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I'm running a project on survey data where I have a bunch of very similar operationalizations of my DV (four different indices of my DV). Let's call it support for X behavior. All of them are normalized via min max normalization (if that's relevant). Because I only have so much space in a paper, I've been told it may be best combine all of the items into a composite mean index (and report analyses for each individual index in the appendix). How do I justify this?

The alpha for the composite is very high (0.93). The average interitem correlation is about .60 (ranges from about .40 to about .85). I've ran a one factor CFA and it wasn't supported. So, I've ran PCA test. The scree plot definitely suggests one dominant factor (elbow method) and it's about 60% PVE. Then, I went to an EFA test (using various extraction methods that don't assume normality because the data has an overall left skew). Across all models I've ran, the unrotated factor analysis suggsest one factor (with about 80% PVE). But when I ran it rotated (promax and varimax), the PVE splits across three factors and then items load differently across those factors. I've read that rotation makes it more interpetable and it's up to the researcher, but I'm not sure what's the most appropriate. I've reported the main analyses across the individual items. Should I just go with PCA? Or the unrotated test? What's justfiable?

This other stack overflow answer page suggests that reporting an unrotated EFA is fine. I'm looking at the g-factor, I guess. But how would that be justifiable and should it be reported? I'd like to be transparent.

TL;DR: Wanting to justify a composite scale of different operationalizations of a DV. PCA and unrotated EFAs support one factor, rotated EFA does not. What's the best course of action?

tank12758
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    Welcome to CV. First, I think this is too many different analyses already done. You should decide on what you are doing before you do it. CFA, EFA and PCA serve different purposes. Second, the bit about rotated vs. unrotated FA seems very odd. The first factor should be the same, whether you choose to rotate or not, because it is the other factors that are rotated. – Peter Flom Nov 21 '23 at 10:56
  • Hi Peter, thank you for your reply. I'm consistently getting a different PVE and factor loadings when I rotate, regardless if it's Stata or R, type of factor extraction, or type of rotation. This comment page observes the same thing: [link] (https://stats.stackexchange.com/questions/488336/why-is-factor-rotation-always-recommended-though-it-obscures-general-factors). – tank12758 Nov 22 '23 at 04:39
  • FWIW, if these 4 indices are considered to measure the same thing, and they have a Cronbach's alpha of .93, it's standard procedure in many fields to just average the items without conducting any further explorations such as FA or PCA. I might flip the question and ask why you think you shouldn't make the composite? – Sointu Nov 22 '23 at 07:58
  • From my understanding, the PVE of the first factor should not vary. – Peter Flom Nov 22 '23 at 10:21

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