[讨论]Difference Between Probit Analysis from Logit Analysis

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Dear lister:

I am trying to figure out the difference between probit analysis from logit analysis. The stuff that I have read on line doesn't really distinguish the two. Is there a difference? What would dictate the use of one over another.

TIA, Martin Sherman

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关键词：difference Analysis Analysi Between alysis Analysis Probit logit difference Between

Martin, I'm not sure if this is a distinction that necessarily warrants using the logit vs. probit (in the binary response case), but in the logit model the errors follow a logistic distribution and the variance is (3.14^2)/3 = 3.29 whereas for the probit model the distribution of the errors are assumed to follow a normal distribution (I believe the variance is standardized to = 1.0)..........so, I suspect one decision point is whether you assume your errors are normally distributed or not. On page 83 in Regression models for Categorical and Limted DV's Long states that "the choice between logit and probit models is largely one of convenience and convention, since the substantive results are generally indistinguishable....for some users, the simple interpretation of logit coefficients as odds ratios is the deciding factor..or, if an analysis also includes equations with a nominal DV, the logit model may be preferred since the probit model for nominal DV's is computationally!
too demand...in other cases, the need to generalize a model may be an issue. For example, multiple-equation systems involving qualitative DV's are basd on the probit model..................."

Martin, I'm not sure this helped clarify probit vs logit, but awhilst ago I ran analysis using both models, and if I recall correctly my interpretation was not substantively different. I suppose one of the key decisions is your assumption about error variance/error distribution.

Dale Glaser

Dale Glaser, Ph.D.
Principal--Glaser Consulting
Lecturer--SDSU/USD/CSUSM/AIU
4003 Goldfinch St, Suite G
San Diego, CA 92103
phone: 619-220-0602
fax: 619-220-0412
email: glaserconsult@sbcglobal.net
website: www.glaserconsult.com

We have a page that explains this at
http://www.ats.ucla.edu/stat/stata/dae/probit.htm . That part of the
page reads:

Neither the logit model nor the probit model are linear, which makes
things difficult. To make the model linear, a transformation is done on
the dependent variable. In logit regression, the transformation is the
logit function which is the natural log of the odds. In probit models,
the function used is the inverse of the standard normal cumulative
distribution (a.k.a. a z-score). In reality, this difference isn't too
important: both transformations are equally good at linearizing the
model; which one you use is a matter of personal preference. Both
models need to have diagnostics done afterwards to check that the
assumptions of the model have not been violated. Both methods use
maximum likelihood, and so require more cases than a similar OLS model.
Unlike logit models, you don't get odds ratios with probit models. In
general, the logit coefficients are larger than the probit coefficients
by a factor of 1.7. However, this rule often does not apply when an
independent variable has a high standard error (lots of variability).

I hope that this helps.

Christine Wells
Statistical Consulting Group
UCLA Academic Technology Services
http://www.ats.ucla.edu/stat/

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