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Re: st: probit vs. logit


From   "Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: probit vs. logit
Date   Mon, 24 May 2010 23:55:30 -0700

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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