I used ± 0.5 sum contrasts for a mixed effect logistic regression with categorical binary predictors. I know how to get the coefficient estimates for each factor level from the estimated mean in the model summary, but how do I calculate the credible intervals? is there any package in R for this?

The credible intervals for the coefficients should also be in the model summary. If you are interested in credible interval of the *difference* between groups, you should be able to get it by extracting individual samples for both coefficients, then for each sample multiply the coefficients by ± 0.5 (the same way you did to create your design matrix) and add them. This will give you posterior samples of the difference and then you can use `quantile`

to compute the credible interval of this quantity.

Does that make sense?

What I want to know is the coefficient and the credible interval for the reference level of a binary predictor. So if the predictor X has two levels A and B, with sum contrasts I get the average of A and B in the summary together with the CI. So if A is the reference level, to get the estimate for A alone I add the Intercept to the coefficient estimate (model estimate+ intercept= estimate for A). My question is how to get the credible interval for the estimate for A. Hope that is clearer.

So, with half-sum contrasts (i.e. -.5/+.5) the intercept parameter reflects the mean of the two conditions and the effect parameter reflects the difference between the two conditions. To get the posterior for a given condition, you can do this either in the Stan model in the `generated quantities`

section as:

```
generated quantities{
real condition_A = intercept - effect;
real condition_B = intercept + effect;
}
```

Or, if the model was already sampled and it took a long time so you don’t want to re-sample, you can do it in R via:

```
intercept = extract(from_stan_sampling,par='intercept',permute=F)[[1]]
effect = extract(from_stan_sampling,par='effect',permute=F)[[1]]
condition_A = intercept-effect
condition_B = intercept+effect
quantile(condition_A,probs=c(.025,.5,.975))
quantile(condition_B,probs=c(.025,.5,.975))
```

Thank you, this is really helpful. Does it matter if there are more predictors than just one? They are all binary and what about interactions? Is the calculation the same ? or does it change anything?

What I showed is the simple case of wanting to look at the condition means while accounting for just a simple single-2-level predictor. For anything more complicated you can still do things by hand but you’ll probably save yourself some headache by learning a package that does things automatically for you like tidyBayes. My own package, ezStan, has a `get_condition_post()`

function that obtains all condition posteriors if you have a certain type of hierarchical model (see: https://www.youtube.com/watch?v=G75WrqPyQuQ&list=PLu77iLvsj_GNmWqDdX-26kZ56dCZqkzBO&index=23)