Probit Function Family

A Probit Function Family is a function family that is restricted to probit functions (of the form of the form [math]\displaystyle{ P_i = \frac{1}{\sqrt[\sigma]{2\pi}} \intop^{U_i}_{-\infty} \exp\{-1/2(\frac{x-\mu}{\sigma})^2\}\rd x }[/math])

• AKA: Probit Models.
• Context:
  • It can be an input to a Probit Regression Task (which results in a fitted probit function).
  • …
• Counter-Example(s):
  • a Logistic Function Family.
  • a Naive Bayes Model.
  • a Linear Model.
• See: Logit Function, Probit, Binomial Regression, Link Function.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/probit_model Retrieved:2014-6-3.
  • In statistics, a probit model is a type of regression where the dependent variable can only take two values, for example married or not married. The name is from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, if estimated probabilities greater than 1/2 are treated as classifying an observation into a predicted category, the probit model is a type of binary classification model. A probit model is a popular specification for an ordinal or a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. The probit model, which employs a probit link function, is most often estimated using the standard maximum likelihood procedure, such an estimation being called a probit regression. Probit models were introduced by Chester Bliss in 1934; a fast method for computing maximum likelihood estimates for them was proposed by Ronald Fisher as an appendix to Bliss' work in 1935.

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