I would like to carry out an exploratory factor analysis on multiply imputed datasets according to the methodology by Nassiri et al.

They have created an R package for this (mifa), but unfortunately, there doesn't seem an option to dictate which variables should be used as predictors for multiple imputations and which should be used for the EFA (they are not the same in my case).

I would still like to apply their methodology manually. They first estimate the covariance matrix from the imputed sets of data using Rubin's rules, and then apply the EFA on this combined covariance matrix.

My question is: is it ok to use the correlation matrix instead of the covariance matrix? Much of the EFA reading I've come across factor analyses the correlation matrix and it's what I've used for my complete-case analysis. I wonder if there are any cases when the covariances matrix should be used, and why?

  • $\begingroup$ This may help stats.stackexchange.com/questions/53/… $\endgroup$ – Aleksejs Fomins Jun 1 '20 at 14:19
  • $\begingroup$ @AleksejsFomins Thank you! This answered my question. My variables are already z-transformed so I will use the covariance matrix. I can't seem to be able to upvote your answer :'( $\endgroup$ – Dani Jun 1 '20 at 14:39
  • $\begingroup$ Ok, I'll make an answer for you, so you can upvote :) $\endgroup$ – Aleksejs Fomins Jun 1 '20 at 15:55

Dimensionality reduction techniques (such as PCA and FA) can be computed via covariance or correlation matrices, where the latter is equivalent to z-scoring the data by each dimension prior to the calculation. The major difference between the approaches is that results for raw data (covariance) are influenced by combination of individual variance and covariance, whereas results for z-scored data (correlation) are explicitly independent of individual variability

See here for more discussion


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