Hello Peter,

What, exactly, is the problem you and your student are facing? If it's that the determinant of the original inter-variable correlation matrix is small, then that's generally considered positive evidence that the data set is suitable for factoring in the first place. Remember, guidelines are just that: guidance, and not commandments.

The fact that there is apparently a reasonable (both empirically, and theoretically) factor structure suggested by the data via the EFA would be a desirable outcome, in my opinion.

I'm sure you're familiar with common methods for determining whether multicollinearity exists among a set of variables (e.g., tolerance, VIF, and so on), but common factor analysis has as its premise the notion that a set of variables can be influenced by a one or more common (latent) factors.

I wish your student the best of luck in completing the degree.

As David Morse wrote, large correlations between manifest variables are typically desirable for factor analysis as they may indicate that the variables are reliable indicators of one or more common factors. I would not recommend deleting items based on an arbitrary cutoff (e.g., correlation > .7). There are many cases in factor analysis and structural equation modeling where a correlation of .8 or so between manifest variables pertaining to the same common factor is plausible and desirable.

If you have already checked for correlations > 0.8 in absolute value and removed items with bivariate correlations > 0.7 in absolute value, but the determinant of the correlation matrix is still too low, it is possible that multicollinearity is still present in your data. Here are some additional steps you can take to try to address this issue:

It's worth noting that a low determinant of the correlation matrix does not necessarily mean that your factor analysis is invalid or unusable. However, it may indicate that there is some degree of multicollinearity present in your data, which can affect the reliability and interpretability of your factor analysis results. It's important to carefully consider the potential impact of multicollinearity on your research question and the interpretation of your results.

Dear David Morse ,

Many thanks for your answer. The "exact" problem is wanting to present a valid EFA in order to justify the extraction of certain scales from the questionnaire in such a way that it pleases the examiners in a viva. I'm not familiar with how VIF/tolerance work outside of multiple linear regression - do you need to choose a dependent variable? I would really like to get to the bottom of why this matrix demonstrates multicollinearity. I was wondering whether running a PCA on the identified scales and checking their determinants might be a way forward.

Hello Peter,

Even though you're factoring, here's how to explore VIF/tolerance, In a regression program::

Option A:

1. Creating some random variable to "act" as the DV. The only proviso is that there has to be non-zero variance for this ersatz set of scores.

2. Enter your pool of to-be-factored variables as IVs, as if specifying a regression model.

3. Be sure to request the multicollinearity statistics offered by that package.

Option B:

1. One at a time, specify each of your to-be-factored variables as the DV for a regression, with all others as IVs.

2. Run the regression. Tolerance for that variable = 1 - R-squared, and VIF is the inverse of tolerance.

3. Repeat for all other variables.

Option A is, of course, faster as it only requires a single analysis.

Thank you for your perfect answers, David Morse , but I could not catch multicollinearity in the EFA case.

Why EFA itself is not a multicollinearity solution? Because in EFA we just replace some highly correlated variables by factors?

Hello Maksim,

Factoring, and replacing individual variates as IVs with factor scores to which they contribute, _is_ one way to deal with collinearity (most often in linear models, such as regression), so long as you do not rotate the factor structure obliquely.

However, the original query for this thread was asking about the presence of multicollinearity in EFA, so that was the question to which I was responding.

Good luck with your work.

Many thanks to everyone who has provided suggestions on this thread. We are going to follow Christian Geiser 's advice to keep the bivariate limit at 0.8 and David Morse 's advice to run a MLR with a random variable as the DV and all the variables from the stabilised EFA as the IVs and check the multicollinearity statistics. If anything is detected we will remove some variables and re-run.

Just to clarify, I did not advocate for the use of any kind of "limit" or threshold. In general, I would advise against using arbitrary threshold values for just about anything related to statistics. My point was that a high correlation (e.g., .7 or .8) between observed variables that measure the same construct may not only be reasonable/plausible but is also typically desirable. A high correlation may indicate that the variables are highly reliable indicators of a common construct.

Dear Peter Samuels , I should agree that highly correlated items should be and will be removed, but not in the first steps. I mean that at the very first steps, one should stabilize the whole factor system. These highly correlated items may reflect your core ideas about measured constructs. And before removing one of them, one should check their interrelations with items from other factors. For example, one should check residuals. And question is which items should be removed first: highly correlated or items with low factor loadings or items which present in more than one factor? For these reasons may be useful any kind of Pratt's importance measures and one should use some kind of mixed EFA-CFA approach.

I would like to use Factor program by Lorenzo-Seva&Ferrando https://psico.fcep.urv.cat/utilitats/factor/index.html

But I do not use their Pre-Factor for removing items before EFA, but I consider Pre-Factor results someway. And often I try somewhere to limit bootstrapping in this program because it takes so much time.

It's always enjoyable to figure out the number of factors because the BIC, PA and Hull methods all yield different results, and one must keep in mind the criterion for determining the number of factors.