Date:         Mon, 17 Jun 1996 11:37:11 -0500
Reply-To:     abdu elnagheeb <Abdelmoneim.H.Elnagheeb@AEXP.COM>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         abdu elnagheeb <Abdelmoneim.H.Elnagheeb@AEXP.COM>
Subject:      logistic regression question for SAS

To make it more clear, here is an example. Suppose you have 100 observations
with your binary variable (say y) has 25 ones (good) and 75 zeros (bad). You
want your predicted probability of good to be as close to one as possible (I
assume you model Pr(good) here ; Pr(bad)=1-Pr(good) ) for y=1.  Also Pr(good)
for any y=1 should be greater than pr(good) for y=0 (i.e. all goods should
have higher Pr(good) than do the bads.) What SAS does is: create all possible
pairs of good and bads (here it is 75*25) . Then for each pair (of good and
bad) compares the predicted Pr(good).  If Pr(good) for the y=1 is greater
than Pr(good) for y=0, this pair is "concordant". If it is the opposite
it is "discordant", else it is a tie.  Then you count the number of Concordant
divide by 75*25 (all possible pairs) to get the proportion. Do the same for
discordant and ties. I hope this will help.
 
Abdu
 
-------------------------------- ATTACHED NOTE --------------------------------
 
         Date: June 17, 1996
         From:                                             S4BFF09F - MAILHUB1
           To: Multiple recipients of l                    S4BFF0B0 - MAILHUB1
      Subject: logistic regression question for SAS
------------------------------------------------------------------------------
Dear Readers,
        Can someone tell me the meaning of discordant and concordant in
the PROC LOGISTIC procedure in SAS. How are they calculated? Also, does
anyone have references for the correlation indices : Somer' D, Kendall's tau-a,
Goodman-Kruskall gamma, and c. Does anyone have an explanation for the c table
that is also generated in logistic procedure.
thankyou,
Paul Turner