I’m modeling a dataset where *response* is the angular difference between two angles. Let’s say that I have a “correct” angle and participants can press a random point in a circle. So I calculated the deviation from the correct angle, in degrees. The distribution is approximately normal centered on 0 and negative/positive values represent respectively anticlockwise and clockwise “errors”.

Then I have some linear predictors and I’m interested in modeling both the mean and the standard deviation (or k) of the data.

## Models

I’m omitting the priors and other `brm`

arguments just for simplicity.

The first option is the standard Gaussian model:

```
fit_formula_lin <- bf(theta ~ 0 + x1*x2 + (1|id),
sigma ~ 0 + x1*x2 + (1|id))
brm(fit_formula_lin,
data = dat_fit,
family = gaussian())
```

Where `theta `

is the angle difference (converted in radians). This allows me to have an estimation of the mean and the standard deviation for each condition.

The other option

```
fit_formula_von <- bf(theta ~ 0 + x1*x2 + (1|id),
kappa ~ 0 + x1*x2 + (1|id))
brm(fit_formula_von ,
data = dat_fit,
family = von_mises(),
```

I’m wondering which is the best modeling option. In particular, the second model takes a very long time to run and the parameters are, for me, more difficult to interpret. At the same time the Gaussian model is not taking into account the circularity of the data but maybe using angular differences and not raw angles this is somehow mitigated.

What do you think? Maybe I can truncate the gaussian prior to -\pi and +\pi

Thank you!