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Testing overdispersion Gamma glmer

Highland Statistics Ltd 
------------------------------

Message: 2
Date: Mon, 14 Dec 2015 11:45:24 +0100
From: Sophie Waegebaert <sophie.waegebaert at gmail.com>
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Testing overdispersion Gamma glmer
Message-ID:
	<CAGH66HCiv5jiad+_DM+HP91xP3GOHGa1jft8E=KYSJR=i_RYmQ at mail.gmail.com>
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Hello,

I want to compare mean trip duration (length.in.hours) across treatment
conditions and colonies. I have 3 colonies and 2 treatments. So, one half
of a colony gets a DWV treatment and the other half a control treatment.

When a histogram is made, it is clear that the data is skewed to the rigth.
So, I am using a Gamma distribution.

This is the model: fit_length = glmer(length.in.hours~treatment*colony +
(1|RFID), family = Gamma(link = "log"), data = datashort)

I use the log link and not the identity link, because the AIC is lower.
RFID is the code used for each subject in the colonies.

I want to test for the overdispersion assumption by using the following
code:
fit_length      8   5646.758
fit_length_obs  9 -74390.105


There is a clear difference between the AIC values, but I was wondering
wether -74390 is a realistic value? Is it not very low? Or am I using the
wrong method to control for overdispersion?

Thank you for some help!

Kind regards,

Sophie




Sophie,
A Gamma GLM(M) cannot be overdispersed. The parameter r in the variance expression of a Gamma GLM acts
like the sigma parameter in linear regression.

A Poisson GLM can be overdispersed because the variance equals the mean. It has no extra parameter to correct for any
extra variation. Same holds for a binomial (as in binomial..not Bernoulli).

As to why the model with the observation level random effect is much better...well it acts like
a latent variable.

Kind regards,

Alain