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The Somers' D, in logistic regression, provides an estimate of the rank correlation of the observed binary response variable and the predicted probabilities. Thus, it can be used as an indicator of model fit.
Its not difficult to get a Somers' D in Stata once you download the user contributed program somersd written by Roger Newsom. To get the program just type, ssc install somersd, in Stata's command window and follow the prompts to download the program.
Once you have downloaded somersd, run your logistic regression, compute the predicted probability and then run somersd with your binary response variable and the predicted probability.
Example
We will use the hsb2 dataset for this example. It doesn't have a good binary response variable so we will create one by dichotomizing write at the value 60 and calling it honors (for honors English). Then we will use it in a logistic regression with read, female and prog (the type of program each student is in) as predictors. After the logit command we will use predict to get the predicted probabilities.
use http://www.ats.ucla.edu/stat/data/hsb2, clear
generate honors=write>=60 /* create binary response variable */
xi: logit honors read female i.prog
i.prog _Iprog_1-3 (naturally coded; _Iprog_1 omitted)
Logistic regression Number of obs = 200
LR chi2(4) = 62.20
Prob > chi2 = 0.0000
Log likelihood = -84.542348 Pseudo R2 = 0.2689
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .1352861 .0242218 5.59 0.000 .0878123 .18276
female | 1.08343 .4094357 2.65 0.008 .2809511 1.885909
_Iprog_2 | .5559416 .5053125 1.10 0.271 -.4344527 1.546336
_Iprog_3 | .0016408 .6611702 0.00 0.998 -1.294229 1.29751
_cons | -9.41691 1.481922 -6.35 0.000 -12.32142 -6.512397
------------------------------------------------------------------------------
predict pprob
Now that we have the predicted probabilities, pprob, we can run somersd.
somersd honors pprob
Somers' D with variable: honors
Transformation: Untransformed
Valid observations: 200
Symmetric 95% CI
------------------------------------------------------------------------------
| Jackknife
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pprob | .6761648 .05778 11.70 0.000 .5629182 .7894115
------------------------------------------------------------------------------xi: logit honors i.prog
i.prog _Iprog_1-3 (naturally coded; _Iprog_1 omitted)
Logistic regression Number of obs = 200
LR chi2(2) = 16.15
Prob > chi2 = 0.0003
Log likelihood = -107.5719 Pseudo R2 = 0.0698
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Iprog_2 | 1.206168 .4577746 2.63 0.008 .3089465 2.10339
_Iprog_3 | -.3007542 .5988045 -0.50 0.615 -1.474389 .8728812
_cons | -1.691676 .4113064 -4.11 0.000 -2.497822 -.8855303
------------------------------------------------------------------------------
predict pprob2
(option pr assumed; Pr(honors))
somersd honors pprob2
Somers' D with variable: honors
Transformation: Untransformed
Valid observations: 200
Symmetric 95% CI
------------------------------------------------------------------------------
| Jackknife
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pprob2 | .3228084 .0737763 4.38 0.000 .1782095 .4674073
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