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I am trying to use GLMM in R to fit a mixed-effects model (three categorical predictors, one continuous predictor) to trial-level reaction times from a group of participants.

The reaction time distributions (for the sample, experimental groups, and each participant) are ex-Gaussian in shape. From reading and searching the internet, it doesn't seem possible to specify an ex-Gaussian distribution with the family argument of the glmer() function (as would be possible with other distributional functions like family = binomial()).

I would like to ask if there might be a way to fit the mixed-effects model using glmer() and an ex-Gaussian distribution, or if there might be other (non-Bayesian) functions I could use instead.

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As far as I know, it is indeed not possible to fit such a model with glmer(). As an alternative, you can try my GLMMadaptive package that allows you to define your own distribution for the mixed model. An example of how to do this can be found here.

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