BUILT-IN MATHEMATICA SYMBOL

ProbitModelFit

constructs a binomial probit regression model of the form

that fits the

for successive x values

,

, ....

ProbitModelFit

constructs a binomial probit regression model of the form

where the

depend on the variables

.

ProbitModelFit

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

MORE INFORMATION

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, 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.

ProbitModelFit is equivalent to GeneralizedLinearModelFit with ExponentialFamily and LinkFunction.

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:

Fit a probit model to the data:

See the functional forms of the model:

Evaluate the model at a point:

Plot the data points and the models:

Compute the fitted values for the model:

Visualize the deviance residuals:

Define a dataset:

In[1]:=

Fit a probit model to the data:

In[2]:=

Out[2]=

See the functional forms of the model:

In[3]:=

Out[3]=

Evaluate the model at a point:

In[4]:=

Out[4]=

Plot the data points and the models:

In[5]:=

Out[5]=

Compute the fitted values for the model:

In[6]:=

Out[6]=

Visualize the deviance residuals:

In[7]:=

Out[7]=

Scope (10)

Fit data with success probability responses:

Weight by the number of observations for each predictor value:

This gives the same best fit function as success failure data:

Fit a model given a design matrix and response vector:

See the functional form:

Fit the model referring to the basis functions as

and

:

Obtain a list of available properties:

Fit a probit model:

Extract the original data:

Obtain and plot the best fit:

Obtain the fitted function as a pure function:

Get the design matrix and response vector for the fitting:

Examine residuals for a fit:

Visualize the raw residuals:

Visualize Anscombe residuals and standardized Pearson residuals in stem plots:

Fit a probit model to some data:

The estimated dispersion is 1 by default:

Use Pearson's

as the dispersion estimator instead:

Plot the deviances for each point:

Obtain the analysis of deviance table:

Get the residual deviances from the table:

Extract the numeric entries from the table:

Use Grid to add formatting:

Obtain a formatted table of parameter information:

Extract the column of

-statistic values:

Get the unformatted array of values from the table:

Add formatting using Grid:

Add formatting via TableForm:

Fit some data containing extreme values to a probit model:

Check Cook distances to identify highly influential points:

Check the diagonal elements of the hat matrix to assess influence of points on the fitting:

Fit a probit model:

Plot the predicted values against the observed values:

Obtain a table of goodness-of-fit measures for a probit model:

Compute goodness-of-fit measures for all subsets of predictor variables:

Rank the models by AIC:

Generalizations & Extensions (1)

Perform other mathematical operations on the functional form of the model:

Integrate symbolically and numerically:

Find a predictor value that gives a particular value for the model:

Options (8)

The default gives 95% confidence intervals:

Use 99% intervals instead:

Set the level to 90% within FittedModel:

Fit a probit model:

Compute the covariance matrix using the expected information matrix:

Use the observed information matrix instead:

Fit a probit model:

Compute the covariance matrix:

Compute the covariance matrix estimating the dispersion by Pearson's

:

Fit a probit model:

Fit the model with zero constant term:

Fit data to a probit model:

Fit data to a model with a known Sqrt[x] term:

Fit the data, treating the first variable as a nominal variable:

Treat both variables as nominal:

Fit a model using equal weights:

Give explicit weights for the data points:

Use WorkingPrecision to get higher precision in parameter estimates:

Obtain the fitted function:

Reduce the precision in property computations after the fitting:

Properties & Relations (2)

ProbitModelFit is equivalent to a

model from GeneralizedLinearModelFit with

:

LogitModelFit is a

model from GeneralizedLinearModelFit with default

:

ProbitModelFit assumes binomially distributed responses:

NonlinearModelFit assumes normally distributed responses:

The fits are not identical:

Possible Issues (1)

Responses outside the interval from 0 to 1 are not valid for probit models: