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?