Standard errors from exploratory factor analysis

[Matt Nobles]

Greetings,

Are there statistical theoretical reasons why Stata's implementation of common factor analysis (using the factor command) does not produce standard error estimates for the factor loadings? I note that other packages (Mplus and SAS) do support SEs for EFA. Also, multiple articles discuss the conceptual and practical utility of SEs for EFA estimates:

Zhang, G. (2014). Estimating standard errors in exploratory factor analysis. Multivariate Behavioral Research, 49(4), 339-353.

I have searched variously on this forum, the Stata FAQ documents, and product reference manuals and I can't seem to find any substantive discussion of either (a) a reason why Stata doesn't report these estimates using any potentially available technique, nor (b) any demonstrable workaround, other than estimation of the same models with another product. Have I missed the crucial conceptual explanation and/or Stata-based alternative?

Thanks to all for your consideration! [Edit: seeking SEs for factor loadings]

[Joseph Coveney]

. . . why Stata's implementation of common factor analysis (using the factor command) does not produce standard error estimates for the factor loadings?

I suspect that it's because the command is somewhat dated and might have been adopted from a prior user-written command that didn't compute them.

. . . I can't seem to find any substantive discussion of either (a) a reason why Stata doesn't report these estimates using any potentially available technique

There doesn't seem to have been much call for such capabilities over the years at least from what I've seen on the List here. If there were, StataCorp might have been responsive. The few posts on the List's predecessor inquired into bootstrapping (which if you're interested in standard errors of factor loadings is frankly problematic with factor without writing a wrapper program).

In my (admittedly somewhat limited) usage of EFA, I haven't been bothered by the absence of standard errors for the factor loadings, but rather have tended to look at the patterns in the rotated factor structure in more of a big-picture manner, relying on thresholds to blank out weak loadings to reduce clutter. It is exploratory factor analysis after all.

, nor (b) any demonstrable workaround, other than estimation of the same models with another product. Have I missed the crucial conceptual explanation and/or Stata-based alternative?

Again, you can try bootstrapping with the caveat given in the command's help file, or you can try the so-called EFA within a CFA framework and get standard errors etc. for the factor loadings directly using Stata's newer sem command by the technique shown on this Web page.