ProbitModelFit
ProbitModelFit[{{x1,y1},{x2,y2},…},{f1,f2,…},x]
constructs a binomial probit regression model of the form that fits the yi for each xi.
ProbitModelFit[data,{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
![](Files/ProbitModelFit.en/details_1.png)
![](Files/ProbitModelFit.en/details_2.png)
![](Files/ProbitModelFit.en/details_3.png)
- ProbitModelFit attempts to model the data using a linear combination of basis functions composed with the inverse of the probit function (
).
- LogitModelFit is typically used in classification to model probability values.
- ProbitModelFit produces a generalized linear model of the form
under the assumption that the original
are independent realizations of Bernoulli trials with probabilities
.
- The function
is the CDF of the standard NormalDistribution.
- 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,…].
- Possible forms of data are:
-
{y1,y2,…} equivalent to the form {{1,y1},{2,y2},…} {{x11,x12,…,y1},…} a list of independent values xij and the responses yi {{x11,x12,…}y1,…} a list of rules between input values and responses {{x11,x12,…},…}{y1,y2,…} a rule between a list of input values and responses {{x11,…,y1,…},…}n fit the nth column of a matrix - With multivariate data such as
, the number of coordinates xi1, xi2, … should equal the number of variables xi.
- The yi are probabilities between 0 and 1.
- Additionally, data can be specified using a design matrix without specifying functions and variables:
-
{m,v} a design matrix m and response vector v - 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.
List of all options
![](Files/ProbitModelFit.en/details_4.png)
Examples
open allclose allBasic Examples (1)
Scope (13)
Data (6)
Fit data with success probability responses, assuming increasing integer-independent values:
Weight by the number of observations for each predictor value:
This gives the same best fit function as success failure data:
Fit a rule of input values and responses:
Specify a column as the response:
Fit a model given a design matrix and response vector:
Properties (7)
Data & Fitted Functions (1)
Residuals (1)
Dispersion and Deviances (1)
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:
Parameter Estimation Diagnostics (1)
Influence Measures (1)
Generalizations & Extensions (1)
Options (8)
ConfidenceLevel (1)
The default gives 95% confidence intervals:
Set the level to 90% within FittedModel:
CovarianceEstimatorFunction (1)
DispersionEstimatorFunction (1)
LinearOffsetFunction (1)
Fit data to a model with a known Sqrt[x] term:
NominalVariables (1)
WorkingPrecision (1)
Use WorkingPrecision to get higher precision in parameter estimates:
Reduce the precision in property computations after the fitting:
Properties & Relations (4)
ProbitModelFit is equivalent to a "Binomial" model from GeneralizedLinearModelFit with "ProbitLink":
LogitModelFit is a "Binomial" model from GeneralizedLinearModelFit with default "LogitLink":
ProbitModelFit assumes binomially distributed responses:
NonlinearModelFit assumes normally distributed responses:
ProbitModelFit will use the time stamps of a TimeSeries as variables:
Rescale the time stamps and fit again:
ProbitModelFit acts pathwise on a multipath TemporalData:
Text
Wolfram Research (2008), ProbitModelFit, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbitModelFit.html.
CMS
Wolfram Language. 2008. "ProbitModelFit." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ProbitModelFit.html.
APA
Wolfram Language. (2008). ProbitModelFit. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ProbitModelFit.html