[RE] Response time modeling: Warning message with non-normal RAs

Dear Gabriel,

as no one of the real professionals stepped in yet, I will try to
provide some thoughts:

(1) In my experience, Gamma GLMMs with an identity link are very buggy
all the time, so normally, when I am confronted with positive continuous
data, I mostly never consider them in the first place...why not use
another link function when using GLMMs, because that's exactly the goal
they were invented for: modeling data that does not belong to a normal
distribution by using an appropriate link function.

(2) I see why you don't want to transform the raw RT data and use an
ordinary LMM, but in my opinion, using a Gamma GLMM with a log-Link is a
valid option. Especially because you can insert the raw RT as a DV and
then model it on the scale of the linear predictor and after that, get
all parameter estimates and (which is much more valuable in my opinion)
the predicted values on the scale of the dependent variable without any
hard work, just use the invert link function (e.g., use the effects
package with lme4 and get the raw RT predictions). The interpretation if
such a model is much easier as you can directly get the predictions on
the scale of the DV.

Is it totally reasonable with regards to power? That's another question
that a real RT specialist should answer...

(2) I know the article you mentioned and skimmed it again. I really
wonder why they do not mention a log-link function as a valid option and
just compare the LMM with the transformed DV against a Gamma GLMM with
the identity link or an inverse Gaussian with identity link. It seems to
my that the Gamma GLMM with a log link is never really discussed. But,
as they also use the inverse Gaussian with the following link function
in lme4:

invfn <- function() {
    ## link
    linkfun <- function(y) -1000/y
    ## inverse link
    linkinv <- function(eta)  -1000/eta
    ## derivative of invlink wrt eta
    mu.eta <- function(eta) { 1000/(eta^2) }
    valideta <- function(eta) TRUE
    link <- "-1000/y"
    structure(list(linkfun = linkfun, linkinv = linkinv,
                   mu.eta = mu.eta, valideta = valideta,
                   name = link),
              class = "link-glm")
}

Why not try this when you want to go along the line the authors suggest?
The parameter estimates in their analyses seem really comparable between
Gamma and inverse Gaussian GLMMs to me. Just have a look at the
supplement! ;-)

Try to play around with your generated data with the log-link function
and with the inverse Gaussian to see which one recovers your parameters
best and go from there...!

Greetings,

Ulf

Am 17.10.2018 um 11:06 schrieb Baud-Bovy Gabriel:

[RE] Response time modeling: Warning message with non-normal RAs

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