I am trying to finalize my model and I am somehow biased that my independent variables are also moderators. However, if I only present them as moderators, I cannot get a good model fit. On the other hand, if I make a path from the IVs to the DVs and to the relationship they are moderating, I get a good model fit. According to what I read, a variable can only have one role in a relationship. I am very much confused. Pls help.
Moderation is just another name for an interaction effect that involves two independent variables.
A variable can serve as both an independent variable (IV) and a moderator in the same model, as long as the roles are conceptually and statistically justified. The key is understanding how the variable functions:
• If a variable directly affects a dependent variable (DV), it’s an IV.
• If it changes the strength or direction of the relationship between another IV and the DV, it’s a moderator.
I'm not quite sure of the question but ... the simplest moderation/interaction model is:
Y = b0 + b1X1 + b2X2 + b3X3
where X3 = X1 x X2 (i.e., is the product X1X2 of the variables X1 and X2).
X3 (or equivalently X1X2) is the interaction effect and its coefficient is the test of the interaction effect.
Classically in statistics predictors X1, X2 and X3 all need to be in the model for X3 to be a test of the interaction effect. (In my view none of these are necessary IVs as that terminology is restricted to experimental designs - so predictors is a better term*) If X1 or X2 is omitted then X3 will predict variation in Y that would normally be attributable to X1 or X2. So many would argue that X3 should never be included in the model without X1 and X2. This is known in statistics as the marginality principle.
As as an aside: Many people advocate entering X1 and X2 prior to computing X3 in order to aid interpretation of the coefficients. Interestingly however the test of X3 works out the same whether X1 and X2 are centred in this way or not.
Finally David L Morgan correctly says that a mediation is just an interaction model. However, in mediation it's conventional to designate one of X1 and X2 as a moderator and the other as the focal variable. This is arbitrary (from a mathematical point of view) but is usually selected based on context and some people argue implies you are making a causal claim when you do this (I don't think that's necessarily true in the strong sense). It's also common to refer to interactions with at least one continuous predictor as moderation.
* Software such as SPSS sometimes incorrectly uses terms like IV in this context. I'm not sure if this is the origin of the error but it probably helped spread it.
Yes, in SEM it is methodologically acceptable for a variable to serve as both an independent variable and a moderator, as long as the roles are conceptually and statistically justified. SEM allows for complex models with multiple roles, and what matters is clarity in how each path is defined and interpreted. For instance, if your IV has a direct effect on the DV and also moderates another relationship, you can model both—just ensure this dual role is theoretically sound and clearly explained.
A poor model fit when modeling only moderation could indicate omitted direct effects, which SEM is sensitive to. So your decision to include both paths may be empirically and theoretically correct. Just avoid redundancy or multicollinearity, and clarify in your discussion why the variable holds dual roles. Several published SEM studies have taken similar approaches when justified by theory.
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