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How does SAS calculate 'xbeta' output in proc logistic?

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New Contributor
Posts: 4

How does SAS calculate 'xbeta' output in proc logistic?

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,

Respected Advisor
Posts: 2,655

Re: How does SAS calculate 'xbeta' output in proc logistic?

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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