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

 From Ronnie Babigumira To statalist@hsphsun2.harvard.edu Subject Re: st: linear probability model vs. probit/logit Date Tue, 03 Oct 2006 22:22:36 +0200

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 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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