## Simulating data

We will use the “broken stick” approach to simulate data from the Dirichlet - trinomial model. This model assumes that the group proportions for each observation are Dirichlet, but the observed values are either 0, the total sample size (N) or a number between 0 and N.

Our `broken_stick`

function can be called as follows,

```
y = broken_stick(n_obs = 10,
n_groups = 10,
tot_n = 100)
```

The object `y`

is a list with 2 elements, (1) the true underlying compositions (p) and the realized data (X_obs). They can be accessed as

By default, the simulation function assumes a uniform prior for the Dirichlet, with hyperparameters = 1. We can change this by specifying our own values of hyperparameters. Using the argument `p`

, we can simulate new values with a slightly larger effective sample size, and pass that into `broken_stick`

```
p = gtools::rdirichlet(1, alpha = rep(2,10))
y = broken_stick(n_obs = 10,
n_groups = 10,
tot_n = 100,
p = p)
```