because it is common and because the general factor as a dependent variable is influenced by all these observed and unobserved factors.

Yes, I left out the indicators to show the differences in the structure among the factors.

And no, the general factor is not influenced BY the observed and unobserved variables/factors--it is the presumed CAUSE of these variables. Simply take a look on your own path diagram and especially the direction of the errors.

All the best,

Holger