Dear Stan community,

I have been trying to set priors and do a prior predictive check for an ex-gaussian regression model using brms v2.7.

The ex-gaussian regression model that I use is a hierarchical model in which RTs are predicted by two within-subject conditions with sigma and beta of the exgaussian distribution as constant parameters.

The model in brms:

```
> M1 <- brm(RT ~ VisualSync * SyncTarget + (VisualSync*SyncTarget|participantID),
> data = StimComp[StimComp$Detected == 1,], family = exgaussian(), prior = prior,
> chains = 4, iter = 4000, cores = 4, save_all_pars = T, sample_prior = "only")
```

I have set the following priors:

```
> prior <- c(prior("normal(0,.1)", class = "b", coef = ""),
> prior("lognormal(log(0.6), log(1.7))", class = "Intercept", coef = ""),
> prior("lognormal(log(0.06), log(1.2))", class = "sigma", coef = ""),
> prior("gamma(2.5,0.5)", class = "beta", coef = ""),
> prior("lkj(1)", class = "cor"),
> prior("student_t(3, 0, 0.02)", class = "sd"))
```

When I then use posterior predictive checks the prior distribution is symmetrical around 0, while the distribution of the fitted values looks like an ex-gaussian with RTs > 0 and a clear skew.

So, I assume that the residual error is too large and therefore introduces a distribution of RTs that allows for negative RTs.

I tried to allow less variance and more variance for the prior of the random effects (i.e., class â€śsdâ€ť), but this did not change the posterior predictive distribution much. It still remained symmetrical around zero.

So I donâ€™t know how to troubleshoot this, as I donâ€™t understand where the large standard errors may be coming from.

I saw that there was quite a lot of uncertainty in the estimate of the bĂ¨ta parameter of the exgaussian. Does the prior for bĂ¨ta allow to many values?

Any tips would be much appreciated!

Kind regards,

Hanne