st: Survival Forecasting....help needed replicating results outside of Stata

[Jon Haveman <jon@beaconecon.com>]

Hi All,
I am working with mortgage data and am trying to forecast the  
probability of default in each of the next 72 months for particular  
loans.  I have a question at the bottom about how to take Stata's  
predictions and replicate them outside of Stata.

My data are organized on a monthly basis, with time varying covariates  
(e.g., home price appreciation).

Here is my approach:

1) stset a sample of historical data

stset enddate, time0(startdate) origin(time omonths)
	enter(time omonths) exit(prepay==1 time thismonth)
	id(numericloanid) failure(default==1)

where 	enddate is the current month and startdate is enddate - 1
	omonths is the month in which the loan was originated
	different loans are indicated by numericloanid
	default is a dummy variable for default
	prepay is a dummy variable for prepayment
	thismonth indicates the current month and right censoring for
		any loan that is still alive today

2) streg <covariates>, distribution(llogistic) iter(100)

3) stset a loan that is still alive, for which I want to predict default

stset enddate, time0(startdate) origin(time omonths)
	enter(time origmonths) exit(prepay==1 time thismonth+72)
	id(numericloanid) failure(default==1)

This is the same as before, but moves the right censoring out 72  
months.  All of the underlying covariates have been forecast out 72  
months.

4) predict survival rate: 	predict s, surv
   predict the hazard rate:	predict h, haz

5) generate the conditional probability of default in each month

		f = s * h;


Now, I get very sensible results this way, but I'm a bit confused on  
several matters.  I had thought that I should be able to replicate (S)  
using the following:

gen s = (1+(exp(-xb)*_t)^(1/gamma))^(-1)

But this obviously does not work:

. predict s, surv;

. gen gamma = exp(-.657325);

. predict xb, xb;

. gen s1 = 1/(1+(exp(-xb)*_t)^(1/gamma));

. list enddate _t _t0 s s1;

     +-------------------------------------------+
     | enddate    _t   _t0          s         s1 |
     |-------------------------------------------|
  1. |     554     1     0   .9727553   .9526516 |
  2. |     555     2     1   .9034937   .8407519 |
  3. |     556     3     2   .8404005   .7034764 |
  4. |     557     4     3   .8025259   .5773274 |
  5. |     558     5     4   .7860863   .4721465 |
     |-------------------------------------------|
  6. |     559     6     5   .7856199    .393317 |
  7. |     560     7     6   .7904842   .3272628 |
  8. |     561     8     7   .7988772   .2743748 |
  9. |     562     9     8   .8090085   .2328688 |
 10. |     563    10     9   .8190303   .1975901 |


My question is how do I replicate "s" without using the predict command?

Is this possible?  Is this sensible?

Any assistance that anybody can provide would be very much appreciated.


Thanks in advance,

Jon


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