In the Stan manual section **4.5. Missing Multivariate Data**, the example likelihood for a model with two outcomes and missing values looks like this:

```
y[ns12] ~ multi_normal(mu, Sigma);
y[ns1] ~ normal(mu[1], sqrt(Sigma[1, 1]));
y[ns2] ~ normal(mu[2], sqrt(Sigma[2, 2]));
```

… where the `multi_normal`

is applied for rows with both outcomes present, and the `normal`

s applied when only outcome 1 or 2 present respectively.

My question is, if you are using the cholesky decomposition form of the multivariate normal, can this subsetting by done in an analgous fashion ? In other words, if instead of `Sigma`

I have an `L_Sigma`

formed by cholesky decomposition, is it legitimate to do this:

```
y[ns12] ~ multi_normal_cholesky(mu, L_Sigma);
y[ns1] ~ normal(mu[1], sqrt(L_Sigma[1, 1]));
y[ns2] ~ normal(mu[2], sqrt(L_Sigma[2, 2]));
```

Or do I need to manipulate `L_Sigma`

first ? Or is it just best to stay with the `multi_normal`

, even though that may come with performance deficits ?