When researchers create wealth indexes, it seems that standard practice involves using a varimax rotation of the data within a series of principal component analyses. This seems anomalous because the variables under consideration are usually claimed to be correlated with each other - even strongly so according to some researchers. I have trouble seeing why variables that are regarded as correlated would be subjected to an orthogonal rotation. Wouldn't it be more consonant to use an oblique rotation?
Hello Robert,
What's the old joke: How do you get 13 different opinions? Ask 12 economists for a recommendation.
Unless the research aim was to reconstruct manifest variables into independent linear composites, I would agree with you that oblique rotation makes more sense (as well, unless one was confident that the manifest variables were error-free and non-specific, common factor analysis would be preferable to PCA). If the inter-component/inter-factor correlations were judged to be negligible, then one could argue for the choice of orthogonal rotations.
Now, you can await the other 12 opinions!
David Morse, thanks for diving in, and with some humour to boot. A bit of humour is sometimes necessary . . .
I'll do some pondering about what you've written, but right now I'll volunteer that there is quite a lot about wealth indexes - not only the method of rotation - that troubles me, particularly given that I have done some reading and am working with "real" data collected by a colleague.
In almost all cases, PCA rather than EFA is used (is that primarily because PCA is the default in SPSS and researchers simply do what others have done before them?);
the analyses use dichotomised data (based on a question such as: Does the household have this characteristic, or doesn't it?), which surely is a shaky foundation (i.e., a foundation of dichotomised data) on which to conduct either PCA or EFA;
the interitem correlations seem to struggle to get much higher than .30 (is that a function of the items being dichotomised?);
the % of variance accounted for in the first component/factor seems to be consistently less than 20% (never much higher), both in my experience and according to the literature; and
only the first component/factor is usually taken into account when constructing the index, despite the prospect that the second and subsequent components/ factors might have something to "offer".
Something that your answer tapped into is that, despite the claim that the items would/should be correlated with each other, in the data I'm currently working with, the interfactor correlation is down at .15.
Given some of the above, using a varimax rotation seems justified. But why, then, do some researchers claim that the variables used in a wealth index should be, or inevitably are, (strongly) correlated with each other?
I think I have other concerns, but that'll do pro tem.
Thanks for walking some of the road with me on this. It's reassuring to know I'm not alone.
IMO, Preacher & MacCallum (2003) do a great job of discussing the relevant issues.
http://quantpsy.org/pubs/preacher_maccallum_2003.pdf
And yes, I think one reason the "little jiffy" method of PCA followed by Varimax rotation is so frequently used is that this is the default in SPSS and in SAS, IIRC.
Bruce Weaver, thanks for reminding me of this article. It's one of my favourites (I have a heavily annotated/highlighted copy), along with the Fabrigar et al. article (also heavily annotated and highlighted). I'll go back to it to see what both of those articles might have to offer in this context.
I appreciate what else you've written.
Hello and politeness
Dear Robert Trevethan
Do not use reliability analyzes such as
Inter-rater Reliability
Intraclass Correlation Coefficient
Not a good solution?
Abolfazl Ghoodjani, thanks for trying to help. Unfortunately, I'm not sure what you mean - whether you are recommending that I not use, or should use, stats such as interrater reliability and ICC. Anyway, I'm pretty sure that neither of those avenues would be appropriate for addressing my concerns when researchers create a wealth index.
Thanks, again, for trying to help. Please feel free to get back and elaborate on your suggestions if I have misunderstood you.
Yes, this means that these analyzes can also be a good solution.
Of course, this is my idea.
With respect
Abolfazl Ghoodjani, again, thanks for trying to help. Unfortunately, I think those stats wouldn't address the original issue about why orthogonal rotations are used when there is an underlying assumption that the variables in question are correlated with each other.
What you have suggested might be useful when determining how household characteristics should be dichotomised - but that's a different matter.
Thanks, again.
Yes, thank you, dear Robert Trevethan
It is clear that I am at the beginning of the learning path.
Thank you very much for your kindness and response
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