[R-lang] analysis of raw RTs w/ glmer and inverse gaussian

[João Veríssimo]

Dear all,

I've been trying to analyse response times following Lo &
Andrews' (2015) proposal here:
https://doi.org/10.3389/fpsyg.2015.01171

Specifically, they propose that raw RTs can be analysed without any
transformation, by using a GLMM that assumes a Gamma or inverse Gaussian
distribution.

For example:
glmer(rt ~ (1|subject) + (1|item) + prime * form * group + scale(trial),
mydata, family=inverse.gaussian(link="identity"))

Has anyone tried this? Any disadvantages or issues that I should be
aware of? I have noted a few issues that concern me (relatively to an
lmer model on log RTs):

1. If using treatment contrasts, I get different t-values for
interactions, depending on the reference level.

For example, these are the 3-way interactions when using one of the
levels of "form" as the reference:

primeType2:formInf:groupL2  -39.094     15.266   -2.56  0.01044 *  
primeType3:formInf:groupL2  -37.020     15.495   -2.39  0.01689 *  

And here the are same interactions when using the other level of "form"
as the reference:

primeType2:formFinite:groupL2  39.0939    17.5759   2.224   0.0261 *  
primeType3:formFinite:groupL2  37.0203    18.0101   2.056   0.0398 *

The estimates are exactly the same (as expected), but the SEs are larger
in the second case.

2. The estimate for the Intercept is not close to mean RTs for the
reference condition (e.g., mean of raw RTs for that condition is 891 ms;
Intercept is 1020 ms). I imagine this has something to do with assuming
a skewed distribution, but the difference seems quite large.

3. Convergence is much more difficult, especially for the inverse
Gaussian, and required a number of modifications: a) removal of random
slopes, b) scaling of trial number, rather than just centering, c) use
of bobyqa optimizer, and d) increasing the number of iterations to
20000.

I'd be grateful for any opinions on this type of models, as well as for
explanations for these behaviours.

Thank you!
João