ProbitModelFit
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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
- 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.
Examples
open allclose allBasic Examples (1)Summary of the most common use cases
https://wolfram.com/xid/08up4vfz7944zbg-nx93sc
Fit a probit model to the data:
https://wolfram.com/xid/08up4vfz7944zbg-b76n5q
Evaluate the model at a point:
https://wolfram.com/xid/08up4vfz7944zbg-ejfopq
Plot the data points and the models:
https://wolfram.com/xid/08up4vfz7944zbg-bgck4y
Scope (13)Survey of the scope of standard use cases
Data (6)
Fit data with success probability responses, assuming increasing integer-independent values:
https://wolfram.com/xid/08up4vfz7944zbg-f0aete
https://wolfram.com/xid/08up4vfz7944zbg-pq11cz
Weight by the number of observations for each predictor value:
https://wolfram.com/xid/08up4vfz7944zbg-ip5td1
This gives the same best fit function as success failure data:
https://wolfram.com/xid/08up4vfz7944zbg-d7ev2y
https://wolfram.com/xid/08up4vfz7944zbg-crr960
https://wolfram.com/xid/08up4vfz7944zbg-0fncw
Fit a rule of input values and responses:
https://wolfram.com/xid/08up4vfz7944zbg-bdruu3
Specify a column as the response:
https://wolfram.com/xid/08up4vfz7944zbg-c6j5sl
https://wolfram.com/xid/08up4vfz7944zbg-cvtnuc
https://wolfram.com/xid/08up4vfz7944zbg-g2ag1e
Fit a model given a design matrix and response vector:
https://wolfram.com/xid/08up4vfz7944zbg-mddglo
https://wolfram.com/xid/08up4vfz7944zbg-lem1zl
Fit the model referring to the basis functions as and :
https://wolfram.com/xid/08up4vfz7944zbg-ccq2tc
Obtain a list of available properties:
https://wolfram.com/xid/08up4vfz7944zbg-dwx16i
https://wolfram.com/xid/08up4vfz7944zbg-fc1fp9
Properties (7)
Data & Fitted Functions (1)
https://wolfram.com/xid/08up4vfz7944zbg-on8wnl
https://wolfram.com/xid/08up4vfz7944zbg-fj8t12
https://wolfram.com/xid/08up4vfz7944zbg-na9fdf
https://wolfram.com/xid/08up4vfz7944zbg-btkjeg
Obtain the fitted function as a pure function:
https://wolfram.com/xid/08up4vfz7944zbg-2573y
Get the design matrix and response vector for the fitting:
https://wolfram.com/xid/08up4vfz7944zbg-cn4kx5
Residuals (1)
https://wolfram.com/xid/08up4vfz7944zbg-c8o5a0
https://wolfram.com/xid/08up4vfz7944zbg-e4h1qz
https://wolfram.com/xid/08up4vfz7944zbg-c6mebv
https://wolfram.com/xid/08up4vfz7944zbg-iyrir
Visualize Anscombe residuals and standardized Pearson residuals in stem plots:
https://wolfram.com/xid/08up4vfz7944zbg-fc0pug
Dispersion and Deviances (1)
Fit a probit model to some data:
https://wolfram.com/xid/08up4vfz7944zbg-bvfu5x
The estimated dispersion is 1 by default:
https://wolfram.com/xid/08up4vfz7944zbg-c0a7u8
Use Pearson's as the dispersion estimator instead:
https://wolfram.com/xid/08up4vfz7944zbg-buuvqn
Plot the deviances for each point:
https://wolfram.com/xid/08up4vfz7944zbg-bvma5v
Obtain the analysis of deviance table:
https://wolfram.com/xid/08up4vfz7944zbg-xre76
Get the residual deviances from the table:
https://wolfram.com/xid/08up4vfz7944zbg-dv5b70
Parameter Estimation Diagnostics (1)
Influence Measures (1)
Fit some data containing extreme values to a probit model:
https://wolfram.com/xid/08up4vfz7944zbg-dxjd2
Check Cook distances to identify highly influential points:
https://wolfram.com/xid/08up4vfz7944zbg-fbslf9
Check the diagonal elements of the hat matrix to assess influence of points on the fitting:
https://wolfram.com/xid/08up4vfz7944zbg-fjhhjr
Prediction Values (1)
Goodness-of-Fit Measures (1)
Obtain a table of goodness-of-fit measures for a probit model:
https://wolfram.com/xid/08up4vfz7944zbg-f1m5pa
https://wolfram.com/xid/08up4vfz7944zbg-oijifv
https://wolfram.com/xid/08up4vfz7944zbg-cys2tt
Compute goodness-of-fit measures for all subsets of predictor variables:
https://wolfram.com/xid/08up4vfz7944zbg-o0qvw9
https://wolfram.com/xid/08up4vfz7944zbg-ol11p
Generalizations & Extensions (1)Generalized and extended use cases
Perform other mathematical operations on the functional form of the model:
https://wolfram.com/xid/08up4vfz7944zbg-i4rgx5
Integrate symbolically and numerically:
https://wolfram.com/xid/08up4vfz7944zbg-brsld4
https://wolfram.com/xid/08up4vfz7944zbg-ly2tj7
Find a predictor value that gives a particular value for the model:
https://wolfram.com/xid/08up4vfz7944zbg-pmp2d
Options (8)Common values & functionality for each option
ConfidenceLevel (1)
The default gives 95% confidence intervals:
https://wolfram.com/xid/08up4vfz7944zbg-ecoitr
https://wolfram.com/xid/08up4vfz7944zbg-j4wn3
https://wolfram.com/xid/08up4vfz7944zbg-b58ly3
https://wolfram.com/xid/08up4vfz7944zbg-l2hd6e
https://wolfram.com/xid/08up4vfz7944zbg-qrf46
Set the level to 90% within FittedModel:
https://wolfram.com/xid/08up4vfz7944zbg-ihsmr4
CovarianceEstimatorFunction (1)
https://wolfram.com/xid/08up4vfz7944zbg-cpmdpa
https://wolfram.com/xid/08up4vfz7944zbg-e6g1ik
Compute the covariance matrix using the expected information matrix:
https://wolfram.com/xid/08up4vfz7944zbg-imv9d3
Use the observed information matrix instead:
https://wolfram.com/xid/08up4vfz7944zbg-fosnc8
DispersionEstimatorFunction (1)
https://wolfram.com/xid/08up4vfz7944zbg-brkjy3
https://wolfram.com/xid/08up4vfz7944zbg-crq2bc
Compute the covariance matrix:
https://wolfram.com/xid/08up4vfz7944zbg-ks68gb
Compute the covariance matrix estimating the dispersion by Pearson's :
https://wolfram.com/xid/08up4vfz7944zbg-c7pfx
IncludeConstantBasis (1)
LinearOffsetFunction (1)
https://wolfram.com/xid/08up4vfz7944zbg-wt8sn
https://wolfram.com/xid/08up4vfz7944zbg-dyqi6m
Fit data to a model with a known Sqrt[x] term:
https://wolfram.com/xid/08up4vfz7944zbg-etvp7m
NominalVariables (1)
https://wolfram.com/xid/08up4vfz7944zbg-i1novh
Fit the data, treating the first variable as a nominal variable:
https://wolfram.com/xid/08up4vfz7944zbg-eo2qfz
https://wolfram.com/xid/08up4vfz7944zbg-jn6rqi
Treat both variables as nominal:
https://wolfram.com/xid/08up4vfz7944zbg-gds1vr
Weights (1)
WorkingPrecision (1)
Use WorkingPrecision to get higher precision in parameter estimates:
https://wolfram.com/xid/08up4vfz7944zbg-olb75
https://wolfram.com/xid/08up4vfz7944zbg-cpb4wl
https://wolfram.com/xid/08up4vfz7944zbg-uefph
Reduce the precision in property computations after the fitting:
https://wolfram.com/xid/08up4vfz7944zbg-cjjn8p
Properties & Relations (4)Properties of the function, and connections to other functions
ProbitModelFit is equivalent to a "Binomial" model from GeneralizedLinearModelFit with "ProbitLink":
https://wolfram.com/xid/08up4vfz7944zbg-b9gwqs
https://wolfram.com/xid/08up4vfz7944zbg-cesyb7
https://wolfram.com/xid/08up4vfz7944zbg-do6sv3
LogitModelFit is a "Binomial" model from GeneralizedLinearModelFit with default "LogitLink":
https://wolfram.com/xid/08up4vfz7944zbg-escszz
https://wolfram.com/xid/08up4vfz7944zbg-l37ovw
ProbitModelFit assumes binomially distributed responses:
https://wolfram.com/xid/08up4vfz7944zbg-c4lezd
https://wolfram.com/xid/08up4vfz7944zbg-ifep8u
NonlinearModelFit assumes normally distributed responses:
https://wolfram.com/xid/08up4vfz7944zbg-g4yusx
https://wolfram.com/xid/08up4vfz7944zbg-1zgny
https://wolfram.com/xid/08up4vfz7944zbg-d7xe8
ProbitModelFit will use the time stamps of a TimeSeries as variables:
https://wolfram.com/xid/08up4vfz7944zbg-2mh1vu
https://wolfram.com/xid/08up4vfz7944zbg-8vunzb
https://wolfram.com/xid/08up4vfz7944zbg-c50i1w
Rescale the time stamps and fit again:
https://wolfram.com/xid/08up4vfz7944zbg-hiel46
https://wolfram.com/xid/08up4vfz7944zbg-7d00cg
https://wolfram.com/xid/08up4vfz7944zbg-emgg00
https://wolfram.com/xid/08up4vfz7944zbg-siexdh
ProbitModelFit acts pathwise on a multipath TemporalData:
https://wolfram.com/xid/08up4vfz7944zbg-1mqe20
Wolfram Research (2008), ProbitModelFit, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbitModelFit.html.
Text
Wolfram Research (2008), ProbitModelFit, Wolfram Language function, https://reference.wolfram.com/language/ref/ProbitModelFit.html.
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.
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
Wolfram Language. (2008). ProbitModelFit. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ProbitModelFit.html
BibTeX
@misc{reference.wolfram_2024_probitmodelfit, author="Wolfram Research", title="{ProbitModelFit}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ProbitModelFit.html}", note=[Accessed: 08-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_probitmodelfit, organization={Wolfram Research}, title={ProbitModelFit}, year={2008}, url={https://reference.wolfram.com/language/ref/ProbitModelFit.html}, note=[Accessed: 08-January-2025
]}