Adding a covariate to EFA, and get traditional EFA results

[Kristín Hulda Kristófersdóttir]

Hi everyone!

I'm conducting EFA using lavaan. The problem is that I need to add a covariate to the model, which is easy if I define the model myself and use cfa(). However, I have not found a way to do that using efa(). I would prefer to use efa() because the summary output is much more like the traditional EFA output one would get from other packages. I need to be able to get, for example, the communalities, how much each factor explains etc.

Maybe I'm missing something obvious. Hopefully someone can give me some pointers :)

Thanks!

[Daniel Morillo Cuadrado]

I understand that what you need is to add an observable exogenous variable as a covariate that predicts one or more latent variables, did I get it right?

If that is the case, there are a few things that possibly need to be sorted out first.

• In an EFA you don't know for sure how many latent variables you have in advance, nor how to interpret them. If you wanted to add a covariate, you would probably need to "predict all of them at a time" (and then test whether those regression weights are statistically significant). As far as I know, this is not common in EFA and I don't think it can be done in any available software. It might be possible, but at least you would need to specify the number of factors you expect to find (which possibly undermines the purpose of the EFA itself, partially at least).
• In a CFA you have a clear idea of what factors you are modelling, how many, and what each of them represents, so it makes better sense to add covariates to predict one or more, and you can easily do it as you already know.
• In any case, none of the previous models with covariates added should be understood as a factor-analytic model, as I understand it, but as a Structural Equation Model in the more general sense. The latter case (the CFA) resembles what is usually referred to as a MIMIC model. In the case of the EFA, as I said above, I don't think there is such a thing in the literature, but if there is, it should be probably understood as an "Exploratory SEM" (ESEM), although I think this term is usually reserved to cases where the non-exploratory part of the model only implies correlations among the unique variances of the indicators.
• If your concern is how the results are output, you should be able to obtain all of those indicators from the CFA model as well. It may look less familiar and/or require more work, but it is ultimately possible to get them. To my understanding, the criterion for choosing EFA over CFA should be that you do not have a clear theoretical understanding of what is the internal structure representing your data.

I'm sorry that I can't be more helpful. I hope this helps you gain a clearer insight into the problem, in any case.

Best,

Daniel

--

Daniel Morillo, Ph.D.

GitHub | ORCID

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