Scale Parameter

Fit Analyses

Scale Parameter

A scale parameter is related to the dispersion parameter $\phi$ and is given by

Normal: ${{\sigma} = \sqrt{\phi}}$
Inverse Gaussian: ${{\sigma} = \sqrt{\phi}}$
Gamma: ${{\nu} = 1 / \phi}$
Poisson: 1
Binomial: 1

The scale parameter is 1 for Poisson and binomial distributions. SAS/INSIGHT software provides different scale parameter estimates for normal, inverse Gaussian, and gamma distributions:

MLE: the maximum-likelihood estimate
Deviance: the mean deviance
Pearson: the mean Pearson $\chi^2$
Constant: the value in the Constant entry field

When maximum-likelihood estimation is used, the Hessian H and the gradient u also include the term for the scale parameter.

Note You can request an exponential distribution for the response variable by specifying a gamma distribution with scale parameter set to 1.

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