Built-in Mathematica Symbol

LogitModelFit

LogitModelFit[{y₁, y₂, ...}, {f₁, f₂, ...}, x]
constructs a binomial logistic regression model of the form

that fits the y_i for successive x values 1, 2, ....

LogitModelFit[{{x₁₁, x₁₂, ..., y₁}, {x₂₁, x₂₂, ..., y₂}, ...}, {f₁, ...}, {x₁, x₂, ...}]
constructs a binomial logistic regression model of the form

where the f_i depend on the variables x_k.

LogitModelFit[{m, v}]
constructs a binomial logistic regression model from the design matrix m and response vector v.

MORE INFORMATION

LogitModelFit returns a symbolic FittedModel object to represent the logistic model it constructs. The properties and diagnostics of the model can be obtained from model["property"].

The value of the best-fit function from LogitModelFit 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 x_i1, x_i2, ... should correspond to the number of variables x_i.

The y_i are probabilities between 0 and 1.

Data in the form {y₁, y₂, ...}, is equivalent to data in the form {{1, y₁}, {2, y₂}, ...}.

LogitModelFit produces a logistic model of the form under the assumption that the original n_i y_i are independent observations following binomial distributions with mean .

In LogitModelFit[{m, v}], the design matrix m is formed from the values of basis functions f_i 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 f_i can be specified using the form LogitModelFit[{m, v}, {f₁, f₂, ...}].

LogitModelFit is equivalent to GeneralizedLinearModelFit with ExponentialFamily->"Binomial" and LinkFunction->Automatic.

LogitModelFit takes the same options as GeneralizedLinearModelFit, with the exception of ExponentialFamily and LinkFunction.

EXAMPLES

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Basic Examples (1)

Define a data set:

Fit a logistic 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 data set:

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Fit a logistic 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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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 x and y:

Obtain a list of available properties:

Fit a logit 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 logit model to some data:

The estimated dispersion is one by default:

Use Pearson's

² 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 logit 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 logit model:

Plot the predicted values against the observed values:

Obtain a table of goodness of fit measures for a logit 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 logit model:

Compute the covariance matrix using the expected information matrix:

Use the observed information matrix instead:

Fit a logit model:

Compute the covariance matrix:

Compute the covariance matrix estimating the dispersion by Pearson's

²:

Fit a logit model:

Fit the model with zero constant term:

Fit data to a logit 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)

A default "Binomial" model from GeneralizedLinearModelFit is equivalent to the model for LogitModelFit:

ProbitModelFit is equivalent to a "Binomial" model with "ProbitLink":

LogitModelFit 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 logit models: