Possible Duplicate:
Including the interaction but not the main effects in a model

I'm studying logistic regression now. And I have a question:

Suppose I have a logistic regression model as below:

$$y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3(x_1 x_2)$$

$\beta_0$ is the "constant" coeffficient (I wonder if that is a correct name), $\beta_1$ is the coefficient for $x_1$, $\beta_2$ for $x_2$, and $\beta_3$ is the coefficient for the interaction term $x_1 x_2$.

During the variable selection processing, is it appropriate to include $x_2$ as an interaction term only, but not the main effect? I think this imply that $x_2$ itself has no effect on the outcome, but has effect when interacting with $x_1$. I wonder this kind of partial variable selection is an appropriate way to do modelling.


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  • $\begingroup$ Good catch, @rolando. If this question were about how to assess interaction in logistic regression it should stand on its own, but it's not: it's really a general question about interactions in regression. As a check, I notice the replies and comments here would be appropriate in the duplicate question as well. I think it's best to merge the two threads. $\endgroup$ – whuber Jan 10 '12 at 14:02