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Re: st: probit vs. logit


From   Nick Winter <nwinter@virginia.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: probit vs. logit
Date   Tue, 25 May 2010 10:17:33 -0400

I'll go further -- I've never seen a case where the choice of one or the other makes *any* substantive difference in the substantive effects estimated. (That is, in predicted probabilities or in the impact of IVs on those probabilities.)

I'd also say that if you find an example where your conclusions do differ, you would then be forced to make a choice based on theory about the precise nature of unobserved disturbances -- I seriously doubt most field have theories precise enough to make that choice with any confidence.

- Nick

On 5/25/2010 2:55 AM, Michael N. Mitchell wrote:
I agree with Martin, that the choice of "logit" vs. "probit" appears to
be largely discipline specific. If this is for publication or
presentation, then it might be useful to see what the customs are for
your audience.

If someone gets picky with you and really wants to see a comparison of
the model fit of the two models, I think you could use -estimates store-
and -estimates stats- (as shown below) to compare the fit of the models
using the AIC and/or BIC (where a smaller value means better fit). As in
the example below, the two values are nearly identical, and I think we
all expect that this would generally be the case.

--- snip ---

. sysuse auto
(1978 Automobile Data)

. logit foreign mpg price weight

Iteration 0: log likelihood = -45.03321
Iteration 1: log likelihood = -22.244792
Iteration 2: log likelihood = -18.069284
Iteration 3: log likelihood = -17.184699
Iteration 4: log likelihood = -17.161975
Iteration 5: log likelihood = -17.161893
Iteration 6: log likelihood = -17.161893

Logistic regression Number of obs = 74
LR chi2(3) = 55.74
Prob > chi2 = 0.0000
Log likelihood = -17.161893 Pseudo R2 = 0.6189

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

foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------

mpg | -.1210918 .0956855 -1.27 0.206 -.308632 .0664483
price | .0009264 .0003074 3.01 0.003 .000324 .0015288
weight | -.0068497 .0019996 -3.43 0.001 -.0107688 -.0029306
_cons | 14.42237 5.414367 2.66 0.008 3.81041 25.03434
------------------------------------------------------------------------------


. estimates store model1

. probit foreign mpg price weight

teration 0: log likelihood = -45.03321
Iteration 1: log likelihood = -20.083125
Iteration 2: log likelihood = -17.363271
Iteration 3: log likelihood = -17.152935
Iteration 4: log likelihood = -17.151715
Iteration 5: log likelihood = -17.151715

Probit regression Number of obs = 74
LR chi2(3) = 55.76
Prob > chi2 = 0.0000
Log likelihood = -17.151715 Pseudo R2 = 0.6191

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

foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------

mpg | -.0723615 .0556501 -1.30 0.193 -.1814337 .0367106
price | .0005185 .0001651 3.14 0.002 .000195 .0008421
weight | -.0038232 .0010392 -3.68 0.000 -.00586 -.0017864
_cons | 8.150001 2.962982 2.75 0.006 2.342664 13.95734
------------------------------------------------------------------------------


. estimates store model2

. estimates stats model1 model2

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

Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------

model1 | 74 -45.03321 -17.16189 4 42.32379 51.54005
model2 | 74 -45.03321 -17.15171 4 42.30343 51.51969
-----------------------------------------------------------------------------

Note: N=Obs used in calculating BIC; see [R] BIC note

--- snip ----

I hope that helps,

Michael N. Mitchell
Data Management Using Stata - http://www.stata.com/bookstore/dmus.html
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
Stata tidbit of the week - http://www.MichaelNormanMitchell.com



On 2010-05-24 11.36 PM, Maarten buis wrote:
--- On Mon, 24/5/10, SR Millis wrote:
Logistic regression is generally preferred over the probit
model because of the wider variety of fit statistics. Also,
exponentiated logit coefficients can be interpreted as odds
ratios---which is not the case with probit coefficients.

A general preference for one or the other is to a large
extend discipline dependent. For example, within economics
the probit is the "default" method. I like interpreting
effects in terms of odds ratios as a way of identifying the
scale, which is unidentified in a probit model (it is
identified by fixing the residual variance to one, which
has all kinds of nasty consequences when interpreting
interaction terms). So, I tend to use the -logit-.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------




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Assistant Professor                             434.924.3359 f
Department of Politics                  nwinter@virginia.edu e
University of Virginia          faculty.virginia.edu/nwinter w
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