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

# DispersionEstimatorFunction

 DispersionEstimatorFunction is an option for generalized linear model fitting functions that specifies the estimator for the dispersion parameter.
• With DispersionEstimatorFunction, the estimator is where is the number of data points, is the number of parameters, and is the variance function for the distribution.
 "Binomial" 1 "Gamma" "Gaussian" "InverseGaussian" "Poisson" 1 "QuasiLikelihood"
• Non-default values can be used to model overdispersion in and models.
• With the setting DispersionEstimatorFunction->f, the common dispersion is estimated by where is the list of observations, is the list of predicted values, and is the list of weights for the measurements .
Fit a Poisson model:
Compute the covariance matrix using the default dispersion estimate:
Estimate the dispersion by Pearson's :
Estimate the dispersion by the mean squared error:
Fit a Poisson model:
 Out[2]=
Compute the covariance matrix using the default dispersion estimate:
 Out[3]=
Estimate the dispersion by Pearson's :
 Out[4]=
Estimate the dispersion by the mean squared error:
 Out[5]=
 Scope   (2)
Define the estimate within the FittedModel:
Fit a logit model:
Estimate the dispersion by the sum of squared errors:
Fit a probit model:
Estimate the dispersion by the mean squared error:
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