TMB Documentation  v1.9.2
density::UNSTRUCTURED_CORR_t< scalartype_ > Class Template Reference

Multivariate normal distribution with unstructered correlation matrix. More...

#include <density.hpp>

Public Member Functions inherited from density::MVNORM_t< scalartype_ >
matrixtype cov ()
Covariance matrix extractor. More...

scalartype operator() (vectortype x)
Evaluate the negative log density.

scalartype operator() (vectortype x, vectortype keep)
Evaluate projected negative log density. More...

## Detailed Description

### template<class scalartype_> class density::UNSTRUCTURED_CORR_t< scalartype_ >

Multivariate normal distribution with unstructered correlation matrix.

Class to evaluate the negative log density of a multivariate Gaussian variable with unstructured symmetric positive definite correlation matrix (Sigma). The typical application of this is that you want to estimate all the elements of Sigma, in such a way that the symmetry and positive definiteness constraint is respected. We parameterize S via a lower triangular matrix L with unit diagonal i.e. we need (n*n-n)/2 parameters to describe an n dimensional correlation matrix.

For instance in the case n=4 the correlation matrix is given by

$\Sigma = D^{-\frac{1}{2}}LL'D^{-\frac{1}{2}}$

where

$L=\begin{pmatrix} 1 \\ \theta_0 & 1 \\ \theta_1 & \theta_2 & 1 \\ \theta_3 & \theta_4 & \theta_5 & 1 \end{pmatrix}$

(lower triangle filled row-wise) and

$D=diag(LL')$

Example:

// Construct density object of dimension 4
vector<Type> theta(6);
UNSTRUCTURED_CORR_t<Type> nll(theta);
res = nll(x); // Evaluate neg. log density
Remarks
Sigma is available via MVNORM_t::cov , e.g.
nll.cov();
Sigma has 1's on its diagonal. To scale the variances we can use VECSCALE_t , e.g.
vector<Type> sds(4);
sds.fill(2.0); // Set all standard deviations to 2.0
res = VECSCALE_t(nll,sds)(x);
Examples:
multivariate_distributions.cpp, and sdv_multi_compact.cpp.

Definition at line 260 of file density.hpp.

The documentation for this class was generated from the following file: