# Logit v. Probit: A fight to the death

#### terzi

##### TS Contributor
Again, the only conceptual reason I know to choose between logistic or probit regression is that Probit models can be hard to estimate and unstable when the outcome is rare. This means that in cases when the number of "1's" in your dataset is low the model may have problems, even if you have a huge dataset. Logit models, on the other hand, are way better when handling rare outcomes. I assume that most studies work in understanding the probabilities of something unusual happening, so logit models may be more appropriate for these particular situations. That is why I think logit is far more common.

#### noetsi

##### No cake for spunky
I think most simply find the "log of the odds" (logit) easier to understand than say probit and that probit did not generate an odds ratio in commercial software.

#### Jrb599

##### New Member
Terzi,

I believe you have backwards. As stated on an earlier page - probit is better for rare outcomes than logit.

Also, to derail again, I've worked in all industries as a consultant and they all bring their Ph.D. statisticians

#### Miner

##### TS Contributor
Minitab used the following reference for selection criteria: D.W. Hosmer and S. Lemeshow (2000). Applied Logistic Regression. 2nd ed. John Wiley & Sons, Inc.

I also found the following link that gives a reasonable explanation. This conforms to the use of Probit analysis in Reliability to model stress to failure. While stress is a continuous variable, in practice, it is usually applied in discrete steps.

#### bryangoodrich

##### Probably A Mammal
That's interesting Miner. I've never read about Probit being cast as using a dichotomous dependent variable as a proxy to a latent continuous variable. The reasoning make sense, on that assumption.

#### spunky

##### Can't make spagetti
I've never read about Probit being cast as using a dichotomous dependent variable as a proxy to a latent continuous variable.
but...but... but that's like the essence of factor analysis/structural equation modelling with categorical data! and item response theory where a latent continuum (ability in something like a math test or so) manifests itself in the binary responses to the items of a test!

HAVE YOU BEEN IGNORING ME ALL THESE YEARS?!!?

#### Dason

That's interesting Miner. I've never read about Probit being cast as using a dichotomous dependent variable as a proxy to a latent continuous variable. The reasoning make sense, on that assumption.
I haven't gone through and reread this thread but I think this was one of the "nice" things I pointed out about probit. You can think of it as there actually being an underlying normally distributed random variable along with a threshold that determines "success" and "failure". Like if you assume a normal distribution for height and then make a threshold of 6'9" as "tall" or something - then a probit is a natural model if that "tall" indicator is your dependent variable.

You can make a similar type of argument for logistic regression but you don't see that point get made often.

#### bryangoodrich

##### Probably A Mammal
but...but... but that's like the essence of factor analysis/structural equation modelling with categorical data! and item response theory where a latent continuum (ability in something like a math test or so) manifests itself in the binary responses to the items of a test!

HAVE YOU BEEN IGNORING ME ALL THESE YEARS?!!?
Yes.

And you do probit models? I understand the idea of latent structures, but I never read about probit models being in that category. Of course, my background is vastly different, and the only exposure to probit I've really seen is from silly economists