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From |
"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: probit vs. logit |

Date |
Tue, 25 May 2010 12:53:22 -0500 |

Here's another way to look at it: If you approximate a standard normal CDF, say PHI(x), by a logistic one F(x) = exp(th*x)/(1 + exp(th*x)) where th = 1.701 (best nonlinear LS fit) the maximum difference occurs at about x = 2.04 (PHI(x) = 0.979; F(x) = 0.970). Thus unless you had enough binary observations to distinguish a "success" rate of 97.9% from one of 97.0% near x = 2.04, either model would fit equally well. A limiting case would be if all your observations were at x = 2.04 (of course you wouldn't be doing regression in that case). In this situation if you had 2000 observations with 1958 "successes" , the nominal success rate would be 0.979 with 0.970 being just outside the lower 95% confidence limit. So a rough guideline would be that you need at least 2000 observations to distinguish a probit model from a logit model. Al Feiveson -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Michael N. Mitchell Sent: Tuesday, May 25, 2010 12:05 PM To: statalist@hsphsun2.harvard.edu Subject: Re: st: probit vs. logit Dear Everyone responding on this thread... These are all great ideas about "logit" and "probit"... I think this thread has gravitated lots of thoughts and perspectives that I see discussed "on the street" but not written about. It is like statistical water cooler conversation. Thanks! 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 2010-05-25 5.00 AM, Maarten buis wrote: > --- On Tue, 25/5/10, Michael N. Mitchell wrote: >> I agree with Martin, that<snip> > http://www.stata.com/statalist/archive/2010-02/msg00840.html > >> 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. > > Michael shows that in his example he finds a BIC difference of > .02036. To give it a bit of perspective: Adrian Raftery (1995) > propsed the following categorization of BIC differences: > > 0-2 : Weak evidence > 2-6 : Positive evidence > 6-10 : Strong evidence >> 10 : Very strong evidence > > So the kind of difference that Michael found would to all > intends and purposes mean that the logit and probit models are > indistinguishable. > > Hope this helps, > Maarten > > Adrian E. Raftery (1995) "Bayesian Model Selection in Social > Research", Sociological Methodology, Vol. 25, pp. 111-163. > > -------------------------- > Maarten L. Buis > Institut fuer Soziologie > Universitaet Tuebingen > Wilhelmstrasse 36 > 72074 Tuebingen > Germany > > http://www.maartenbuis.nl > -------------------------- > > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: probit vs. logit***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**Re: st: probit vs. logit***From:*"Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>

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