# How to build a simple hierarchical model with different samples in Stan/rstan?

I’m a newbie in stan.

I’m trying to build a simple hierarchical model.

First of all I create five normally distributed samples for modelling with random mean and standard deviation.

library(rstan)

set.seed(10)

mus    = rnorm(5,2,2)
sigmas = rlnorm(5,3,1)

N=40
J=5
y = matrix(NA,nrow = N,ncol = J)

# make data matrix
for (i in 1:5) {
y[,i] = rnorm(N,mus[i],sigmas[i])
}

model = stan_model(paste0(dir,"NormalHierarchical.stan"))
fit = sampling(model,list(N=N,J=J,y=y),iter=200,chains=1)


In the data level each sample has a normal distribution N(\mu,\sigma).
In the process level, \mu \sim N(\tau,\omega) and \sigma \sim logN(\lambda,\delta).

Where logN is the lognormal distribution.

And the top level priors are:
\tau \sim N(0,1)
\omega \sim logN(0,1)
\lambda \sim N(0,1)
\delta \sim logN(0,1)

My stan code is as follows and doesn’t work

data {
int<lower=1> N; //salple length
int<lower=1> J; //number of samples
matrix[N,J] y;  //data matrix
}

parameters {
vector[J] mu;
vector[J] sigma;

real tau;
real<lower=0> omega;
real lambda;
real<lower=0> delta;
}

model {
//priors
tau ~ normal(0,1);
omega ~ lognormal(0,1);
lambda ~ normal(0,1);
delta ~ lognormal(0,1);

for(j in 1:J) {
mu[j] ~ normal(tau,omega);
sigma[j] ~ lognormal(lambda,delta);
y[,j] ~ normal(mu,sigma);
}
}


The error code

SAMPLING FOR MODEL 'NormalHierarchical' NOW (CHAIN 1).
Chain 1: Unrecoverable error evaluating the log probability at the initial value.
Chain 1: Exception: normal_lpdf: Location parameter has dimension = 5, expecting dimension = 40; a function was called with arguments of different scalar, array, vector, or matrix types, and they were not consistently sized;  all arguments must be scalars or multidimensional values of the same shape.  (in 'model31c0139f25ab_NormalHierarchical' at line 27)

[1] "Error in sampler\$call_sampler(args_list[[i]]) : "
[2] "  Exception: normal_lpdf: Location parameter has dimension = 5, expecting dimension = 40; a function was called with arguments of different scalar, array, vector, or matrix types, and they were not consistently sized;  all arguments must be scalars or multidimensional values of the same shape.  (in 'model31c0139f25ab_NormalHierarchical' at line 27)"
[4] "In readLines(file, warn = TRUE) :"
[5] "  incomplete final line found on '/.../NormalHierarchical.stan'"
error occurred during calling the sampler; sampling not done


I’m trying to make the output for a vector of posteriors for each sample i.e. mu[1],mu[2],mu[3]… and sigma[1],sigma[2],sigma[3]

Maybe a data matrix is not the right approach? As said, I’m only using stan since a few weeks.

The error indicates that

    y[,j] ~ normal(mu,sigma);


is expecting y[,] to be a vector with 5 elements. Changing

  matrix[N,J] y;  //data matrix


to

  matrix[J,N] y;  //data matrix


should fix it.