# DispersionEstimatorFunction

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 DispersionEstimatorFunction->Automatic, 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 DispersionEstimatorFunction->f, the common dispersion is estimated by f[y,,w] 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.

# Examples

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## 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:

## 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:

Wolfram Research (2008), DispersionEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html.

#### Text

Wolfram Research (2008), DispersionEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html.

#### CMS

Wolfram Language. 2008. "DispersionEstimatorFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html.

#### APA

Wolfram Language. (2008). DispersionEstimatorFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html

#### BibTeX

@misc{reference.wolfram_2024_dispersionestimatorfunction, author="Wolfram Research", title="{DispersionEstimatorFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html}", note=[Accessed: 12-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_dispersionestimatorfunction, organization={Wolfram Research}, title={DispersionEstimatorFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/DispersionEstimatorFunction.html}, note=[Accessed: 12-July-2024 ]}