# Simulating data

####

#### 2024-01-24

Let’s load the necessary packages:

    library(zoid)

## 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

    y$p
    y$X_obs

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)