constructs a binomial probit regression model of the form that fits the yi for successive x values 1, 2, .

constructs a binomial probit regression model of the form where the fi depend on the variables xk.

constructs a binomial probit regression model from the design matrix m and response vector v.

Details and OptionsDetails and Options

  • ProbitModelFit returns a symbolic FittedModel object to represent the probit model it constructs. The properties and diagnostics of the model can be obtained from model["property"].
  • The value of the best-fit function from ProbitModelFit at a particular point x1, can be found from model[x1,].
  • With data in the form {{x11,x12,,y1},{x21,x22,,y2},}, the number of coordinates xi1, xi2, should correspond to the number of variables xi.
  • The yi are probabilities between 0 and 1.
  • Data in the form {y1,y2,} is equivalent to data in the form {{1,y1},{2,y2},}.
  • ProbitModelFit produces a probit model under the assumption that the original are independent observations following binomial distributions with mean .
  • In ProbitModelFit[{m,v}], the design matrix m is formed from the values of basis functions fi at data points in the form {{f1,f2,},{f1,f2,},}. The response vector v is the list of responses {y1,y2,}.
  • For a design matrix m and response vector v, the model is where is the vector of parameters to be estimated.
  • When a design matrix is used, the basis functions fi can be specified using the form ProbitModelFit[{m,v},{f1,f2,}].
  • ProbitModelFit is equivalent to GeneralizedLinearModelFit with ExponentialFamily->"Binomial" and LinkFunction->"ProbitLink".
  • ProbitModelFit takes the same options as GeneralizedLinearModelFit, with the exception of ExponentialFamily and LinkFunction.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Define a dataset:

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Fit a probit model to the data:

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See the functional forms of the model:

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Evaluate the model at a point:

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Plot the data points and the models:

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Compute the fitted values for the model:

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Visualize the deviance residuals:

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Introduced in 2008
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