library("knitr") opts_chunk$set(message = FALSE, warning=FALSE, fig.width = 5.5)
Let's load the necessary packages:
library(zoid)
We will use the "broken stick" approach to simulate data from the Dirichlet - trinomial model. This model assumes that the group proportions for each observation are Dirichlet, but the observed values are either 0, the total sample size (N) or a number between 0 and N.
Our broken_stick
function can be called as follows,
y = broken_stick(n_obs = 10, n_groups = 10, tot_n = 100)
The object y
is a list with 2 elements, (1) the true underlying compositions (p) and the realized data (X_obs). They can be accessed as
y$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)
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