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      name:  <unnamed>
       log:  U:\projects\misc\probit\probit.txt
  log type:  text
 opened on:  30 Aug 2013, 09:54:18

. 
. //  Simulate data 
. clear 

. set scheme s1mono

. set seed 12345678

. set obs 5000
obs was 0, now 5000

. gen x1 = rchi2(1)+2

. 
. gen pr1 = exp(-1+0.1*x1) /(1+exp(-1+0.1*x1))

. gen y = rbinomial(1, pr1)

. 
. 
. // Program likelihood evaluator 
. program probit_lf
  1.         version 12
  2.         args todo b lnf
  3.         tempvar xb lj
  4.         mleval `xb' = `b'
  5.         * latent variable assumed cumm standard normal
.         qui gen double `lj'  = normal( `xb')  /*
>              */ if $ML_y1 == 1
  6.         qui replace    `lj'  = normal(-`xb')  /*
>              */ if $ML_y1 == 0
  7.         qui mlsum `lnf' = ln(`lj')
  8. end

. 
. ml model d0 probit_lf (y= x1) 

. ml search
initial:       log likelihood = -3465.7359
alternative:   log likelihood = -3216.5732
rescale:       log likelihood = -3216.5732

. *set trace on
. ml maximize

initial:       log likelihood = -3216.5732
rescale:       log likelihood = -3216.5732
Iteration 0:   log likelihood = -3216.5732  
Iteration 1:   log likelihood = -3183.3714  
Iteration 2:   log likelihood = -3183.3701  
Iteration 3:   log likelihood = -3183.3701  

                                                  Number of obs   =       5000
                                                  Wald chi2(1)    =      43.05
Log likelihood = -3183.3701                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .0826858   .0126015     6.56   0.000     .0579872    .1073843
       _cons |  -.6603764   .0420233   -15.71   0.000    -.7427405   -.5780123
------------------------------------------------------------------------------

. * note parameters are for the cum standard normal but data simualated using 
. * logit model 
. est sto myprobit

. 
. * check predictions
. predict yhat

. sum y yhat

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
           y |      5000         .34    .4737561          0          1
        yhat |      5000   -.4144288     .118727  -.4950049   .8208762

. 
. * Compare slopes
. lowess y x1, scale(0.5) 

. line yhat x1, sort

. 
. * compare to Stata's probit
. probit y x1

Iteration 0:   log likelihood = -3205.1774  
Iteration 1:   log likelihood = -3183.3725  
Iteration 2:   log likelihood = -3183.3701  
Iteration 3:   log likelihood = -3183.3701  

Probit regression                                 Number of obs   =       5000
                                                  LR chi2(1)      =      43.61
                                                  Prob > chi2     =     0.0000
Log likelihood = -3183.3701                       Pseudo R2       =     0.0068

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .0826858   .0126015     6.56   0.000     .0579873    .1073843
       _cons |  -.6603765   .0420233   -15.71   0.000    -.7427405   -.5780124
------------------------------------------------------------------------------

. est sto probit

. 
. est table myprobit probit, stat(ll)

----------------------------------------
    Variable |  myprobit      probit    
-------------+--------------------------
eq1          |
          x1 |  .08268576               
       _cons |  -.6603764               
-------------+--------------------------
y            |
          x1 |               .08268578  
       _cons |              -.66037649  
-------------+--------------------------
Statistics   |                          
          ll | -3183.3701   -3183.3701  
----------------------------------------

. 
. 
. log close
      name:  <unnamed>
       log:  U:\projects\misc\probit\probit.txt
  log type:  text
 closed on:  30 Aug 2013, 09:54:25
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