How does SAS calculate 'xbeta' output in proc logistic? I am using censored data and the Heckman Two-Step method to run a regression analysis, so here's the dilemma:
Heckman Two-Step Method:
1. Regress binary censored variable (eq 1 if censored, 0 otherwise) on RHS variables.
proc logistic data=all_data;
model censored = RHS_variables / link=probit;
output out=probit xbeta=xbeta stdxbeta=stdxbeta;
run;
2. Regress dependent variables of interest on RHS variables and Inverse Mills Ratio of (-Xi(beta/sigma))
data probit;
set probit;
imr=pdf('NORMAL', xbeta)/cdf('NORMAL',xbeta);
label imr='Inverse Mills Ratio';
run;
proc reg data=probit;
model dep_var=RHS_variables imr / acov;
where censored=1;
output out=heckman;
run; quit;
Essentially, is xbeta (calculated by SAS) equal to (-Xi(beta/sigma))? If so, then the above code is accurate. If not, then how do I calculate (-Xi(beta/sigma))?
Thank you for your help,
In PROC LOGISTIC, xbeta contains the estimates of the linear predictor. It is not scaled by sigma, I beleve you will have to divide through by the pooled error estimate to get what you need.
Steve Denham
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