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Mathematica > Data Manipulation > Numerical Data > Statistical Model Analysis > DispersionEstimatorFunction >
Mathematica > Data Manipulation > Statistical Data Analysis > Statistical Model Analysis > DispersionEstimatorFunction >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Statistical Model Analysis > DispersionEstimatorFunction >
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DispersionEstimatorFunction

DispersionEstimatorFunction
is an option for generalized linear model fitting functions that specifies the estimator for the dispersion parameter.
MORE INFORMATION
  • 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 .
EXAMPLESCLOSE ALL
Basic Examples   (1)
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:
In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
Compute the covariance matrix using the default dispersion estimate:
In[3]:=
Click for copyable input
Out[3]=
Estimate the dispersion by Pearson's :
In[4]:=
Click for copyable input
Out[4]=
Estimate the dispersion by the mean squared error:
In[5]:=
Click for copyable input
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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