# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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 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:

Fit a probit model to the data:

 Out[2]=

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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