Hi,

I want to use the *index* coding approach with brms, but I wonder if I have applied and understood it correctly. Most examples illustrate how to apply the case of one categorical factor with multiple levels, but in my case, I have two factors with several levels, and I want to look at the interactions between them. Each participant also has multiple observations at each level of the factors. I have specified three models that I want to compare:

```
modA <- brm(data = d,
family = gaussian,
performance ~ 0 + course + (0 + course | bib),
prior = c(prior(normal(0, 0.5), class = b),
prior(student_t(3, 0, 2.5), class = sigma),
prior(student_t(3, 0, 2.5), class = sd),
prior(lkj(2), class=cor)),
control = list(adapt_delta = 0.95),
file = "modA_test",
iter=4000, cores = 4, seed = 1337)
modB <- brm(data = d,
family = gaussian,
performance ~ 0 + course + day + (0 + course + day | bib),
prior = c(prior(normal(0, 0.5), class = b),
prior(student_t(3, 0, 2.5), class = sigma),
prior(student_t(3, 0, 2.5), class = sd),
prior(lkj(2), class=cor)),
control = list(adapt_delta = 0.95),
file = "modB_test",
iter=4000, cores = 4, seed = 1337)
modC <- brm(data = d,
family = gaussian,
performance ~ 0 + course + day + course:day + (0 + course + day + course:day | bib),
prior = c(prior(normal(0, 0.5), class = b),
prior(student_t(3, 0, 2.5), class = sigma),
prior(student_t(3, 0, 2.5), class = sd),
prior(lkj(2), class=cor)),
control = list(adapt_delta = 0.95),
file = "modC_test",
iter=4000, cores = 4, seed = 1337)
```

In **modA**, I want to examine the difference between the courses, ignoring information about the Day factor.

In **modB**, I want to explore the estimated change/improvement from day 1 to day 5.

In **modC**, I want to understand if the changes were different in the three courses.

Given my goal, are the model formulas correctly specified? Or do I have to use a use **brms** non-linear syntax? In this book, 8 Conditional Manatees | Statistical rethinking with brms, ggplot2, and the tidyverse: Second edition, it seems that it is only necessary to use the non-linear syntax when you have an interaction between a categorical factor and a continuous variable. Please correct me if I am wrong.