I have a logistic regression (in SAS, for reference) with continuous and categorical predictors (with reference coding), and an interaction term between one of each type (assume for now that the categorical variable in question has three response levels, reference coded to $c_1$ and $c_2$):
$logit(p) = a + (continuous terms) + (categorical terms) + b_1 (c_1 x) + b_2 (c_2 x)$
where $b_1$ and $b_2$ are the estimated coefficients from my code. From this I can obviously get an expression for the probability $p$ of my outcome. I want to estimate the average p by plugging in the means of the continuous terms and the proportions of the categorical terms. But what do I do with the interaction term(s)? Do I set $(c_i x) = mean(x)$? Or do I set it to $proportion(c_i)mean(x)$?