To part 16.3b STAN

Stan Code:

```
# Declare our data types (J is number of distinct children in our model)
# Vectorize our data, where N is the total number of observations we have

data {
int<lower=0> N;
int<lower=1,upper=J> child[N];
vector[N] x;
vector[N] y;
vector[N] u1;
vector[N] u2;
}

# Declare the data types of our parameters, where sigma_a and sigma_y are
# Uniform(0,100) random variables

parameters {
vector[J] b;
vector[3] beta;
real mu_b;
real mu_beta;
real<lower=0,upper=100> sigma;
real<lower=0,upper=100> sigma_b;
real<lower=0,upper=100> sigma_beta;
}

transformed parameters {
vector[J] y_hat;

for (i in 1:N)
y_hat[i] <- b[child[i]] + beta[1] * time[i] + beta[2] * baseage[i] + beta[3] * treatment[i];
}

model {
b ~ normal(0, sigma_b);
mu_b ~ normal(0, 1);

mu_beta ~ normal (0,1);
beta ~ normal (100 * mu_beta, sigma_beta);

y ~ normal(y_hat, sigma);
}

```

From R, call up the the package rstan using library(rstan). Copy and paste the code above into a variable. Create a list with your data. The syntax for running the model is:

fit<- stan(model_code = code_above, data = your_data, iter= 1000, chains = 4)