In a little regression model of mine, I estimate the following formula a a negative binomial regression type (it would hold for a Poisson regression as well):
$$ y = \beta * var1 + \gamma * var1 * binary + \delta * X + \epsilon $$ where $X$ is a matrix of control variables that are all on a discrete scale. $var1$ however is not discrete while $binary$ of course is a binary variable. The second term, $ \gamma * var1 * binary$ is dedicated to check how $var$ acts different if $binary=1$.
Now I compute marginal effects, say with the mfx
package for R
. Since count data models are GLM, the marginal effects are evaluated at some value of all the other variables (typically the mean). But I wonder whether it is meaningful to evaluate $\partial y/\partial var1$ while holding $var1 * binary$ at the mean. Or did I misunderstand the concept of average marginal effects for GLMs?