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DispersionEstimatorFunction

DispersionEstimatorFunction
is an option for generalized linear model fitting functions That specifies the estimator for the dispersion parameter.
  • With DispersionEstimatorFunction->"PearsonChiSquare", the estimator is where n is the number of data points, p is the number of parameters, and v 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 "Binomial" and "Poisson" models.
  • With the setting DispersionEstimatorFunction->f, the common dispersion is estimated by where y={y1, y2, ...} is the list of observations, is the list of predicted values and w={w1, w2, ...} is the list of weights for the measurements yi.
Fit a Poisson model:
Compute the covariance matrix using the default dispersion estimate:
Estimate the dispersion by Pearson's Chi2:
Estimate the dispersion by the mean squared error:
Fit a Poisson model:
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Compute the covariance matrix using the default dispersion estimate:
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Out[3]=
Estimate the dispersion by Pearson's Chi2:
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Estimate the dispersion by the mean squared error:
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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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