Understand interaction effect that becomes insignificant when controling for additional variable

Question

I am struggeling with interpreting the following scenario and was hoping that some of you could help me.

I calculated a moderated regression with PROCESS to study the effect of Product type (product 0 and product 1) and time of purchase (time 0 and time 1) on the intention to buy the product. Product type is positive and significant. Time of purchase is negativ and insignificant. The interaction is positiv and significant.

Looking at the interaction reveals that, for product 0, purchase intention is significantly higher at time 0 compared to time 1, whereas the reverse is true for product 1.

The thing is, if I control for the perceived product benefits (which is a significant predictor), only the effect of product type remains significant. How can this be interpreted? I am wondering, because the described differences in the product and time of purchase conditions obviosuly are still significant. In a statistical sense, does that mean that perceived benefits explain a part of the variance of the DV, which was previously attributed to the interaction?

Answer 1

The key is to not think so much about statistical significance and, instead, think about what the model means.

When you have an interaction that is large enough to matter, then you need to include the main effects that go into that interaction, with very rare exceptions that I won't go into now.

A model with interactions but without the main effects will, in pretty much all cases, have very strange interpretations.

You already answer your own question:

Looking at the interaction reveals that, for product 0, purchase intention is significantly higher at time 0 compared to time 1, whereas the reverse is true for product 1.

That's the interpretation.