I am running a path analysis and I have requested estimates of specific indirect effects. For one of my indirect pathways, the unstandardized estimate is significant (the 95% confidence interval does not contain zero), but the standardized estimate is NOT significant (the 95% confidence interval DOES contain zero). I obtained the standardized confidence interval from the section of output labelled "Confidence intervals of standardized total, total indirect, specific indirect, and direct effects." I was under the impression that standardized estimates are merely in a different metric than unstandardized estimates and that standardization should not change the level of significance of the estimate. Could you please advise me as to why my results differ when I look at the standardized CIs? Thank you very much for your time.
The ratio or the parameter estimate to its standard error and therefore confidence interval can differ slightly for raw and standardized coefficients. The standardized standard errors are not rescaled raw standard errors. See
Standardized Coefficients and Their Standard Errors
Thank you Dr. Muthen for your prompt response, which was very helpful. I am now curious whether you would recommend reporting the unstandardized or the standardized solution, given that they provide a different pattern of results.
I would go with the unstandardized SEs and CIs (but you can still report the standardized parameter point estimates). But I would assume that the CIs are not very different so that significance in the unstandardized case means that the CI barely excludes zero - in which case I wouldn't make a big deal out of that significance.