ProbitModelFit

ProbitModelFit[{y1, y2, ...}, {f1, f2, ...}, x]
constructs a binomial probit regression model of the form that fits the for successive x values , , ....

ProbitModelFit[{{x11, x12, ..., y1}, {x21, x22, ..., y2}, ...}, {f1, f2, ...}, {x1, x2, ...}]
constructs a binomial probit regression model of the form where the depend on the variables .

ProbitModelFit[{m, v}]
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 , ... can be found from .
  • With data in the form , the number of coordinates , , ... should correspond to the number of variables .
  • The are probabilities between 0 and 1.
  • Data in the form is equivalent to data in the form .
  • 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 at data points in the form . The response vector v is the list of responses .
  • 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 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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