If multivariate normality( I assume both DVs are normal is how you know?) is met the variables should be fine. The x's are measured without error in the model assumptions so nP there.You can use bootstrap for almost anything. I would recommend searching on Brad Efron Bootstrap for full details. If the x's are measured with a "signicant" error you might consider errors in variables models which most people ignore whether needed or not. Best wishes, D. Booth

David Eugene Booth's recommendations are certainly on target. To give me further clarification, I also wonder, more specifically, if your intent is to bootstrap the "a*b" indirect term? I suspect so. You may intend to use one of Hayes' bootstrap macros. From that, a nice rendering of a bootstrapped CI, as well as the normal based Sobel test is rendered; so you would have both the test with normality assumed, and without. The difference is often interesting. As the problem becomes more complex, a SEM approach may become more profitable.

The beauty of the bootstrap is that the only distributional assumption you are making is that the sample at hand is distributed as is the population to which you wish to infer. Although this may not be the case, if not, my judgement is that inference itself should be off limits. The bootstrap is explicitly for situations in which you are not able to make parametric assumptions.

My best on your research,

John

David Eugene Booth and John Morris thank you very much..

histograms for DVs seem normal.

The AMOS test of normality results says Multivariate kurtosis c.r = 4.32

Disclaimer: I profess no expertise in SEM. But surely, any normality assumptions must apply to the errors rather than to the outcome variable(s). See this short note, for example:

• https://curranbauer.org/can-i-estimate-an-sem-if-the-sample-data-are-not-normally-distributed/

HTH.

Bruce Weaver is SEM not just another regression model with more terms using errors in variables estimation?. SEM was originally done with regression software as was path analysis in its day. There is a lot of similarity here. eg google sewall wright and path analysis history. Further google moderation and see that is exactly what R A Fisher called interaction on Factorial experiments. Now since regression models have only the residual distribution on the RHS and the DV distribution on LHS one can say something about one from the other. Here the claim was that theDVs are normal which implies that of the residuals. I admit histograms alone are not the best way to decide. However Sorry for my terse writing. Best wishes, David Booth BTW errors in variables models often model the errors in Xs as normal.

you might want to look at my comments on dealing with moderation as a regression effect, in other of these questions.

SEM software combines these things into a fairly complicated pakage. that once mastered is fairly easy to use to do all of this at once. I admit I have oversimplified for example soime sort of errors in variables estimation is often used in SEM. For greater detail, see also: https://www.google.com/search?source=hp&ei=5SDMXZfqC8O7tgWChqy4Dg&q=difference+between+structural+equation+modeling+and+regression&oq=Structural+equation+models+and+regressio&gs_l=psy-ab.1.6.0i22i30l10.4401.36069..49104...0.0..0.169.4248.23j17......0....1..gws-wiz.......0j0i131j0i333j0i22i10i30.Ld3OYLoJm5s

Again I apologize for terseness and oversimplification..