Probit model

In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit.^[1] 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, classifying observations based on their predicted probabilities is a type of binary classification model.

A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function.^[2] It is most often estimated using the maximum likelihood procedure,^[3] such an estimation being called a probit regression.

^ Oxford English Dictionary, 3rd ed. s.v. probit (article dated June 2007): Bliss, C. I. (1934). "The Method of Probits". Science. 79 (2037): 38–39. Bibcode:1934Sci....79...38B. doi:10.1126/science.79.2037.38. PMID 17813446. These arbitrary probability units have been called 'probits'.
^ Agresti, Alan (2015). Foundations of Linear and Generalized Linear Models. New York: Wiley. pp. 183–186. ISBN 978-1-118-73003-4.
^ Aldrich, John H.; Nelson, Forrest D.; Adler, E. Scott (1984). Linear Probability, Logit, and Probit Models. Sage. pp. 48–65. ISBN 0-8039-2133-0.

[1] Oxford English Dictionary, 3rd ed. s.v. probit (article dated June 2007): Bliss, C. I. (1934). "The Method of Probits". Science. 79 (2037): 38–39. Bibcode:1934Sci....79...38B. doi:10.1126/science.79.2037.38. PMID 17813446. These arbitrary probability units have been called 'probits'.

[2] Agresti, Alan (2015). Foundations of Linear and Generalized Linear Models. New York: Wiley. pp. 183–186. ISBN 978-1-118-73003-4.

[3] Aldrich, John H.; Nelson, Forrest D.; Adler, E. Scott (1984). Linear Probability, Logit, and Probit Models. Sage. pp. 48–65. ISBN 0-8039-2133-0.

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