= Component and marginal effects in zero-inflated regression
{title2=$E(Y)=(1-\pi)\mu$}
A logarithmic count-component contrast $b$ multiplies the susceptible mean by $e^b$, while a zero-logit contrast $g$ multiplies the structural-zero odds by $e^g$. If the baseline zero predictor is $\eta$, the marginal mean ratio is
$$
e^b\frac{1+e^{\eta}}{1+e^{\eta+g}}.
$$
Thus the count ratio alone is not a population-average effect when a covariate changes both components. With <interaction terms>, the relevant count contrast must first include the interactions for the stated reference group.
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