Is it "moderator" and "independent variable (predictor)" interchangeable?

Question

I'm reading the answer to this question: "Moderation" versus "interaction"?

The first answer is

"The way to think about what an interaction is, is that if you were to explain your findings to someone you would use the word 'depends'. I will make up a story using your variables (I have no way of knowing if this is accurate or even plausible): Lets say someone asks you, "if people research a product, do they purchase it?" You might respond, "Well, it depends. For men, if they research a product, they typically end up buying one, but women enjoy looking at and thinking about products for its own sake; often, a woman will research a product, but have no intention of buying it. So, the relationship between researching a product and buying that product depends on sex." In this story, there is an interaction between product research and sex, or sex moderates the relationship between research and purchasing. (Again, I don't know if this story is remotely correct, and I hope no one is offended by it. I only use men and women because that's in the question. I don't mean to push any stereotypes.)"

I'm wondering whether the moderator and predictor are interchangeable? Can we say the search moderates the relationship between sex and purchasing?

If they are interchangeable, I'm very confused about the picture like this (using the software WarpPLS):

(Source: http://www.icommercecentral.com/open-access/the-moderating-role-of-risk-security-and-trust-applied-to-thetam-model-in-the-offer-of-banking-financial-services-in-canada.php?aid=37979) Why in this picture, they put Risk as moderator to that two arrows? Why not the other way around? Is that marketing research is more about making up stories rather than "show me the data"?

Answer 1

I'm wondering whether the moderator and predictor are interchangeable?

The math beyond moderation is a simple interaction: y ~ x1 + x2 + x1*x2. That means, mathematically, the predictor (IV) and moderator (M) can be seen as mathematically interchangeable. A lot of times, people rely on theory to tell what the primary variable of interest is (IV) and the moderator that the relationship between the IV and DV depends on. When I analyze interactions in my work, I probe the interactions in both ways. First, I look as if x1 is the IV and x2 is the moderator; then, I look as if x2 is the IV and x1 is the moderator.

But because the interaction term is simply multiplication, they are mathematically the same.

Why in this picture, they put Risk as moderator to that two arrows? Why not the other way around?

They did not do it the other way around because of their theoretical knowledge. They know that ease of use increases perceived usefulness and attitudes toward using, which in turn increase intention to use.

They seem to be looking at: Well, what about risk? Where does attitudes about risk come in? They show that the relationship between the mediators perceived use and attitudes toward using) depend on risk.

Is that marketing research is more about making up stories rather than "show me the data"?

This is a loaded question, but one that is very good to ask. Often these "path models" imply that there is some causal effect going on. However, they are often done in cross-sectional data. That means that there are other ways to arrange these variables that might yield similar model fit.

Here lies the value of replication: If someone can show that this model holds with different participants in a different situation and/or using slightly different methods that represent the same hypothetical constructs, than it adds to their argument.

It would be even better if they, in a series of experiments, manipulated the independent variables and/or moderators of interest to see if the relationships hold.

Answer 2

Moderation is interaction. In the answer you quoted, not only does sex moderate the relationship between research and purchasing, but research moderates the relationship between sex and purchasing.

The diagram appears to not be one of moderation but mediation.