Method to transform fixed effect parameter estimates back on to the response scale [after glmer() with family=Gamma(link = "log")] ??

Subject: Method to transform fixed effect parameter estimates back on to
the response scale [after glmer() with family=Gamma(link = "log")] ??

Dear lme4 experts,

I am using lme4 to model human reaction-time (RT; in milliseconds)
responses. My model includes both nested and fully crossed random
intercepts, and fixed effect ?predictor? factors.

lmer() seems to work quite well for this, and is nice since I can use the
fixed effect parameter estimates (beta and Std.Errors) for interpretation
to say that for every unit of the ?predictor? that changes, we expect a
change of ~beta units in RT on the response scale (milliseconds). Pretty
happy with the results?.BUT?

glmer() may be the better option since the response distribution has a
positive skew with no zero values (typical RT distribution), and glmer()
allows the same model specification as my lmer() model, except using
family=Gamma(link = "log") to account for the skewed response

This seems to work well and gives very similar results to the equivalent
lmer() model, but with somewhat improved residual plots, so I guess the
glmer() with family=Gamma(link = "log") is a more valid approach since it
explicitly accounts for the shape of response distribution.

PROBLEM: Is there a way to transform the fixed effect parameter estimates
and Std.Errors from the glmer() with family=Gamma(link = "log"), back to
the response scale (i.e. back to RT in milliseconds). It would be nice/aid
interpretation to say that for every unit of the ?predictor? that changes,
we expect a change of ~beta units on the response scale.

Thank you so much for your time!!

Cheers
Dan


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