When SPSS produces output associated with exploratory factor analyses (EFAs), that output usually includes parallel lists of communalities, the first list for initial communalities and the second list for extraction communalities.
Presenters on YouTube, as well as authors of books and journal articles about EFA, either fail to indicate which of these communalities should be reported when EFAs are written up (they simply skip over the "issue"), or they give contradictory advice.
Can anyone indicate which set of communalities should be reported, and preferably why, please?
I believe the communalities from the initial extraction are considered. You can probably find more on this in Andyfield's Discovering Statistics with SPSS (2007).
Siddharth Garg, thanks, again, for your suggestion. I don't have a copy of any of Andy Field's books on hand - though I've used them in the past. However, I've looked at his YouTube presentation about factor analysis:
(https://www.youtube.com/watch?v=UWP9OEoaNnE)
and he skips quickly past communalities - as do most YouTube presenters.
I have had a careful look through six of the books specifically about SPSS on my own bookshelves, and could find nothing really helpful. Most of them, within their chapters about factor analysis, actually deal solely with principal components analysis (not EFA), so the issue of initial versus extraction communalities doesn't arise because all of the initial communalities are 1.
The same "problem" occurs in a high proportion of the YouTube demonstrations about factor analysis: Despite purporting to be about factor analysis, most are about principal components analyses - and, as a result, they don't address the issue that I have raised.
So, despite recommendations by people such as Hair et al. (2014 - ref below) that communalities provide valuable advice about how satisfactory an EFA is, I am still at a loss to know which of the communalities to report: the initial ones, or the extracted ones.
I am inclined to report the extraction communalities because they are based on the extracted factors, but I'm not confident about my line of argument - which is why I'm seeking advice.
Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2014). Exploratory factor analysis. In J. F. Hair Jr., W. C. Black, B. J. Babin, & R. E. Anderson (Eds.), Multivariate data analysis (pp. 89–149). Harlow, UK: Pearson.
Hello,
I checked my copy of "Discovering Statistics with R" and did not find an exact mention of which communalities to report, but based on what's in the book, I am inclined to believe that the output produced by SPSS (the communalities table) is derived from squared multiple correlation through factor analysis. I am attaching a .txt file containing an excerpt of that topic to this message.
Perhaps the best solution is to email Andy Field or other perceived experts in the area of psychometrics, and ask them for help. It may help move things faster then waiting for others to reply on a RG discussion thread.
Siddharth Garg, thank you for following up on this. Actually, I'd emailed three "experts" about this (I didn't think to contact Andy Field) and only one has responded so far. He's certainly willing to help, but needed a bit of time to think about the issue and is burdened with work at the moment as well as going down with the flu.
In the last day, I've been reading the books on my shelves, looking carefully at sites on the web, and examining the SPSS output relating to different samples' data that we've been working with, and I've come to the conclusion that the extraction communalities are the ones to report because they relate to the specific factor model that is being "proposed".
One problem that I was encountering was that we were often not getting those (extraction) communalities from SPSS, so it was an issue if they were the ones that needed to be reported. I've discovered, however, that it's important NOT to disengage the "Unrotated solution" option in the Display box within the Extraction field in SPSS. For some reason, disengaging that option ends up without a list of extraction communalities being produced.
Thanks, again, for walking on this journey with me. With a bit of luck our experience might be of use to other researchers who end up on this site.
No problem. Actually, your doubt made me realize something. We often rush into research and statistics without fully understanding the intricacies of the method for example, until recently I believed that Likert items and Likert scales are the same, and that data produced from them is ordinal (ordinal as the level in Stevenson's levels of measurement) but we use linear regression and other methods for interval/ratio data. I never understood why, until I read the paper by Carifio and Perla (2007) on the topic. The paper is free to download from RG, if you are interested:
Article Ten Common Misunderstandings, Misconceptions, Persistent Myt...
Siddharth Garg, I share your view about how we often engage in stats without fully understanding them. I certainly have a ceiling with regard to my own stats knowledge, but too often I'm concerned at the blatantly low level of understanding of stats that is exhibited in publications.
The Carifio and Perla article is one of my favourites. I came across it about 3 years ago, and read it with delight. They know how to mix authoritative ideas with palatability. In particular, I like them referring to such things as "laundry list" and "fuzzy jumble" analyses. Those kinds of analyses crop up far too often in publications.
Hello Robert,
I'd prefer extraction communalities over initial communality estimates, and here's why. The classic "initial" estimate of communality was (and still is, for a number of factoring programs) squared multiple correlation (R-squared) for the variable, found by using that variable as a DV and all the other variables as IVs in a regression model.
The reason that this might be less preferable than a final/extraction estimate is, it presumes that all of the variance in the other variables is common. Sums of squared loadings is a better indication, IMO, of what portion of variance associated with a specific variable is shared in common with the (final) factor model. This is one reason that the two sets of communality estimates typically differ, with final/extraction values typically being lower in value.
I agree that initial estimates may be helpful in deciding whether a data/variable set is suitable for factoring in the first place, along with other common indicators, such as measure of sampling adequacy (MSA) and Bartlett's test for whether the correlation matrix is an identity matrix.
Good luck with your work!
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