In Stata it is very easy to get the area under the ROC curve following either logit or logistic by using the lroc command. However, with lroc you cannot compare the areas under the ROC curve for two different models. It is possible to do this using the logistic linear predictors and the roccomp command.Here is an example:
use https://stats.idre.ucla.edu/stat/stata/notes/hsb2.dta, clear
generate hon=write>=60 /* create binary response variable */
logit hon female, nolog
Logit estimates Number of obs = 200
LR chi2(1) = 3.94
Prob > chi2 = 0.0473
Log likelihood = -113.6769 Pseudo R2 = 0.0170
------------------------------------------------------------------------------
hon | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | .6513707 .3336752 1.95 0.051 -.0026207 1.305362
_cons | -1.400088 .2631619 -5.32 0.000 -1.915876 -.8842998
------------------------------------------------------------------------------
lroc, nograph
Logistic model for hon
number of observations = 200
area under ROC curve = 0.5785
predict xb1, xb /* create linear predictor for model 1 */
logit hon female read, nolog
Logit estimates Number of obs = 200
LR chi2(2) = 60.40
Prob > chi2 = 0.0000
Log likelihood = -85.44372 Pseudo R2 = 0.2612
------------------------------------------------------------------------------
hon | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | 1.120926 .4081028 2.75 0.006 .321059 1.920793
read | .1443657 .0233337 6.19 0.000 .0986325 .1900989
_cons | -9.603365 1.426404 -6.73 0.000 -12.39906 -6.807665
------------------------------------------------------------------------------
lroc, nograph
Logistic model for hon
number of observations = 200
area under ROC curve = 0.8330
predict xb2, xb /* create linear predictor for model 2 */
We have run two different models and have areas under the ROC curve of .5785 and .8330. Next, we will use the two linear predictors with the roccomp command to get a test of the differences in area under the ROC curve.
roccomp hon xb1 xb2, graph summary
ROC -Asymptotic Normal--
Obs Area Std. Err. [95% Conf. Interval]
-------------------------------------------------------------------------
xb1 200 0.5785 0.0254 0.52870 0.62828
xb2 200 0.8330 0.0305 0.77329 0.89274
-------------------------------------------------------------------------
Ho: area(xb1) = area(xb2)
chi2(1) = 50.18 Prob>chi2 = 0.0000
Using roccomp with linear predictors from logistic regression will work with both nested and non-nested models.
Thanks to Sid Port for suggesting this approach.
Reference
Mario A. Cleves, From the help desk: Comparing areas under receiver operating characteristic curves from two or more probit or logit models, The Stata Journal (2002) 2, No. 3, pp 301-313.