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, sqrt(Sigma[1, 1])); y[ns2] ~ normal(mu, sqrt(Sigma[2, 2]));
… where the
multi_normal is applied for rows with both outcomes present, and the
normals 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, sqrt(L_Sigma[1, 1])); y[ns2] ~ normal(mu, 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 ?