Hello!! I wish to understand whether I could conduct Exploratory Factor Analysis with binary data (correct/ incorrect). According to Bartholomew, Steele, Moustaki and Galbraith (2008) the options are either using a Pearson's product moment correlation matrix or tetrachoric matrix as the basis for EFA. Also, I should mention that I do not wish to construct parcels.
Could you please provide any references that argue for either approach? Any suggestions would be helpful.
Thanks in advance!!
IRT has shown that SEs are distorted with FAs of binary response data.
Another, unmentioned option is to use full-info response analyses via IRT to ensure adequate recovery of paramter estimates.
Hope this helps,
Matt
Hello Ionanis,
The developers of the freely available program, FACTOR, have assembled quite a list of this and related issues associated with factor analysis: http://psico.fcep.urv.es/utilitats/factor/Documentation.html
Good luck with your work!
Best regards to all the researchers for their helpful answers!!!
It depends why your data are binary. If they're binary but you believe the underlying trait is continuous (for example, if people pass or fail a training course, or at test item which reflects some continuous trait) then tetrachoric is the way to go. If it's categorical (e.g., male/female) this makes no sense. Have a look at Chapter 5 in my book "Psychological Testing".
Dear Ioannis,
as said by Colin, it strongly depends on the reason why your data are binary. If they come from a "binarisation" of an underlying continuous trait, then tetrachoric correlation is a better estimate of correlation than Pearson's (I remember a paper with some simulations supporting this statement, but at the moment I can't find it). It is worth knowing that tetrachoric correlation (just as polychoric correlation if you have more than two levels) estimates the correlation of the underlying traits, not of their discrete measures, and this can be an advantage in some cases.
Just be aware that tetrachoric and polychoric correlations, when used to estimate a correlation matrix, often result in something that is called "non positive semidefinite matrix", which is theoretically nonsensical. In other cases (e.g. when using Pearson's estimators) it should be an alert that something weird might be going on, but if you get this by tetrachoric estimators then it is less suspicious - there are some ways to force your matrix to be positive semidefinite.
Hope this helps!
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