This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# LogitModelFit

 LogitModelFit constructs a binomial logistic regression model of the form that fits the for successive x values 1, 2, .... LogitModelFitconstructs a binomial logistic regression model of the form where the depend on the variables . LogitModelFitconstructs a binomial logistic regression model from the design matrix m and response vector v.
• 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 , ... 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 .
• LogitModelFit produces a logistic model of the form under the assumption that the original are independent observations following binomial distributions with mean .
• In LogitModelFit, 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 LogitModelFit.
Define a dataset:
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 dataset:
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 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:
Obtain a formatted table of parameter information:
Extract the column of -statistic values:
Get the unformatted array of values from the table:
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:
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:
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 :
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:
A default model from GeneralizedLinearModelFit is equivalent to the model for LogitModelFit:
ProbitModelFit is equivalent to a model with :
LogitModelFit assumes binomially distributed responses:
NonlinearModelFit assumes normally distributed responses:
The fits are not identical:
Responses outside the interval from 0 to 1 are not valid for logit models:
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