Hello Bram Ten Barge

what made you think this is not possible? Everything you describe checks out for me. You will find a plethora of literature on CFA, some more generic, some tailored to specific programmes such as Mplus or R.

Best of luck

Marcel

Hello Bram,

As Marcel indicates, of course you can proceed with cfa. The only decision you'll need to make is how to characterize a score on a single, 7-option, Likert-type response scale.

If you consider it as metric/interval strength, then no further adjustments are necessary. (Statisticians won't consider the scale as interval.)

If you consider it as ordinal, then you may either use sem/cfa software that allows for ordinal measures (many packages will do so), or opt for polychoric correlations (instead of Pearson correlations) as the starting point for observed relationships among the items/variables. The final option is to use IRT (item response theory), which has several options (such as the graded response model) for handling ordered response/score scales. This, too, can be a way to explore dimensionality of a set of items (though some would find this last approach more challenging).

Good luck with your work.

David Morse Marcel Grieger thanks for your answers! Sorry if my question was unclear. As David pointed out correctly, I questioned whether I could proceed with CFA due to the ordinal nature of Likert scale, which violates the interval/ratio assumption of CFA. So, it is sufficient to choose for the polychoric correlation instead of the pearson correlation? Or should I also look for substitutes for PCA and the varimax rotation I wanted to use?

Hi Bram Ten Barge

I guessed this was the issue you were driving at. All I can say in addition to David's answer is that in case you use Mplus, the programme allows you to specify categorical variables as such with CFA. Whether polychoric - funny, I have always pronounced that as "polychloric" - correlations are disadvantageous in some way exceeds my knowledge, I am afraid.

However, there is no need to use PCA and varimax rotation, neither in your case - you work within the confirmatory not exploratory framework - nor ever if I may be so bold to state that.

Best

Marcel

Marcel Grieger and for the literature I was also unclear. I meant literature about CFA and the additional steps you had to take when you have an ordinal variable, which i could not find. Indeed, as you point out correctly, there is plenty of literature on CFA :)

Everything David mentioned above is spot on. I just want to add few more details:

Run polychoric correlation --> save that correlation and covariance matrix-->feed that as your data input --> run CFA

Whether you are an R user or not, I find Revelle's psychometrics book helpful. https://personality-project.org/r/book/ (read chapter 6).

D. Eastern Kang Sim thanks for your answer! The only thing that I do not understand is the benefit of running a correlation in general. For CFA I know which items belong to what latent factor, so what is the additional benefit of running a polychoric correlation before running the CFA?

To the best of my knowledge, all structural equation modeling software (or packages) take a raw data and convert them into a matrix form prior to analysis. SPSS, for instance, uses Pearson's correlation by default. I may be wrong, but I think SAS uses Pearson by default as well.

If you run CFA/SEM without selecting correct correlation/covariance structure, your path coefficients may be off and produce misleading results. Unfortunately, some of the general statistical software (e.g. SPSS) does not provide users an option to select the correct correlation matrix. This means users are stuck with Pearson whether they like it or not. One way to bypass this potentially misleading data processing step is that you run your own correlation and covariance matrices and use those information as data input.

Moreover, simply because you know which item belongs to what latent factor does not guarantee that your factor loading would be significant. I assume you read many validation papers using CFA, and the results almost always vary by context. More modern approach of validating the latent construct is called bifactor analysis. As you adapt more modern approach, small differences can make a big difference.

In your case, however, my gut feeling is that the results you get from Pearson (default in many software) and Polychoric matrices may not be different by significant amount. This is because I view the 7-point Likert scale as continuous variable. Of course, this assumption cannot be confirmed without item-level evaluation.

In my quick Google search, this is an article I found: Article Polychoric versus Pearson correlations in Exploratory and Co...

Hope this clarified some of your questions.

D. Eastern Kang Sim thanks again for your comprehensive answer! I'm indeed using spss, so I am afraid that I can not use the polychloric correlation.. However, I do not completely understand what you mean with 'item-level evaluation'. I get that I have to confirm the assumption of continuity to use the Pearson correlation, but how can I do that?

Hello again, all,

Opting for polychoric correlations is not difficult. Here's a freely available program which offers that along with a host of nice additions and features relevant to factor analysis: https://psico.fcep.urv.cat/utilitats/factor/Download.html

Stay safe!

Thanks David for providing the link. I may use it when I teach a class next semester. :)

Bram: it has been few years since the last time I used SPSS, so I googled if there has been any update from IBM. I think SPSS still uses Pearson by default; however, there's a SPSS syntax that can compute polychoric correlation from SPSS. https://www.youtube.com/watch?v=9aJu5MIWCBU

If you are using SPSS AMOS to run CFA, you can use the polychoric correlation matrix as data input: https://youtu.be/hrLz05bRZes

If you want to learn more about item-level evaluation, you can study item response theory (David Morse mentioned this in his response above). It is often used for a scale development in psychology. SPSS does not have a built-in function for IRT, but it is a powerful technique. I use 'mirt' package in R.

D. Eastern Kang Sim David Morse It's finally all clear to me! Great to see that polychoric correlation is possible with spss in combination with using it as input for CFA. Again, thank you for your great input, it helped me a lot!

Forgive me professors, one final question. I am using the syntax file of D. Eastern Kang Sim . For the number of bootstrap samples I assume that I just have to fill in the number of my observed respondents?

Bram: your sample size won't change. Bootstrapping is a statistical procedure, and it is optional.

Hey all,

I am following the instruction video of D. Eastern Kang Sim for the CFA analysis in SPSS Amos with the polychoric correlation table. However, I get an error message when I click on the 'calculate estimates' button. In the attachment you can find my model, input and the respective error message. Could someone help me out, because I don't know what the problem is.

Thanks in advance!

Bram