to be able to use a linear mixed effects model

The other model was another study but using the same task, just had an extra variable - as there were two groups. I thought it was the same thing, but ignore it please. 47 participants, 1000 trials each, though on average only 800 were included in the analysis (outlier removal and only correct responses were included). Block is a 5 level variable, we compare it consecutively - 1vs2, 2vs3, 3vs4, 4vs5. I am interested in determining whether there is an effect of type of trial; and whether this effect increases with time spent on the task, i.e. trial type * block and trial type * block * session

Sorry, just added the information to this post for the linear model. This is a simple response time task with one of the variables representing two types of trials in the task congruent or incongruent, block which is the within session time dimension and the final one - session because participants were tested twice, this is a repeated measures study.

I posted some plots of the linear model here: stats.stackexchange.com/questions/482141/…

I was thinking about using either the gamma or the ex-guassian distribution as I have seen both being recommended for response time data. Just added the qqplot() it does seem to deviate quite substantially.

@BenBolker Would that be a better option than glmer with the ex-gaussian family?

How does one know if the deviation from normality is too pronounced? I compared the lmer and glmer and the AIC is much higher for the glmer. npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) Model 37 -40576 -40215 20325 -40650 Model.glmer 37 1494498 1494859 -747212 1494424 0 0 1

But you would consider that they deviate too much from normality right?

I was not clear, I did the log transform after checking the residuals of the lmer model with the RT without any transformation, they were skewed (I was not refering to the raw data).

This is all residuals of a lmer model after log transformation, not the response times. I initial did the log transformation because the RTs are obviously skewed. This approach tends to be used in my department, but I know it is not the best one.