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I have data on whether an audition was successful or not and some data that could help explain the success/failure up to some extent (I have about 10 categorical variables and 2 continuous). So the outcome of the model is binary (audition was successful or not) and the covariates both categorical and continuous. Which model would fit in this case? Is Probit the one to go with? Does this command for the explanatory variables to fulfill some conditions? How do you deal with the assumptions, that the explanatory variables might not be fully independent of each other?

Do you have good suggestions on literature or other sources on the Probit model and its application in the field?

Thank you in advance!

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closed as too broad by Michael Chernick, kjetil b halvorsen, Jeremy Miles, Peter Flom Feb 4 at 11:24

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  • $\begingroup$ Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. $\endgroup$ – gung Feb 4 at 2:25
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Unless you have a compelling reason to prefer probit (*), I would reach for a logistic regression in this situation. This will estimate the conditional probability that an auction is successful, given the explanatory variables you have measured:

$$ P(\text{Auction is Successful} \mid X) $$

In general, regression models do not make strong assumptions on the explanatory variables themselves, certainly not that they are independent or even uncorrelated. Strong correlation between variables does make it more difficult to interpret the results of the models, as the effect of two strongly correlated variables on the conditional probability that the auction is a success are hard to disentangle, but this is not a statistical assumption, instead a constraint on the scientific interpretability of the results.

It is much more important to capture accurately the relationships between the independent variables and the target, and for this tools such as splines are useful.

(*) There may be such compelling reasons, but I do not know of them in practice. Logistic regression differ only very slightly in results from logistic regressions, and there is much better technological support (both computational and mathematical) available for logistic regression.

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  • $\begingroup$ Thank you for such a quick reply and the thourough explanation. I'm the user236391 from above but new here and postet outside the orbit of my registered account. One follow up question though: you say "Logistic regression differ only very slightly in results from logistic regressions". Am I getting something wrong here, i.e. a sublime difference? Otherwise logistic regression and logistic regressions sound pretty much the same. Thanks! $\endgroup$ – 3000emus Feb 3 at 21:10
  • $\begingroup$ Logit and Probit only differ in the distribution of their errors (Logistic vs Normal) - In vast majority of cases these 2 models will give you the same results (up to scale transformation) - In practice Logistic models are more popular because historically easier to implement (The standard conditional logit model does have a closed form solution and then does not require simulation procedures unlike Probit) - Probit does overcome some key limitations of the Logit - You can easily accommodate panel nature of data (if relevant) and relax the independence of irrelevant alternatives property $\endgroup$ – Umka Feb 5 at 23:10

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