I am working with a relatively small data set where the presence of a response is binary coded (1 = present). The design was nested such that there were unique participants within unique groups within 2 conditions.

My formula is:

```
CR_fmla <- bf(CR_Present ~
Training_Lev +
Category +
Category:Training_Lev +
(1 | Training_Lev / Group / Grp_Spkr))
```

I have set family to “bernoulli”

I am trying to create some visualizations of the fitted model by showing the predicted probabilities of the response being present (1).

Is `add_fitted_draws`

the correct function for this? Is the returned `.value`

the predicted probability?

A box plot of the data:

“CR” is the response I’m interested in.

When I plot the fitted model with 'add_fitted_draws` as follows:

```
Data %>%
select(-Speaker) %>%
distinct() %>%
add_fitted_draws(
Mod,
allow_new_levels = TRUE,
value = "Probability"
)
```

I get the following figure:

In this figure it looks as though CR being present is more likely in the postgrads in the IF category.

A `pp_check`

seems okay:

To try a different approach, I calculated the proportions of CR present responses for individuals and groups and then fitted a `zero_one_inflated_beta`

model and plotted the fitted proportions, again using `add_fitted_draws`

, which resulted in the following figure:

The pp_check for the beta model does not look great:

Are these the right pp_checks to be examining?

Is there something else I should be doing to manually calculate posterior probabilities?

Due to collapsing the data to conduct the beta regression on proportions, I’m not able to subject the two models to a `loo_compare`

since the number of observations is different.