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BUILT-IN MATHEMATICA 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 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.
Examplesopen all
Basic Examples (1)
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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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