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How to fix a gamma model with poor fit?

Phillip Alday 
A few quick comments:

1. The QQ-plot diagnostic needs to be against the appropriate
distribution. For a gamma model, the theoretical quantiles comes from
the gamma distribution, not the normal distribution.
2. You have a log link but your reaction-time data looks to be in
seconds, not milliseconds. Note that log10(0.1) = -1 and log10(1) = 0,
but log10(100) = 2 and log10(1000) = 3, so you'll get very different
answers for seconds vs. milliseconds. The reason why log transforms are
so nice for reaction times is not "just" the skew, but rather that there
is an underlying power law driving the effects *on the milliseconds* scale.

Are you using a gamma model because of the Lo and Andrews paper? I've
indicated my skepticism about that work previously, but these are my
critical points:

- there's still a transformation going on, it's just in the link function
- having a nonlinear link complicates interpretation of the coefficients
- gamma models are much harder to fit numerically (and I believe that
codepath is less well tested in lme4; it's a known problem in
MixedModels.jl)
- the usual tests on residuals, etc. now have to be done against a gamma
distribution, not a normal, but a lot of diagnostics use the normal by
default
- I don't understand the obsession with "satisfying normality
assumptions" (from their abstract) in a GLMM -- half the point of the
*generalized* bit is that you can swap in a different distributional
assumption (the other half is the use of a link function)


When thinking about using a model from a particular family/distribution,
note that the distributional assumption is *on the residuals* so the
skew in your raw data may or may not be present in the residuals. So
maybe you don't need a Gamma model at all.

Looking at your model output, it looks like you're using sum contrasts
-- great! But checkout contr.Sum from the car package for nicer looking
labels. :)

Phillip
On 13/7/21 6:18 pm, C?tia Ferreira De Oliveira via R-sig-mixed-models wrote:

Thread (4 messages)

Cátia Ferreira De Oliveira How to fix a gamma model with poor fit? Jul 13 Phillip Alday How to fix a gamma model with poor fit? Jul 13 Cátia Ferreira De Oliveira How to fix a gamma model with poor fit? Jul 13 Phillip Alday How to fix a gamma model with poor fit? Jul 14