# ProbitModelFit

ProbitModelFit[{y1,y2,},{f1,f2,},x]

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

ProbitModelFit[{{x11,x12,,y1},{x21,x22,,y2},},{f1,f2,},{x1,x2,}]

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

ProbitModelFit[{m,v}]

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

# Details 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.

# Examples

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## Basic Examples(1)

Define a dataset:

 In:= Fit a probit model to the data:

 In:= Out= See the functional forms of the model:

 In:= Out= Evaluate the model at a point:

 In:= Out= Plot the data points and the models:

 In:= Out= Compute the fitted values for the model:

 In:= Out= Visualize the deviance residuals:

 In:= Out= ## Possible Issues(1)

Introduced in 2008
(7.0)