Suppose I have three measurable variables (A, B, C on figure below) and one latent (L) in my SEM model. This one latent one is a construct/dimension consisting of 5 questions from some questionnaire (Likert scales). Instead of inserting them into the model as a construct (latent variable and its five components) I would prefer to insert a questionnaire result -> that's why I would like to see if I can create one consistent dimension -> that's why I check the consistency of this dimension using PCA - principal component analysis - and Cronbach's alpha -> both PCA and Alpha indicate that this is one coherent dimension, one factor, with good reliability -> I calculate its sum and put in a finished result instead of a latent variable.
Technically, I check PCA and reliability on a slightly different sample, and the main reasons for using single variable are the following: a small sample (so the more constructs the more difficult it is to control the model); uncertainty whether the author's questionnaire works correctly; and interest in relationships between dimensions and not exploring the correctness of tools (at the SEM level).
The question is - are there any technical contraindications of such surgery? Can anyone indicate to me in the literature the reason why what I have done is not allowed?
P.S. Of course, I realize that using PLS-SEM could give more reliable results, but I'm not asking about it. :)
Hi Tomasz,
Regarding your procedure, my only concern is that with Cronbach's alpha you just check reliability of Likert scales, but not the validity, at least the factorial and convergent (AVE) ones.
Besides this, some papers like Marôco & Garcia-Marques (2006) show that "Cronbach’s α underestimates the true reliability specially when the scale’s items are heterogeneous, dichotomous, or define multi-factorial structures."
Attached I send Marôco & Garcia-Marques' (2006) paper which unfortunatelly is in Portuguese (authors are from Portugal and I couldn't find an English version).
Maybe the abstract or some reference can ilustrate what I'm saying.
Regarding your technical justification for PCA/Alpha ("interest in relationships between dimensions and not exploring the correctness of tools"), I think this is a risky approach because if your tool is not correct the relationships you have studied can be spoilled and you don't realize this.
If I had the opportunity to perform a regular SEM I'd rather instead of PCA/Alpha.
Regards.
Dear Alcides Barrichello - thank you very much for this answer. I will of course have to look for some equivalents in English, because the article you indicated is biased with language barrier for me - but I will get it somehow.
Naturally, the reasons you mentioned are roughly known to me. I understand all this, however, in the category (let's call it this) a greater probability of correct structure. What do you think?
I mean that the general correctness of the tool can be measured by many different methods and the more restrictive it is, the more likely we'll get final model that will not be biased with the effect of a bad tool. Naturally, Alpha and even different PCA variants are not as restrictive and good as CFA, but ultimately a good tool should give good results in all methods. This is not a transitive condition, i know - it just increases the chance for correctness.
However, my question does not apply to which method is better - because naturally SEM / PLS-SEM are methods for me with a higher quality model - the only question is whether assuming a slightly lower power of model I can take such an action. Actually, is it technically totally incorrect to do this?
Thank you again for the tips.
Hi Tomasz,
Your approach is not "technically" incorrect : it has been used widely before the generalization of SEM modeling.
Rather than summing (or averaging) indicators to build a composite variable, you can use a more accurate method based on factor scores. In sum, you perform a factor analysis on your construct, and save the factor scores for individuals (it's esasy on SPSS or R). Those factor scores can then be used in subsequent analysis.
You can see Devlieger & Rosseel (2017) for a detailed (and bias corrected) procedure
Alain
Article Factor Score Path Analysis: An Alternative for SEM?
Here's another reference justifyining factor score path analysis
Regards
Alain
Lu, I. R., Kwan, E., Thomas, D.R. & Cedzynski, M. (2011). Two new methods for estimating structural equation models: An illustration and a comparison with two established methods. International Journal of Research in Marketing, 28, 258–268. doi: 10.1016/j.ijresmar.2011.03.006
Hi again, Tomasz.
Considering your comment about Power ("the only question is whether assuming a slightly lower power of model I can take such an action"), I would say that your action is not technically totally incorrect.
I had used such approach in some early papers where I promoted an EFA + Regression Analysis to perform relationships among constructs I had in my model.
Nowadays, I prefer to use CFA + SEM, but what you propose is not wrong (maybe not as precise as SEM, but...).
Attached is a paper (DiStefano, Zhu, & Mîndrilă, 2009) in which the authors treat the use of factor score which in my opinion, is quite close to what your are doing (you mentined CFA and the article presents EFA, but, in essence, the proposal is similar).
Take a look and see if this can give some support to what you are doing.
Hope it helps.
Regards.
Rene Nob That's what I understand. However, at this moment it is not, as I think, an argument for incorrectnes, but only for the "loss" of some information about the model, right?
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