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

 From Nishant Dass To statalist@hsphsun2.harvard.edu Subject Re: st: linear probability model vs. probit/logit Date Tue, 3 Oct 2006 13:37:23 -0700 (PDT)

```Hi Richard,
First of all, my apologies for flipping the no. of obs.;
indeed, it's more in the OLS and less in -logit-.

Hi Ronnie,
Thanks for your very helpful example.  Yes, I see it now -
the header of my output shows that many indicator variables
of mine "predict failure perfectly" and yes, those
observations get dropped!  (I have some 60 odd indicators.
And the reason I was hesitant in pasting my output here is
that it is too large - I have some 85 regressors including
the indicator variables.)

So yes, I know why the observations are being dropped but
... is it then wrong to compare the OLS and -logit-?

N

--- Ronnie Babigumira <rb.glists@gmail.com> wrote:

> 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
> -------------+------------------------------
>         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
> -------------+------------------------------
>         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
>
>
> 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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> >>
> >> -------------------------------------------
> >> Richard Williams, Notre Dame Dept of Sociology
> >> OFFICE: (574)631-6668, (574)631-6463
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> >>
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> >
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