- Probit model
In
statistics , a probit model is a popular specification of ageneralized linear model , using theprobit link function. A probit regression is the application of this model to a given dataset. Probit models were introduced byChester Ittner Bliss in 1935, and a fast method of solving the models was introduced byRonald Fisher in an appendix to the same article. Because the response is a series of binomial results, the likelihood is often assumed to follow thebinomial distribution . Let "Y" be a binary outcome variable, and let "X" be a vector of regressors. The probit model assumes that:
where "Φ" is the
cumulative distribution function of the standardnormal distribution . The parameters "β" are typically estimated bymaximum likelihood .While easily motivated without it, the probit model can be generated by a simple
latent variable model . Suppose that:
where , and suppose that is an indicator for whether the latent variable is positive:
:
Then it is easy to show that
:
References
* Bliss, C.I. (1935). The calculation of the dosage-mortality curve. Annals of Applied Biology (22)134-167.
* Bliss, C.I. (1938). The determination of the dosage-mortality curve from small numbers. Quarterly Journal of Pharmacology (11)192-216.
*
ee also
*
Generalized linear model
* Logit Model
*Multivariate probit models
*Ordered probit andOrdered logit model
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