I am dealing with count data that is over-dispersed and hence I consider using the negative binomial family (with glm()) instead of the gaussian family, as the link function.

To find out the advantages of using the negative binomial family given the distribution of the data I did a power simulation for a glm(family = gaussian(link = log)(package: Base) with randomly initiated coefficients and for glm.nb(link = log) (package: MASS).

Though the NegBin model showed to have more power holding all the other variables in the grid of the simulation setup, the type I error was higher too. This is problematic for my applications. See plot:

power simulation

I found a similar problem here, but the solution lies in the code of this person so I can't generalise the solution to my case. Correct me if I am wrong. Otherwise, what can cause this?

  • $\begingroup$ I need to add to this that - NA is a 5% increase in group B in contrast to A. - Lift: 0% is where the two groups are drawn from an equally parametrised negative binomial distribution. - only one independent variable is used: control or test group. $\endgroup$ – Alex Alvarez Pérez Feb 5 at 14:38

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