I have a simple model:
$A$ is hypothesized to be a predictor / regressor / explanatory / input variable
$B$ is hypothesized to be the response / regressand / explained / outcome variable
So, the relationship looks something like:
Additionally, $C$ is hypothesized to be a moderator of the relationship between $A$ and $B$.
When I run the regression by including all the variables ("enter" procedure in SPSS), none of the relationships are significant.
When I use "step-wise" regression, and let SPSS choose the variables to include, $C\times A$ has a statistically significant effect on $B$, but SPSS stops the "step-wise" regression procedure before including $A$. I suppose one can assume that $A$ doesn't have a statistically significant effect on $B$ (after the inclusion of $C\times A$ in the model).
Thus, I have a statistically significant moderation term $(C\times A)$ , but the main term $(A)$ has not been included in the model.
What can I do with such a result? I was taught that moderation effects are not valid if main effects were not included in the model. Is there a way around that admonition? Is there some way I could still employ this result profitably?