In the context of regression, methods for detecting collinearity are well described in the literature. In the context of exploratory factor analysis (EFA), however, I am facing a situation where I get highly unstable factor loadings and factor correlations from different boot-strapped samples (despite a sample size of more than 700), which I assume is due to multicollinearity. I am not sure how to explore its source. The common methods rely on the intercorrelation among explanatory variables (i.e., the latent factors in EFA), but the intercorrelation its-self is highly unstable.
My search for finding references on this topic was not much successful. Any explanation and/or reference on multicollinearity in EFA would be appreciated.
Thank you in advance,
Ali
Hi,
there is (to my knowledge) no such thing as colinearity in factor models. To the contrary: Highly correlating indicators should lead to a much more stable situation was those indicators would be clearly load onto the same factor.
Best
Holger
Agree very much with the previous answer.
With exploratory factor analysis you are looking for correlated variables, that you can then reduce to underlying factors.
Hi,
Actually, this is an EFA and still you have the pattern unclear, then you have to first do a Goodness-of-Fit test-Communalities. This would help you weed out the unfit items(nuisance) in the study and then you can have a clear pattern. Remember, this unfit items might not load well on any Factor Component by the time you run a Rotated Component Matrix. Therefore, you have to drop and not continue with them in your study- Whatever number of Factors you fetched in your PCA, these unfit items did not contribute a thing.
I agree that high inter-correlations between indicators in a factor model can lead to a stable factor solution. However, when the correlation between variables is extremely high, it can create problems in factor analysis, particularly when using a maximum likelihood estimation method. To address this issue, you could either remove one of the highly correlated variables or use a less sensitive method to multicollinearity, such as principal components analysis. The following article could be helpful.
Watkins, M. W. (2018). Exploratory factor analysis: A guide to best practice. Journal of Black Psychology, 44(3), 219–246. https://doi.org/10.1177/0095798418771807
Good luck,
Holger Steinmetz Brian Kelly Busari Yusuf Mohialdeen Alotumi
Thank you all,
In my situation, the indicators are not highly correlated; I think the problem is the multicollinearity among latent variables. Here is a reproducible example of what I think the problem is:
M
Dear all,
My problem was solved, but not the way I expected; I share the results here as others may also face a similar problem.
I posted the question on SEMNET, and Dr. Ed Rigdon mentioned that the inflated variance of bootstrap solutions might be due to factor swapping across samples; the first factor in one boot sample may not be the same factor in the other sample, which can lead to variance inflation.
When I performed bootstrap and reordered loading matrices, the problem was solved.
It seems that the 'psych' package does not consider the matter of factor swapping when calculating boot CIs. Not sure about the reason, but reordering loading matrices may not be straightforward when we do not have a prespecified solution. Note that in my work, I used a target rotation, so there was a prespecified solution, and I could reorder the matrices according to that structure.
Thank you.
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