DispersionEstimatorFunction

is an option for generalized linear model fitting functions that specifies the estimator for the dispersion parameter.

Details

• DispersionEstimatorFunction is an option for GeneralizedLinearModelFit, LogitModelFit, and ProbitModelFit.
• With DispersionEstimatorFunction->"PearsonChiSquare", the estimator is where is the number of data points, is the number of parameters, and is the variance function for the distribution.
• With , the following estimates are used:
•  "Binomial" 1 "Gamma" "Gaussian" "InverseGaussian" "Poisson" 1 "QuasiLikelihood"
• Nondefault values can be used to model overdispersion in "Binomial" and "Poisson" models.
• With the setting , the common dispersion is estimated by f[y,,w] where y={y1,y2,} is the list of observations, ={1,2,} is the list of predicted values, and w={w1,w2,} is the list of weights for the measurements yi.

Examples

open allclose all

Basic Examples(1)

Fit a Poisson model:

 In[1]:=
 In[2]:=
 Out[2]=

Compute the covariance matrix using the default dispersion estimate:

 In[3]:=
 Out[3]=

Estimate the dispersion by Pearson's :

 In[4]:=
 Out[4]=

Estimate the dispersion by the mean squared error:

 In[5]:=
 Out[5]=