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In SAS proc genmod with dist=tweedie, when would you use scale=pearson or scale=deviance?

In either case we get a message

The Tweedie dispersion parameter was held fixed.

but without scale option it says

The Tweedie dispersion parameter was estimated by maximum likelihood.

Wouldn't it be better to estimate the dispersion parameter, i.e. not use the scale option? And why are standard errors smaller in that case?

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The SCALE= option is designed for distributions that do not contain a parameter that scales the variance (for example, Poisson). For those distributions, you can use the SCALE= option to account for overdispersion.

In contrast, the Tweedie distribution contains a scaling/dispersion parameter as part of the three-parameter distribution. So, yes, it would be better to estimate this parameter by MLE. There is no need to use the SCALE= option for Tweedie.

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