If you have

4 IVs -> 2 moderators -> 3 DVs

You could try a structural equation model (requires a decent sample though)

The first question you should ask yourself: are you really interested in a multivariate hypothesis, i.e. do you want to answer how the predictors relate to the variate that explains maximum variance across all DVs or are you interested in the effect of your IVs and moderators for each DV. If the latter one, you should not use a multivariate approach, since it does not protect familywise for alpha error and does not answer your research question.

If you really want to conduct a multivariate regression, you should give more information which statistical program you use. Otherwise it is pretty straight forward.

P.S.: if you want to include covariates, you should check if you really have to adjust for them or not, for example with a DAG.

With a structural equation model, you could include a single "unmeasured" variable with the three indicators as you your dependent variable. Moderator analysis is also relatively straightforward with SEM.

Depending on what software you are using, you might need a specialized module, such as AMOS for SPSS.

David L Morgan maybe we have a different perception of "straightforward" ;-) Unless you only have manifest variables and do path analysis, moderation in SEM with latent variables is quite complicated in my opinion. There are several product indicator approaches, as well as distribution analytic approaches. Within R there is a nice package "modsem", by now, easy to use, but the methods remain complicated imho (as compared to moderation in regression or path analysis).

Rainer Duesing I see the bigger problem here as how to deal with the multiple DVs, which is much more problematic with either regression or path analysis. In terms of the complexity of moderation, a lot depends on the nature of the moderators -- e.g., dichotomous or more complex

Dear David L Morgan ,

maybe I am missing something, but as long as you have only manifest variables in a path analysis and all of your dependent variables are predicted by the same set of variables, it should not matter if you model the residual correlations between the dependent variables or not, should it? For more complex models, with different paths from the predictor variables, I would agree that it is useful to use a multivariate regression or SEM. But as I understood the OP, he wants to predict each DV with the same set of predictors.

Please correct me, if I am missing something here. Of course, the residual correlation might be quite informative, but this should not change the parameter estimation for the predictors.

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Added:

This should be true, if you do not assume any causal / direted effect from one DV to another of course, but this seems not to be intended by the OP:

Rainer Duesing If you conduct three separate analyses on each DV, how will you test whether the coefficients for the IVs are the same? And even you have hypotheses about how the three DDVx might differ, how are you going to assess them?

Alternatively, if all the DVs are meant to measure the same underlying concept, then SEM is the way to go.

David L Morgan maybe we are talking past each other and I am not sure what you mean with your last post. Just let me explain, what I am talking about:

Imagine we have 3 correlated DVs (which maybe measure different aspects of the same area, like the OP, different forms of empathy, but which all may be relevant). We want to predict each DV with three predictors x1, x2, and x3 (interactions wont change anything, if we incorporate the same for each DV). So we could conduct three separate multiple regressions (I use R, therefore this code):

lm(Y1 ~ x1 + x2 + x2, data = data)

lm(Y2 ~ x1 + x2 + x2, data = data)

lm(Y3 ~ x1 + x2 + x2, data = data)

or conduct a multivariate multiple regression

lm(cbind(Y1, Y2, Y3) ~ x1 + x2 + x2, data = data)

or do this in lavaan, to get the residual correlations:

pathmod

Yes, I understand what it means to conduct a path analysis with three correlated DVs. So, you will have a path from each relevant IV into each DV, with correlations among the errors for the DVs, but how will you test for differences in those coefficients?

For example if, you want to know if IV #1 has a larger effect on DV #1 than on DV #2 or #3, how work you test that?

Ah, I see what you mean, now. Thanks for your clarification!

Was this a question by the OP? He asked about moderation between the predictors and not if one predictor has different coefficients for different DVs. I would agree that for such a question it would be useful to compare restricted and unrestricted models, but if this not the question in the first place, do we need SEM?