Like the OUTPUT statement that I suggested earlier, PLM's SCORE statement will give you predictions for specified gender and age (note that you can use the ILINK option in PLM to get the predictions on the mean scale instead of on the linear predictor scale). But, as I mentioned, if you want predictions for specified levels of age without specifying gender (essentially averaging over genders as determined by the coefficients specified), then the ESTIMATE statement approach for doing an LS-mean-like calculation is helpful. ... View more

If you want the predicted mean for any given age in a given gender, that is in your OUTPUT OUT= data set.  Just find the observation with the given age and gender.  If what you want is a predicted mean for age averaged over the genders, then this would be something the LSMEANS statement would do for you if age were a CLASS (categorical) variable in the model.  Since it's not, you can use the ESTIMATE statement to compute an estimate similar to an LS-mean.  For example, assuming there are two genders and you want to treat them as having equal proportions in the population, then this statement would estimate the mean for age=20:   estimate 'age=20' intercept 1 gender .5 .5 age 20; ... View more

That parameter by itself is just a log odds ratio for the effect of a unit increase of the sanc_PY predictor. That has nothing to do with a "difference in difference" analysis which involves two binary predictors and looks at the effect of changing the level of the first predictor while at one level of the second predictor (the first difference) compared to the effect of changing the level of first predictor while at the other level of the second predictor (the second difference). The difference of those two differences is the interaction parameter of the two predictors. There is no interaction in your model. ... View more

The interaction parameter in a two-way logistic model with binary variables estimates the difference in difference of log odds. (For an ordinary regression model, it estimates the difference in difference of means). If you want to estimate the difference in difference of probabilities, then you need to apply the inverse of the logit link to obtain each probability. This can be done with either the NLEstimate macro or using the ESTIMATE statement in PROC NLMIXED.   For example, if A and B are both binary with values 1 and 2, and Y is binary with values 0 and 1, the PROC LOGISTIC statements below fit the logistic model with interaction. The interaction parameter estimates the difference in difference of log odds. The MEANS, TRANSPOSE, and DATA steps use the saved estimated probabilities and log odds (xbeta) to compute the difference in difference of probabilities and of log odds. NLMIXED then refits the logistic model. The first ESTIMATE statement shows that the difference in difference of log odds is just the interaction parameter. The second ESTIMATE statement applies the inverse logit link (via the LOGISTIC function) to each part to compute the difference in difference of probabilities.   proc logistic data=mydata; class a b / param=ref; model y(event="1")=a|b; output out=out p=p xbeta=xb; store log; run; %NLEstimate(instore=log, label=diff in diff probs, f=(logistic(b_p1+b_p2+b_p3+b_p4)-logistic(b_p1+b_p2)) - (logistic(b_p1+b_p3)-logistic(b_p1)), df=100) %NLEstimate(instore=log, label=diff in diff log odds, f=((b_p1+b_p2+b_p3+b_p4)-(b_p1+b_p2)) - ((b_p1+b_p3)-(b_p1)), df=100) proc means data=out mean nway; class a b; var p xb; output out=probs mean=; run; proc transpose data=probs out=tprobs; var p xb; run; data tprobs; set tprobs; difdif=(col1-col3)-(col2-col4); run; proc print noobs; var _label_ difdif; run; proc nlmixed data=mydata; p=logistic(b0 + b1*(a=1) + b2*(b=1) + b3*(a=1 and b=1)); model y ~ binary(p); estimate "(a1b1-a1b2)-(a2b1-a2b2)" ((b0+b1+b2+b3)-(b0+b1)) - ((b0+b2)-(b0)); estimate "(Pa1b1-Pa1b2)-(Pa2b1-Pa2b2)" (logistic(b0+b1+b2+b3)-logistic(b0+b1)) - (logistic(b0+b2)-logistic(b0)); run; ... View more