Probit
From DDWiki
The term Probit was first used by Chester Bliss in 1934. It is short for "probability unit". Probit is an extension of generalized linear models which uses the cumulative normal probability distribution. The Logit model is extremely similar and often used in place of the Probit because of its relative simplicity, but the Probit is still preferred in cases when the data shows an underlying normal distribution. Below is the plot of a Cumulative Normal Distribution.
General equations
The Probit model is generally defined as:
Where Y is a binary outcome variable, Φ is the standard probability distribution, and β is from maximum likelihood data. The function will look similar to the Cumulative Normal Distribution plotted above. The log-likelihood equation for the Probit model is:
Applications
The Probit model is used to predict consumer choices in a competitive market place. More specifically, the probability that a buyer will choose one product over another can be found. Information is gathered by observing choices that consumers have previously made, either in a controlled environment or in the real world. These predictions are very useful when finding an optimal design for a product.
