As mentioned in the Details section in the Margins macro documentation, the standard errors are computed using the delta method. I don't see anything odd about the standard error estimates and believe they are correctly computed.
All of the computations for predictive margins and/or marginal effects occur following the fitting of the model that you specify in the macro. That model always has an intercept unless you tell it to omit the intercept. The code earlier will show the results of the model fit in PROC GENMOD and it includes an intercept (4.2604).
I should note that there is an alternative approach to estimating the marginal effect in the range of the two variables that you mentioned. This alternative does not estimate the same quantity as I showed earlier using the average of the marginal effects computed using contrasts=. Note that after the specified model is fit, the macro uses the fitted model to compute the marginal effect at each observation in the data set and then averages them. The method shown earlier fixes the two at= variables at each observed combination in the atwhere= range to obtain the marginal effect on each observation and then their average which is shown in the results. An alternative is to compute the marginal effect for all observations without fixing the two variables (although they end up being fixed at their means if you use atmeans) and then to compute a single average marginal effect be averaging only over the observations that are in the specified range. That can be done using within= instead of at=, atwhere=, and contrasts= as shown below. You will have to decide which of these two methods is best for your situation.
%Margins(data = x.atmeansdata,
class = t7cgender t7marorder_c,
response = MAR_8,
dist = negbin,
model = t7cgender t7cnuage t7dmar_c t7marorder_c t7C_can_neg t7c_can_pos t7C_AT_EC
MAR_7 t7dmar_c*t7C_can_neg t7C_AT_EC*t7C_can_neg t7dmar_c*t7C_AT_EC t7dmar_c*t7C_AT_EC*t7C_can_neg,
effect = t7dmar_c,
within = 3<t7c_can_neg<4 and 5<t7c_at_ec<6,
options = cl atmeans )
... View more
