Hello Amanda,

your question boils down to the question about the meaning of a "common factor".

Here is some threads that could give some background, key terms, and references.

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

https://www.researchgate.net/post/Dear_scholars_how_to_design_a_Structural_Equation_Modeling_surveys#view=5c0cdaf3c7d8ab762f591a75

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

https://www.researchgate.net/post/How_to_deal_with_Single_and_Multiple_Item_latent_variables_in_Structural_Equation_Modeling#view=5e849fe521137522f2332355

If there are question left, we can proceed from here.

All the best,

--Holger

Hello Amanda,

In addition to Holger's suggestions, let me offer my two cents' worth.

For me, the answer hinges on what use(s) you intend to make of the scores from this scale , your theory, and what evidence exists already for the distinguishability of the three subscales vs. just the overall scale.

Your CFA could, of course, evaluate: (a) a single factor model (just the one scale, with 10 indicator variables); (b) three correlated factors (the subscores you refer to); or (c) a second-order model, in which three correlated factors serve as indicators for a second-order factor. Unfortunately, given just the information in your query, I can't offer any advice as to what path here might make the most sense. Your choice should be informed by the elements mentioned above.

Good luck with your work.

Thank you Holger Steinmetz - your time and help is so appreciated!

Hello again, Amanda,

Assuming these are all observed/manifest variables, it really makes no difference. You can successfully answer questions about evidence for or against mediation effects either way. An ordinary least squares regression program/module could also be used (though model-data fit indices aren't as plentiful).

Good luck with your work.

Hello Amanda and David,

the procedure heavily depends on the true underlying causal structuring in the "scale". "Scales" are just sets of measures and it is in 99% completely unclear how the structuring is (even for "validated" scales). Why do I say "structuring" and not "dimensionality"? The reason is that dimensionality still involves the idea that the set of items is caused by underlying common factors whereas we should be openminded and at least have it within our horizon that the structuring may by a network structure. At the extreme, there may be no common factors at all involved--then no matter what factor analytical approach you take, you will fail to fit the right model.

Often, "scales" are created by means of a principal component analysis, erroneously equated with a factor analysis or deliberately reflect an aggregate construct intending to comprise an essential set of existing facets. Before you start, you have to understand these concepts and apply them to the constructs in your study and the measures that you use (never equate both).

All the best,

--Holger

Read this useful article. It describes step by step how you can analysis multidimensional constructs

Hello Abdallah,

please don't get me wrong. You recommended this paper and you find use and guidelines in it. That is fine. But please at least take into consideration that there may be some things which are critical (where I would argue blatantly wrong). If you disagree that's also fine--at least you have seen the other side of the coin (and Amanda, too).

I have only scanned through the paper and would object their presentation of the superordinate construct (SC) as the typical mis-presentation of second-order factor models. How you perceive the SC depends on the exact definition of what THE construct is all about. Wright et al. present the SC as a multidimensional construct. Whether this is true depends on what exactly the core of the construct is. There are two options

1) The overall set of dimensions (4 primary factors plus the second-order factor) is the construct. In this case, they are right--the SC is multidimensional

2) The second-order factor is the construct. In this case, they conduct the typical error of describing the SC as multidimensional (having a "domain") but that is simply wrong. A second-order factor is as one-dimensional as any other factor or variable. It is a singular, thin line one which entities vary. This can not only directly be concluded from the path diagram (where the factor is ONE factor (and that is, ONE dimension) but also from the algebraic equation which represents the graph.

For instance, the effect of IT relatedness on IT marketing strategy on page 8 can be described by

IT making strategy := ga01*IT relatedness + zeta1

which shows that IT relatedness is ONE thing (=variable). Hence, IT relatedness is a one-dimensional construct.

If you go one step further and perceive an SEM and its graph/path diagram as a reflection of a causal process (which it is and should be because arrows represent assumed effects) than IT relatedness is the cause of IT making strategy. Hence, it is a misrepresentation to speak of the four dependent variables/outcomes as "dimensions of IT relatedness"--they are its outcomes. In this regard, the primaries are not dimensions of the second-factor in the same manner as items are not dimensions of a primary factor--they are its causal reflections (like shadows being the reflections of an underlying light source).

If you, in contrast, think that the overall set of factors (case #1 above) comprises the construct than, yes, the overall SC is multidimensional. However, in this case, the difference between the superordinate construct and the aggregate construct (which is also multidimensional) is only that in the first case, you propose a specific causal structure among the dimensions--namely a second-order structure as aforementioned) whereas the aggregate constructs leaves the relationships and their reasons unspecified. They could be uncorrelated, they could comprise a causal network where facets affect each other or--again--a second order factor. Everything is in the dark.

Their further misrepresentation of the second-order factor is shockingly obvious when they say that "These resources are distinct, yet they are also interdependent. Moreover, they mutually support and reinforce each other." A model in which the primary factors mutually affect each other is a network structure and a clear alternative to the second-order factor. As argued before. The second-order factor proposes that the primaries covary BECAUSE of the common effect of the second-order factor. That is not my perception but follows from the path diagram. In this regard, the second-order factor is a common cause structure as any other one with a specific set of implications (namely, that the covariances of the primaries become zero once the common cause is held constant. Further, the second-order factor model implies not causal interactions among the primary factors nor effects of the primary factors on outcomes as the "main big thing" is the second-order factor.

I cannot say much about the rest of the paper--although I noticed their further strange path model in Figure 4 where suddenly ALL effects are formative (indicators --> primaries --> second order formative variable. It is much more reasonable (and would put the whole model on a realist basis) to have reflective indicators of the primaries and perceive the SC as an aggregate of the primaries (while this part turns if into an operationalist mode in most cases). "Operationalist mode" simply means that you create something ("adding up" ) which does not exist beyond the exact operation (again "adding up") that YOU as a researcher applied). This is often not avoidable but has costs.

So sorry, for the rant. As I said, take it, accept it or reject. Everything is ok.

All the best,

Holger