residuals from probit model?

[River Huang]

Dear All, Is the following code approproate for obatining residuals fom probit regressions?

sysuse auto, clear
probit foreign price mpg weight
predict phat
gen resid=foreign-phat

Thanks.

[Andrew Musau]

Sure, that will give you ordinary residuals in the context of a generalized linear model. But note that these residuals are problematic in the case of nonlinear models. See the discussion in Cook and Tsai's 1985 article that suggests an alternative.

[River Huang]

Dear Andrew, Thanks for the information. I winder why Stata does provide such an option?

[Andrew Musau]

You can get the predictions directly if you estimate the model using glm with a probit link.

sysuse auto, clear
probit foreign price mpg weight, nolog
predict phat
gen resid1=foreign-phat
glm foreign price mpg weight, family(binomial) link(probit) nolog
predict resid2, res
assert round(resid1, 5)==round(resid2, 5)

Res.:

. probit foreign price mpg weight, nolog

Probit regression                               Number of obs     =         74
                                                LR chi2(3)        =      55.76
                                                Prob > chi2       =     0.0000
Log likelihood = -17.151715                     Pseudo R2         =     0.6191

------------------------------------------------------------------------------
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       price |   .0005185   .0001651     3.14   0.002      .000195    .0008421
         mpg |  -.0723615   .0556501    -1.30   0.193    -.1814337    .0367106
      weight |  -.0038232   .0010392    -3.68   0.000      -.00586   -.0017864
       _cons |   8.150001   2.962982     2.75   0.006     2.342664    13.95734
------------------------------------------------------------------------------

. 
. predict phat
(option pr assumed; Pr(foreign))

. 
. gen resid1=foreign-phat

. 
. glm foreign price mpg weight, family(binomial) link(probit) nolog

Generalized linear models                         Number of obs   =         74
Optimization     : ML                             Residual df     =         70
                                                  Scale parameter =          1
Deviance         =  34.30342965                   (1/df) Deviance =    .490049
Pearson          =  38.73410124                   (1/df) Pearson  =   .5533443

Variance function: V(u) = u*(1-u)                 [Bernoulli]
Link function    : g(u) = invnorm(u)              [Probit]

                                                  AIC             =    .571668
Log likelihood   = -17.15171482                   BIC             =  -266.9811

------------------------------------------------------------------------------
             |                 OIM
     foreign |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       price |   .0005185   .0001651     3.14   0.002      .000195    .0008421
         mpg |  -.0723615   .0556501    -1.30   0.193    -.1814337    .0367106
      weight |  -.0038232   .0010392    -3.68   0.000      -.00586   -.0017864
       _cons |   8.150001   2.962982     2.75   0.006     2.342664    13.95734
------------------------------------------------------------------------------

. 
. predict resid2, res

. 
. assert round(resid1, 5)==round(resid2, 5)

.

[FernandoRios]

Hi River
Perhaps also to consider, when using probit model in a control function approach, the other option is to use generalized residuals/Score, which is how heckman-two step, or etregress works.
Best wishes
F

[River Huang]

Dear Andrew, Many thanks for the illustrative/helpful code.

[River Huang]

Dear FernandoRios, I am not familiar with those, but will check them out. Thanks a lot.