Lprec

fillLprec

theta2Lprec2C

Precision matrix parametrization helper functions.

Implement some models for
correlation/covariance matrices including two approaches
to model correlation matrices from a graphical structure.
One use latent parent variables as proposed in
Sterrantino et. al. (2024) <doi:10.48550/arXiv.2312.06289>.
The other uses a graph to specify conditional
relations between the variables.
The graphical structure makes correlation matrices
interpretable and avoids the quadratic increase of
parameters as a function of the dimension.
In the first approach a natural sequence of simpler
models along with a complexity penalization is used.
The second penalizes deviations from a base model.
These can be used as prior for model parameters,
considering C code through the 'cgeneric' interface
for the 'INLA' package (<https://www.r-inla.org>).
This allows one to use these models as building
blocks combined and to other latent Gaussian models
in order to build complex data models.

Elias Teixeira Krainski

graphpcor

Models for Correlation Matrices Based on Graphs

Elias Krainski

Denis Rustand

Anna Freni-Sterrantino

Janet van Niekerk

Haavard Rue’

Lprec function

<dl><dt>theta</dt>
<dd>numeric vector of length <code>m</code>.</dd>
<dt>p</dt>
<dd>numeric giving the dimention of Q.
If missing, <code>p = (1+sqrt(1+8*length(theta)))</code>
and Q is assumed to be dense.</dd>
<dt>ilowerL</dt>
<dd>numeric vector as index
to (lower) L to be filled with <code>theta</code>.
Default is missing and Q is assumed to be dense.</dd>
<dt>L</dt>
<dd>matrix as the lower triangle
containing the Cholesky decomposition of
a precision matrix</dd>
<dt>lfi</dt>
<dd>indicator of fill-in elements</dd></dl>

Arguments

<ul>
<li><code>fillLprec()</code>: Function to fill-in a Cholesky matrix</li>
<li><code>theta2Lprec2C()</code>: Internal function to build C</li>
</ul>

Functions

Precision matrix parametrization helper functions. — Lprec

<dl>

<dt>theta</dt>
<dd>numeric vector of length <code>m</code>.</dd>


<dt>p</dt>
<dd>numeric giving the dimention of Q.
If missing, <code>p = (1+sqrt(1+8*length(theta)))</code>
and Q is assumed to be dense.</dd>


<dt>ilowerL</dt>
<dd>numeric vector as index
to (lower) L to be filled with <code>theta</code>.
Default is missing and Q is assumed to be dense.</dd>


<dt>L</dt>
<dd>matrix as the lower triangle
containing the Cholesky decomposition of
a precision matrix</dd>


<dt>lfi</dt>
<dd>indicator of fill-in elements</dd>

</dl>

Lprec: Precision matrix parametrization helper functions.

Description

Usage

Value

Arguments

Functions

Details

Examples