Re: st: generating random number with restriction to add to a variable in current dataset

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 05:45 PM 2/23/2005 -0300, Fabio Soares wrote:
> Dear all,
>
> I want to generate random numbers to add to the linear
> index of a probit model (xb) so that I can predict
> precisely the 1/0 observed outcomes.
> Therefore, for y=1 I want to draw a random number
> (vi)from a N~(0,1) so that xb+v>0 and for y=0 I want
> to draw a random number (vi) so that xb+v<=0. Any idea
> on how I can draw these numbers and add them to the
> index in few steps?
Here is a coding I think I like better than what I suggested before 
(although I am not sure if either one is what you want).  After running a 
probit,

predict xb, xb
gen xb2=xb+invnorm(uniform())
egen y1adjust = min(xb2 - .001) if y==1
egen y0adjust = max(xb2 + .001) if y==0
replace xb2 = xb2 - y1adjust if y==1
replace xb2 = xb2 - y0adjust if y==0
bysort y: sum xb2

Basically, you are adding a random N(0,1) variable to your predicted 
values, and then adding an adjustment factor that will make the new 
prediction always positive when y = 1 and always negative when y = 0.

Using the auto data:

. use http://www.stata-press.com/data/r8/auto.dta, clear
. predict xb, xb
. gen xb2=xb+invnorm(uniform())
. egen y1adjust = min(xb2 - .001) if foreign==1
(52 missing values generated)
. egen y0adjust = max(xb2 + .001) if foreign==0
(22 missing values generated)
. replace xb2 = xb2 - y1adjust if foreign==1
(22 real changes made)
. replace xb2 = xb2 - y0adjust if foreign==0
(52 real changes made)

. bysort foreign: sum xb2

-----------------------------------------------
-> foreign = Domestic

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         xb2 |        52   -4.894559    1.709001  -8.809644  -.0009999

-----------------------------------------------
-> foreign = Foreign

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         xb2 |        22     2.23402    1.401082   .0009999   5.177322


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