In a causal model (such as multiple IVs and single DV) with presence of a mediator or moderator, do we have to consider such mediator or moderator when assessing the parametric assumptions or do we have ignore them and consider only the IV/s and DV in the model?
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To summarize, when testing parametric assumptions, you should primarily consider the IV and DV. Assess the normality, linearity, homoscedasticity, and other assumptions related to these variables. Once you have established that your data meets the necessary assumptions for these variables, you can proceed with mediation analysis, which involves examining the mediating effect of the mediator.
In the mediation analysis itself, you will assess the relationships among all three variables (IV, mediator, DV), but the initial assessment of parametric assumptions is focused on the IV and DV as they relate to the primary research question.
If your moderator/mediator is strongly theoretically defined, then ignoring it in the analysis will lead to faulty conclusions as the effect can be the opposite of what it would be if the mediator was considered.
Since you are going to involve a third variable that will eventually impact your results, you need to take that third variable into account and check for normality and other assumptions before you carry out your final analysis. However, while analysing the IV and DV, if the data is not found to be normally distributed, then a mediator or moderator is less likely to help ensure normality. In such a scenario, you could simply opt for non-parametric tests.
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