Re: st: linear probability model vs. probit/logit

[Ronnie Babigumira <rb.glists@gmail.com>]

Nishant
I agree with Richard, if logit dropped some observations, then reg should as well. Here is an example using the auto 
data. I regress foreign on price and rep78. We know that rep78 has 5 missing cases so we expect that these observations 
will be dropped.

. reg foreign price rep78

      Source |       SS       df       MS              Number of obs =      69
-------------+------------------------------           F(  2,    66) =   17.86
       Model |  5.13051358     2  2.56525679           Prob > F      =  0.0000
    Residual |  9.47818207    66  .143608819           R-squared     =  0.3512
-------------+------------------------------           Adj R-squared =  0.3315
       Total |  14.6086957    68   .21483376           Root MSE      =  .37896
<snip>

. logit foreign price rep78

Iteration 0:   log likelihood = -42.400729
Iteration 1:   log likelihood = -29.263454
Iteration 2:   log likelihood = -27.809797
Iteration 3:   log likelihood = -27.715582
Iteration 4:   log likelihood = -27.714924

Logistic regression                               Number of obs   =         69
                                                  LR chi2(2)      =      29.37
                                                  Prob > chi2     =     0.0000
Log likelihood = -27.714924                       Pseudo R2       =     0.3464
<snip>

----------------------------------------------

That said, I think I have an idea what is happening, I generated a nonsensical variable called bug

gen bug = foreign

then I replace the first 15 cases with 1 (otherwise OLS would basically produce nonsense)

replace bug = 1 in 1/15  //This introduces some variation between bug and foreign so I now run

. reg foreign price rep78 bug

      Source |       SS       df       MS              Number of obs =      69
-------------+------------------------------           F(  3,    65) =   29.77
       Model |  8.45477597     3  2.81825866           Prob > F      =  0.0000
    Residual |  6.15391968    65  .094675687           R-squared     =  0.5787
-------------+------------------------------           Adj R-squared =  0.5593
       Total |  14.6086957    68   .21483376           Root MSE      =  .30769

<snip>

But see what happens when I run a logit

. logit foreign price rep78 bug

note: bug != 1 predicts failure perfectly
      bug dropped and 35 obs not used

Iteration 0:   log likelihood = -22.616945
Iteration 1:   log likelihood = -13.458773
Iteration 2:   log likelihood = -12.034404
Iteration 3:   log likelihood = -11.766442
Iteration 4:   log likelihood = -11.749228
Iteration 5:   log likelihood = -11.749093

Logistic regression                               Number of obs   =         34
                                                  LR chi2(2)      =      21.74
                                                  Prob > chi2     =     0.0000
Log likelihood = -11.749093                       Pseudo R2       =     0.4805

I think therein lies the problem, something in your list of x's is perfectly predicting your y

Anyhow, it is show and tell time for you, you have told, so may be you should show what exactly you typed and the 
headers of the output


hth

Ronnie


Nishant Dass wrote:

> Hi Maarten,
> Thanks for the link.  I read it but I wonder - does perfect
> prediction result in exclusion of those observations?
>
> Hi Richard,
> I checked again and my runs aren't different.  I simply
> replaced the -reg- with -logit- and re-run the command, and
> get a different no. of obs.  I am not sure how useful would
> pasting my command be for you because there's really
> nothing different between the two commands that I am
> running (except the estimation method.)
>
> Nishant
>
>
> --- Richard Williams <Richard.A.Williams.5@ND.edu> wrote:
>
> > That shouldn't be happening.  I suspect there is
> > something different 
> > between your runs, e.g. are you using a different
> > dependent 
> > variable?  Perhaps you could show the commands and
> > output.
> >
> > At 02:11 PM 10/3/2006, Nishant Dass wrote:
> > >Dear list members,
> > >
> > >I am estimating a -probit-/-logit- model and my question
> > is
> > >about its comparison with the linear probability model
> > >(simple OLS).
> > >
> > >When I run the -probit- or -logit-, the number of
> > >observations is the same but much less when compared
> > with
> > >the OLS estimation of the very same model!  (E.g., the
> > no.
> > >of obs. in my probit and logit estimate is 12,000 while
> > >it's only 10,000 in the OLS regression.)
> > >
> > >Could anyone please tell me why do -probit- and -logit-
> > >drop these observations?
> > >
> > >Thank you very much,
> > >
> > >Nishant
> > >
> > >
> > >
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