Probit models postulate some relation between the probit of the observed probability, and unknown parameters of the model.
The most common example is the model
which is equivalent to :
where F() is the cumulative distribution function of the standard normal distribution , a and b are parameters of the model.
The probit models are used mainly to describe the dose-effect relationship for living organisms, e.g. the relationship between the dose of a toxic substance (x) and the probability p of death of experimental animals exposed to the dose x of the substance. The dose x is often measured as the logarithm of the concentration.
There is usually not much difference between the values of y predicted from the probit model and logistic regression model. Today, the logistic regression models are more popular than the probit models.