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Using lavaan, for a simple CFA or SEM with measurement tools, you can use parameterEstimates(fit, standardized=TRUE) to get the standardized factor loadings for the LV, however, the SE and p-values produced for each of the loading are still for the unstandardized estimates (this is also noted in the documentation of lavaan).

If you use standardizedSolution(fit) then you will get standardized SE and p-values.

My questions:

  1. I understand you can report both standardized and unstandardized estimates, but do you also report both versions of SE and p-values?
  2. What happens/what does it mean when the two versions of p-values differ (i.e. significant when standardized, n.s. when unstandardized?)
  3. I see different examples in papers and books, some show the p-values of individual loading (or use symbols with the estimates on the paths), but some don't. What's best practice?
  4. Related to 3. do the p-values of the factor loadings matter? or as long as the underlying theory is sound and the overall fit is not too bad, it doesn't matter?
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  • $\begingroup$ Unstandardized. $\endgroup$ – Jeremy Miles Apr 5 '19 at 20:58

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