I am trying to fit penalized model for binary outcome with few events and correlated covariates. Probit and logistic regression models are among the most widely used models for binary outcome. I am wondering why penalized logistic regression has been developed and codes written but not penalized probit regression?
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1$\begingroup$ Look at stats.stackexchange.com/questions/272723/… Are you sure you really need probit, logit and probit are very close for most uses. $\endgroup$– kjetil b halvorsen ♦Apr 9, 2017 at 22:34
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$\begingroup$ Thank you! yeah I was guessing only LR "had the penalized version" was because they gave similar results but was not sure. Thank you so much! $\endgroup$– HueSXApr 9, 2017 at 22:41
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$\begingroup$ what do you mean by "penalized" probit regression? What is being penalized? $\endgroup$– adibenderApr 1, 2019 at 13:04
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Look at monotonic transformation, probit vs logit and Clarifications about probit and logit models.
Are you sure you really need probit? Logit and probit are very close for most uses. The case where they differs is in multivariate models, like multivariate probit for choice modeling, where the multivariate normal underlying the probit is much more flexible for modeling than multivarite logit. Some references for that is Discrete Choice Methods with Simulation which contains much more. There seems to be little on this site, but there is a tag choice and here a stored site search.
Some papers: Penalized Binary Regression as Statistical Learning Tool for Microarray Analysis, Penalized likelihood estimation of a trivariate additive probit model.
answered Apr 1, 2019 at 12:01