# Generating values from multivariate normal distribution

**URL:** <https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044>\
**Category:** Modeling\
**Tags:** cognitive-science\
**Created:** [December 21, 2018, 12:31am UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044 "2018-12-21T00:31:33Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![gfergadiotis](https://avatars.discourse-cdn.com/v4/letter/g/4da419/32.png) [@gfergadiotis](https://discourse.mc-stan.org/u/gfergadiotis)\
**Post date:** [December 21, 2018, 12:31am UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044/1 "2018-12-21T00:31:33Z")

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Dear Stan users,

We are running a correlation model to compare assessment results from two cognitive tests.

The correlation model runs fine and without errors. We are now trying to run posterior predictive checks on the model and are running into a great deal of trouble simulating data in the generated quantities block. Ultimately, we would like to generate simulated datasets of the same size are the observed dataset (47 patient, 2 observations per patient) at each iteration.

Then, we could compare the generated data against the simulated datasets and/or derive statistics (e.g., correlation from the simulated datasets) and compare them to the correlation based on the observed data.

Currently, we are able to simulate a single vector of simulated test scores per iteration. We could hard code this 47 times. However, we were wondering if there is a more efficient way of doing that.

```
model <- "
// Pearson Correlation
data { 
int<lower=0> n;
vector[2] x[n];
}
parameters {
vector[2] mu;
vector<lower=0>[2] sigma;

real<lower=-1,upper=1> r;
} 
transformed parameters {
cov_matrix[2] T;
// Reparameterization
T[1,1] = square(sigma[1]);
T[1,2] = r * sigma[1] * sigma[2];
T[2,1] = r * sigma[1] * sigma[2];
T[2,2] = square(sigma[2]);
}
model {
// Priors
mu ~ normal(0, 100);
sigma ~ cauchy(0,3);
r ~ uniform(-1, 1);
// Data
x ~ multi_normal(mu, T);
}
generated quantities{
vector[2] PPC1;
vector[2] PPC2;
vector[2] PPC3;
PPC1 = multi_normal_rng(mu, T);
PPC2 = multi_normal_rng(mu,T);
PPC3 = multi_normal_rng(mu,T);
}"
data2 <- extract(samples)
samples<- stan(model_code=model,   
               data=data,
               #init=myinits, # If not specified, gives random inits
               #pars=parameters,
               iter=500,
               warmup = 10,
               chains=2, 
               thin=1,
               cores = 4,
               seed = 100
)

```

---

<div class="post-metadata">

**Author:** ![andre.pfeuffer](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andre.pfeuffer](https://discourse.mc-stan.org/u/andre.pfeuffer)\
**Post date:** [December 21, 2018, 1:25am UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044/2 "2018-12-21T01:25:52Z")

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```
generated quantities{
vector[2] PPC1[n];
vector[2] PPC2[n];
vector[2] PPC3[n];
for(i 1:n) {
PPC1[i] = multi_normal_rng(mu, T);
PPC2[i] = multi_normal_rng(mu,T);
PPC3[i] = multi_normal_rng(mu,T);
}

```

I hope I understood you right.

---

<div class="post-metadata">

**Author:** ![andre.pfeuffer](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andre.pfeuffer](https://discourse.mc-stan.org/u/andre.pfeuffer)\
**Post date:** [December 21, 2018, 1:58am UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044/4 "2018-12-21T01:58:43Z")

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was a typo  
`for(i in 1:n)`

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<div class="post-metadata">

**Author:** ![Alexander\_Swiderski](https://avatars.discourse-cdn.com/v4/letter/a/b5a626/32.png) [@Alexander\_Swiderski](https://discourse.mc-stan.org/u/Alexander_Swiderski)\
**Post date:** [December 21, 2018, 1:59am UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044/5 "2018-12-21T01:59:53Z")

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ha! goes to show where I am at ;)

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<div class="post-metadata">

**Author:** ![gfergadiotis](https://avatars.discourse-cdn.com/v4/letter/g/4da419/32.png) [@gfergadiotis](https://discourse.mc-stan.org/u/gfergadiotis)\
**Post date:** [December 21, 2018, 7:44pm UTC](https://discourse.mc-stan.org/t/generating-values-from-multivariate-normal-distribution/7044/6 "2018-12-21T19:44:00Z")

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Thank you! That worked.