Type:	Package
Title:	Models for Correlation Matrices Based on Graphs
Version:	0.1.15
Maintainer:	Elias Teixeira Krainski <eliaskrainski@gmail.com>
Description:	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:10.1007/s10260-025-00788-y>. 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.
Additional_repositories:	https://inla.r-inla-download.org/R/testing
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Depends:	R (≥ 4.3), Matrix, INLAtools, graph, numDeriv
Imports:	methods, stats, utils, Rgraphviz
Suggests:	knitr, INLA (≥ 25.12.16)
BuildVignettes:	true
VignetteBuilder:	knitr
Packaged:	2026-01-15 08:07:15 UTC; eliask
Author:	Elias Teixeira Krainski [cre, aut, cph], Denis Rustand [aut, cph], Anna Freni-Sterrantino [aut, cph], Janet van Niekerk [aut, cph], Haavard Rue’ [aut]
Repository:	CRAN
Date/Publication:	2026-01-15 08:40:01 UTC

Compute the KLD between two multivariate Gaussian distributions, assuming equal mean vector

Description

Compute the KLD between two multivariate Gaussian distributions, assuming equal mean vector

Usage

KLD10(C1, C0, L1, L0)

Arguments

Details

By assuming equal mean vector we have

KLD = 0.5( tr(C0^{-1}C1) -p - log(|C1|) + log(|C0|) )

The Laplacian of a graph

Description

The (symmetric) Laplacian of a graph is a square matrix with dimention equal the number of nodes. It is defined as

L_{ij} = n_i \textrm{ if } i=j, -1 \textrm{ if } i\sim j, 0 \textrm{ otherwise}

where i~j means that there is an edge between nodes i and j and n_i is the number of edges including node i.

Usage

Laplacian(x)

## Default S3 method:
Laplacian(x)

## S3 method for class 'matrix'
Laplacian(x)

Arguments

Value

matrix as the Laplacian of a graph

Methods (by class)

• Laplacian(default): The Laplacian default method (none)

• Laplacian(matrix): The Laplacian of a matrix

Compute the (lower triangle) Cholesky of the initial precision Q0.

Description

Compute the (lower triangle) Cholesky of the initial precision Q0.

Usage

Lprec0(theta, p, itheta, d0)

Arguments

Details

The (lower triangle) Cholesky factor of the initial precision for a correlation matrix contains the parameters in the non-zero elements of the lower triangle side of the precision matrix. The filled-in elements are computed from them using fillLprec().

Value

lower triangular matrix

Information for a base model for correlation matrices

Description

The basecor class contain a correlation matrix base, the parameter vector theta, that generates or is generated by base, the dimention p, the index itheta for theta in the (lower) Cholesky, and the Hessian around it I0, see details.

Usage

basecor(base, p, parametrization = "cpc", itheta)

## S3 method for class 'numeric'
basecor(base, p, parametrization = "cpc", itheta)

## S3 method for class 'matrix'
basecor(base, p, parametrization = "cpc", itheta)

## S3 method for class 'basecor'
print(x, ...)

Arguments

Details

For 'parametrization' = "CPC" or 'parametrization' = "cpc": The Canonical Partial Correlation - CPC parametrization, Lewandowski, Kurowicka, and Joe (2009), compute r[k] = tanh(\theta[k]), for k=1,...,m, and the two p\times p matrices

A = \left[ \begin{array}{ccccc} 1 & & & & \\ r_1 & 1 & & & \\ r_2 & r_p & 1 & & \\ \vdots & \vdots & \ddots & \ddots & \\ r_{p-1} & r_{2p-3} & \ldots & r_m & 1 \end{array} \right] \textrm{ and } B = \left[ \begin{array}{ccccc} 1 & & & & \\ \sqrt{1-r_1^2} & 1 & & & \\ \sqrt{1-r_2^2} & \sqrt{1-r_p^2} & 1 & & \\ \vdots & \vdots & \ddots & \ddots & \\ \sqrt{1-r_{p-1}^2} & \sqrt{r_{2p-3}^2} & \ldots & \sqrt{1-r_m^2} & 1 \end{array} \right]

The matrices A and B are then used to build the Cholesky factor of the correlation matrix, given as

L = \left[ \begin{array}{ccccc} 1 & 0 & 0 & \ldots & 0\\ A_{2,1} & B_{2,1} & 0 & \ldots & 0\\ A_{3,1} & A_{3,2}B_{3,1} & B_{3,1}B_{3,2} & & \vdots \\ \vdots & \vdots & \ddots & \ddots & 0\\ A_{p,1} & A_{p,2}B_{p,1} & \ldots & A_{p,p-1}\prod_{k=1}^{p-1}B_{p,k} & \prod_{k=1}^{p-1}B_{p,k} \end{array} \right]

Note: The determinant of the correlation matriz is

\prod_{i=2}^p\prod_{j=1}^{i-1}B_{i,j} = \prod_{i=2}^pL_{i,i}

For 'parametrization' = "SAP" or 'parametrization' = "sap": The Standard Angles Parametrization - SAP, as described in Rapisarda, Brigo and Mercurio (2007), compute x[k] = \pi/(1+\exp(-\theta[k])), for k=1,...,m, and the two p\times p matrices

A = \left[ \begin{array}{ccccc} 1 & & & & \\ \cos(x_1) & 1 & & & \\ \cos(x_2) & \cos(x_p) & 1 & & \\ \vdots & \vdots & \ddots & \ddots & \\ \cos(x_{p-1}) & \cos(x_{2p-3}) & \ldots & \cos(x_m) & 1 \end{array} \right] \textrm{ and } B = \left[ \begin{array}{ccccc} 1 & & & & \\ \sin(x_1) & 1 & & & \\ \sin(x_2) & \sin(x_p) & 1 & & \\ \vdots & \vdots & \ddots & \ddots & \\ \sin(x_{p-1}) & \sin(x_{2p-3}) & \ldots & \sin(x_m) & 1 \end{array} \right]

The decomposition of the Hessian matrix around the base model, I0, formally \mathbf{I}(\theta_0), is numerically computed. This element has the following attributes: 'h.5' as \mathbf{I}^{1/2}(\theta_0), and 'hneg.5' as \mathbf{I}^{-1/2}(\theta_0).

Value

a basecor object

Functions

• basecor(): Build a basecor object.

• basecor(numeric): Build a basecor from the parameter vector.

• basecor(matrix): Build a basecor from a correlation matrix.

• print(basecor): Print method for 'basecor'

References

Rapisarda, Brigo and Mercurio (2007). Parameterizing correlations: a geometric interpretation. IMA Journal of Management Mathematics (2007) 18, 55-73. <doi 10.1093/imaman/dpl010>

Lewandowski, Kurowicka and Joe (2009) Generating Random Correlation Matrices Based on Vines and Extended Onion Method. Journal of Multivariate Analysis 100: 1989–2001. <doi: 10.1016/j.jmva.2009.04.008>

Simpson, et. al. (2017) Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statist. Sci. 32(1): 1-28 (February 2017). <doi: 10.1214/16-STS576>

Examples

library(graphpcor)

## A correlation matrix
c0 <- matrix(c(1,.8,-.625, 0.8,1,-.5, -0.625,-.5,1), 3)

## build the 'basecor'
pc.c0 <- basecor(c0) ## base as matrix
pc.c0

## elements
pc.c0$base
pc.c0$theta
pc.c0$I0

## from 'theta' 
th0 <- pc.c0$theta
pc.th0 <- basecor(th0) ## base as vector
pc.th0

## numerically the same
all.equal(c0, pc.th0$base)

## from a numeric vector (theta)
th2 <- c(-1, -0.5)
b2 <- basecor(th2, p = 3, itheta = c(2,3))
b2

## from the correlation matrix
b2c <- basecor(b2$base, itheta = c(2,3))

all.equal(th2, b2c$theta, tol = 1e-4)

## Hessian around the base (and its decomposition, etc.)
b2$I0

Internal functions used by basecor

Description

Internal functions used by basecor

Usage

cholcor(theta, p, itheta, parametrization = "cpc")

Hcorrel(theta, p, parametrization, itheta, C0, decomposition, ...)

Arguments

Value

matrix with lower triangle as the Cholesky factor of a correlation matrix if parametrization is "cpc" or "sap" and of a precision matrix (of a correlation matrix) if parametrization is 'itp' (with 'd0' as the diagonal elements).

list containing the hessian, its 'square root', inverse 'square root' along with the decomposition used

Functions

• cholcor(): Cholesky parametrization for a correlation matrix

• Hcorrel(): Evaluate the hessian of the KLD for a correlation model around a base model.

Information for a base model for correlation matrices

Description

The basepcor class contain a correlation matrix base, the parameter vector theta, that generates or is generated by base, the dimension p, the index itheta for theta in the (lower) Cholesky, and the Hessian around it I0, see details.

Usage

basepcor(base, p, itheta, d0)

## S3 method for class 'numeric'
basepcor(base, p, itheta, d0)

## S3 method for class 'matrix'
basepcor(base, p, itheta, d0)

## S3 method for class 'basepcor'
print(x, ...)

Arguments

Details

The Inverse Transform Parametrization - ITP, is applied by starting with a

\mathbf{L}^{(0)} = \left[ \begin{array}{ccccc} \textrm{p} & 0 & 0 & \ldots & 0 \\ \theta_1 & \textrm{p-}1 & 0 & \ldots & 0 \\ \theta_2 & \theta_p & \textrm{p-}2 & \ddots & \vdots \\ \vdots & \vdots & \ddots & \ddots & 0 \\ \theta_{p-1} & \theta_{2p-3} & \ldots & \theta_m & 1 \end{array}\right] .

Then compute \mathbf{Q}^{(0)} = \mathbf{L}\mathbf{L}^{T}, \mathbf{V}^{(0)} = (\mathbf{Q}^{(0)})^{-1} and s_{i}^{(0)} = \sqrt{\mathbf{V}_{i,i}^{(0)}}, and define \mathbf{S}^{(0)} = diag(s_1^{(0)},\ldots,s_p^{(0)}) in order to have \mathbf{C}= \mathbf{S}^{-1}\mathbf{V}^{(0)}\mathbf{S}^{-1}.

The decomposition of the Hessian matrix around the base model, I0, formally \mathbf{I}(\theta_0), is numerically computed. This element has the following attributes: 'h.5' as \mathbf{I}^{1/2}(\theta_0), and 'hneg.5' as \mathbf{I}^{-1/2}(\theta_0).

Value

a basepcor object

a basepcor object

Functions

• basepcor(): Build a basepcor object.

• basepcor(numeric): Build a basepcor from the parameter vector.

• basepcor(matrix): Build a basepcor from a correlation matrix.

• print(basepcor): Print method for 'basepcor'

Examples

## p = 3, m = 2
bc <- basepcor(c(-1,-1), p = 3, itheta = c(2,3))
bc

round(solve(bc$base), 4)

all.equal(bc, basepcor(bc$base, itheta =c(2,3)))

## p = 4, m = 4
th2 <- c(0.5,-1,0.5,-0.3)
ith2 <- c(2,3,8,12)
b2 <- basepcor(th2, p = 4, itheta = ith2)
b2

Sparse(solve(b2$base), zeros.rm = TRUE)

all.equal(th2, basepcor(b2$base, itheta = ith2)$theta)

## Hessian around the base (and its decomposition, etc.)
b2$I0

Build an cgeneric model for the LKG prior on correlation matrix.

Description

Build an cgeneric model for the LKG prior on correlation matrix.

Usage

cgeneric_LKJ(
  n,
  eta,
  sigma.prior.reference = rep(1, n),
  sigma.prior.probability = rep(NA, n),
  ...
)

Arguments

Details

It uses the Cannonical Partial Correlation (CPC), see basepcor() for details.

Value

a cgeneric object, see INLAtools::cgeneric() for details.

See Also

dLKJ() and basepcor()

Examples

## a cgeneric model for the LKJ prior
## for theta from the CPC parametrization
cglkj <- cgeneric(
    model = "LKJ", n = 3, eta = 2,
    useINLAprecomp = FALSE)##!is.na(packageCheck("INLA", "25.12.16")))

## correlation matrix, p = 3
cc <- matrix(c(1,.8,-.625, 0.8,1,-.5, -0.625,-.5,1), 3)

## CPC parametrization: C(theta)
(bb <- basecor(cc))
th <- bb$theta

## p(theta | eta)
prior(cglkj, theta = th)

## precision inverse
solve(prec(cglkj, theta = th))
solve(prec(cglkj, theta = c(0,0,0)))
solve(prec(cglkj, theta = c(1,1,1)))

Build an cgeneric to implement the Wishart prior for a precision matrix.

Description

Build an cgeneric to implement the Wishart prior for a precision matrix.

Usage

cgeneric_Wishart(n, dof, R, debug = FALSE, useINLAprecomp = TRUE, shlib = NULL)

Arguments

Details

For a random p\times p precision matrix Q, given the parameters d and R, respectively scalar degree of freedom and the inverse scale p\times p matrix the Wishart density is

|Q|^{(d-p-1)/2}\textrm{e}^{-tr(RQ)/2}|R|^{p/2}2^{-dp/2}\Gamma_p(n/2)^{-1}

Value

a cgeneric, INLAtools::cgeneric() object.

Build an cgeneric for a graph, see graphpcor()

Description

From either a graph (see INLAtools::graph()) or a square matrix (used as a graph), creates an cgeneric (see INLAtools::cgeneric()) to implement the Penalized Complexity prior using the Kullback-Leibler divergence - KLD from a base graphpcor.

Usage

cgeneric_graphpcor(
  model,
  lambda,
  base,
  sigma.prior.reference,
  sigma.prior.probability,
  params.id,
  cor.params.fixed,
  ...
)

Arguments

Value

cgeneric object.

See Also

graphpcor()

Build an cgeneric object to implement the PC prior, proposed on Simpson et. al. (2007), as an informative prior, see details in basecor().

Description

Build an cgeneric object to implement the PC prior, proposed on Simpson et. al. (2007), as an informative prior, see details in basecor().

Usage

cgeneric_pc_correl(
  n,
  lambda,
  base,
  sigma.prior.reference,
  sigma.prior.probability,
  params.id,
  cor.params.fixed,
  ...
)

Arguments

Value

a cgeneric object, see INLAtools::cgeneric() for details.

References

Daniel Simpson, H\aa vard Rue, Andrea Riebler, Thiago G. Martins and Sigrunn H. S\o rbye (2017). Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statistical Science 2017, Vol. 32, No. 1, 1–28. <doi 10.1214/16-STS576>

Build an cgeneric object to implement the PC-prior of a precision matrix as inverse of a correlation matrix.

Description

Build an cgeneric object to implement the PC-prior of a precision matrix as inverse of a correlation matrix.

Usage

cgeneric_pc_prec_correl(
  n,
  lambda,
  theta.base,
  debug = FALSE,
  useINLAprecomp = TRUE,
  shlib = NULL
)

Arguments

Details

The Canonical Partial Correlation - CPC parametrization, Lewandowski, Kurowicka, and Joe (2009). step 1: q_i = tanh(\theta_i) step 2:

z = \left[ \begin{array}{ccccc} 1 & & & & \\ q_1 & 1 & & & \\ q_2 & q_n & & & \\ \vdots & & \ldots & \ddots & \\ q_{n-1} & q_{2n-3} \ldots & q_m & 1 \end{array} \right]

step 3: compute L such that the correlation matrix is

C = LL'

, a n \times n (lower triangle) matrix

L_{i,j} = \left\{\begin{array}{cc} 0 & i>j\\ 1 & i=j=1\\ z_{i,j} & j=1 \\ prod_{k=1}^{j-1}\sqrt(1-z_{k,j^2}) & 1<i=j \\ z_{i,j}prod_{k=1}^{j-1}\sqrt(1-z_{k,j}^2) & 1<j<i \end{array}\right.

The prior of the correlation matrix is given as

p(C) = |J_m|*l*exp(-l*r)/(2*pi^(m-1)

following a bijective transformation from

\theta[1:m] \in R^{m} to \{r, \phi[1:(m-1)]\}

where \phi[1:(m-1)] are angles and r is the radius of a m-sphere. That is

r ~ Exponential(\lambda)

\phi[j] ~ Uniform(0, pi), j=1...m-2

\phi[m-1] ~ Uniform(0, 2pi)

J_m is the Jacobian of this transformation

Value

a cgeneric object, see INLAtools::cgeneric() for details.

References

Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. “Generating Random Correlation Matrices Based on Vines and Extended Onion Method.” Journal of Multivariate Analysis 100: 1989–2001.

Build an cgeneric for treepcor())

Description

This creates an cgeneric (see INLAtools::cgeneric()) containing the necessary data to implement the penalized complexity prior for a correlation matrix considering a three as proposed in Sterrantino et. al. 2025 doi:10.1007/s10260-025-00788-y.

Usage

cgeneric_treepcor(
  model,
  lambda,
  sigma.prior.reference,
  sigma.prior.probability,
  ...
)

Arguments

Details

The correlation prior as in the paper depends on the lambda value. The prior for each sigma_i is the Penalized-complexity prior which can be defined from the following probability statement P(sigma > U) = a. where "U" is a reference value and "a" is a probability. The values "U" and probabilities "a" for each sigma_i are passed in the sigma.prior.reference and sigma.prior.probability arguments. If a=0 then U is taken to be the fixed value of the corresponding sigma. E.g. if there are three sigmas in the model and one supply sigma.prior.reference = c(1, 2, 3) and sigma.prior.probability = c(0.05, 0.0, 0.01) then the sigma is fixed to 2 and not estimated.

Value

cgeneric/cgeneric object.

See Also

treepcor() and INLAtools::cgeneric()

The LKJ density for a correlation matrix

Description

The LKJ density for a correlation matrix

Usage

dLKJ(R, eta, log = FALSE)

Arguments

Value

numeric as the (log) density

Function to fill-in a Cholesky matrix

Description

Function to fill-in a Cholesky matrix

Usage

fillLprec(L, lfi)

Arguments

Value

lower triangular matrix with the filled-in elements thus Q0 can be computed.

graphpcor: correlation from nodes and edges

Description

A graphpcor is a graph where a node represents a variable and an edge represent a conditional distribution. The correlation built from a graphpcor consider the parameters for the Cholesky of a precision matrix, whose non-zero pattern is given from the graph.

Usage

graphpcor(...)

## S3 method for class 'formula'
graphpcor(...)

## S3 method for class 'matrix'
graphpcor(...)

## S3 method for class 'graphpcor'
print(x, ...)

## S3 method for class 'graphpcor'
summary(object, ...)

## S3 method for class 'graphpcor'
dim(x, ...)

## S4 method for signature 'graphpcor'
edges(object, which, ...)

## S4 method for signature 'graphpcor,ANY'
plot(x, y, ...)

## S3 method for class 'graphpcor'
Laplacian(x)

## S4 method for signature 'graphpcor'
vcov(object, ...)

## S3 method for class 'graphpcor'
prec(model, ...)

## S3 method for class 'graphpcor'
cgeneric(model, ...)

## S3 method for class 'matrix'
cgeneric(model, ...)

Arguments

Value

a graphpcor object

Methods (by generic)

• edges(graphpcor): Extract the edges of a graphcor to be used for plot

• plot(x = graphpcor, y = ANY): The plot method for graphpcor

• vcov(graphpcor): The vcov method for a graphpcor

Functions

• graphpcor(): The graphpcor generic method for graphpcor

• graphpcor(formula): Each term to represent a node, and each ~ to represent an edge.

• graphpcor(matrix): Build a graphpcor from a matrix

• print(graphpcor): The print method for graphpcor

• summary(graphpcor): The summary method for graphpcor

• dim(graphpcor): The dim method for graphpcor

• Laplacian(graphpcor): The Laplacian method for a graphpcor

• prec(graphpcor): The precision method for 'graphpcor'

• cgeneric(graphpcor): The cgeneric method for graphpcor uses cgeneric_graphpcor()

• cgeneric(matrix): The cgeneric method for matrix uses cgeneric_graphpcor()

Examples

library(graphpcor)

par(mfrow = c(2, 3), mar = c(0,0,0,0))
plot(graphpcor(x~y+v, z~y+v))
plot(graphpcor(x~y,x~v,z~y,z~v))
plot(graphpcor(x~y, v~x, y~z, z~v))
plot(graphpcor(y~x, v~x, z~y, z~v))
plot(graphpcor(y~x+z, v~z+x))
plot(graphpcor(y~x+z, v~x, z~v))

## the graph in Example 2.6 of the GMRF book
g <- graphpcor(x ~ y + v, z ~ y + v)

class(g)
g

par(mfrow=c(1,1))
plot(g)

summary(g) ## the graph: nodes and edges (nodes ordered as given)

ne <- dim(g)
ne

## sometimes we need it
G <- Laplacian(g)
G 

## alternatively
all.equal(G,
          Laplacian(graphpcor(x~y, v~x, y~z, z~v)))
all.equal(G,
          Laplacian(graphpcor(x~y, x~v, z~y, v~z)))

plot(graphpcor(G)) ## from a matrix

## base model (theta for lower triangle Cholesky)
theta0l <- rep(-0.5, ne[2])

## vcov() method for graphpcor computes the correlation
##  if only theta for lower of L is provided
C0 <- vcov(g, theta = theta0l)
C0

## the precision for a correlation matrix
Q0 <- prec(g, theta = theta0l)
Q0

all.equal(C0, as.matrix(solve(Q0)))

## the Hessian matrix around a base model
I0 <- basepcor(theta0l, p = ne[1], itheta = g)
I0

## a base model can also be a matrix
## however it shall give a precision with
## same sparse pattern as the graph
all.equal(I0, basepcor(C0, p = ne[1], itheta = g))

## the 'iid' case would be
vcov(g, theta = rep(0, ne[2]))
vcov(g, theta = rep(0, sum(ne)))

## marginal variance specified throught standard errors
sigmas <- c(0.3, 0.7, 1.2, 0.5)
## the covariance
vcov(g, theta = c(log(sigmas), rep(0, ne[2]))) ## IID
vcov(g, theta = c(log(sigmas), theta0l))

vcov(g, theta = rep(-3, ne[2])) ## no edge 2~3 but high correlation!!!

Evaluate the hessian of the KLD for a graphpcor correlation model around a base model.

Description

Evaluate the hessian of the KLD for a graphpcor correlation model around a base model.

Usage

## S3 method for class 'graphpcor'
hessian(func, x, method = "Richardson", method.args = list(), ...)

Arguments

Value

list containing the hessian, its 'square root', inverse 'square root' along with the decomposition used

Internal functions to map between Euclidean and spherical coordinates

Description

Internal functions to map between Euclidean and spherical coordinates

Usage

rphi2x(rphi)

x2rphi(x)

rtheta(n, lambda = 1, R, theta.base)

dtheta(theta, lambda, theta.base, H.elements)

Arguments

Details

For details, please see the wikipedia entry on 'N-sphere' at N-sphere

Functions

• rphi2x(): Map between spherical to Euclidean coordinates

• x2rphi(): Transform from Euclidean coordinates to spherical

• rtheta(): Drawn samples from the PC-prior for correlation

• dtheta(): PC-prior density for the correlation matrix

treepcor: correlation from tree

Description

A tree with two kind of nodes, parents and children. The parents are nodes with children. The children are nodes with no children. This is used to model correlation matrices, where parents represent latent variables, and children represent the variables of interest.

Usage

treepcor(...)

## S3 method for class 'treepcor'
print(x, ...)

## S3 method for class 'treepcor'
summary(object, ...)

## S3 method for class 'treepcor'
dim(x, ...)

## S4 method for signature 'treepcor'
drop1(object)

## S4 method for signature 'treepcor'
edges(object, which, ...)

## S4 method for signature 'treepcor,ANY'
plot(x, y, ...)

## S3 method for class 'treepcor'
prec(model, ...)

etreepcor2precision(d.el)

## S4 method for signature 'treepcor'
vcov(object, ...)

etreepcor2variance(d.el)

## S3 method for class 'treepcor'
cgeneric(model, ...)

Arguments

Details

In the formula, the left side are parent variables, and the right side include all the children and parents that are also children. The children variables are those with an ancestor (parent), and are identified as c1, ..., cn, where n is the total number of children variables. The parent variables are identified as p1, ..., pm, where the m is the number of parent variables. The main parent (first) should be identified as p1. Except p1 all the other parent variables have an ancestor, which is a parent variable.

Value

a treepcor object

Methods (by generic)

• drop1(treepcor): The drop1 method for a treepcor

• edges(treepcor): Extract the edges of a treepcor to be used for plot

• plot(x = treepcor, y = ANY): The plot method for a treepcor

• vcov(treepcor): The vcov method for a treepcor

Functions

• treepcor(): A tree from a formula for each parent.

• print(treepcor): The print method for a treepcor

• summary(treepcor): The summary method for a treepcor

• dim(treepcor): The dim for a treepcor

• prec(treepcor): The prec for a treepcor

• etreepcor2precision(): Internal function to extract elements to build the precision from the treepcor edges.

• etreepcor2variance(): Internal function to extract elements to build the covariance matrix from a treepcor.

• cgeneric(treepcor): The cgeneric method for treepcor, uses cgeneric_treepcor()

Examples

## for details see
## https://link.springer.com/article/10.1007/s10260-025-00788-y

library(graphpcor)

if(FALSE) {
    
### examples of what is not allowed
    treepcor(p1 ~ p2)
    treepcor(p1 ~ c2)
    
    treepcor(
        p1 ~ c1 + c2,
        p2 ~ c3)
    
    treepcor(
        p1 ~ c1 + c2,
        p2 ~ p1 + c2 + c3)
    
    treepcor(
        p1 ~ c1 + c2,
        p2 ~ p3 + c2 + c3)
    
    treepcor(
        p1 ~ p2 + c1 + c2,
        p2 ~ c2 + c3)

}

### allowed cases

## 3 children and 1 parent
g1 <- treepcor(p1 ~ c1 + c2 - c3)

g1

dim(g1)

summary(g1)

plot(g1)

prec(g1)

(q1 <- prec(g1, theta = c(0)))

v1 <- chol2inv(chol(q1))

v1

cov2cor(v1)

vcov(g1)
vcov(g1, theta = 0)
vcov(g1, theta = -1)
vcov(g1, theta = 1)

cov2cor(vcov(g1))
cov2cor(vcov(g1, theta = -1))
cov2cor(vcov(g1, theta = 1))

## 4 children and 2 parent
g2 <- treepcor(
    p1 ~ p2 + c1 + c2,
    p2 ~ c3 - c4)
g2
dim(g2)
summary(g2)

plot(g2)

prec(g2)
prec(g2, theta = c(0, 0))
prec(g2, theta = c(-1, 1))

cov2cor(solve(prec(g2, theta = c(0,0))))
vcov(g2, theta = c(0,0))
vcov(g2, theta = c(log(4:1), 0,0))

vcov(g2)

g2

## 4 children and 2 parent (notice the signs)
g3 <- treepcor(
    p1 ~ -p2 + c1 + c2,
    p2 ~ -c3 + c4)
g3
dim(g3)
summary(g3)

summary(g2)
summary(g3)

par(mfrow = c(1, 2), mar = c(0,0,0,0))
plot(g2)
plot(g3)

prec(g2)
prec(g3)

prec(g2, theta = c(0, 0))
prec(g3, theta = c(0, 0))

vcov(g2, theta = c(0, 0))
vcov(g3, theta = c(0, 0))

g3


drop1(g2)
drop1(g3) 

prec(g3)
prec(drop1(g3))

n3 <- dim(g3)[1]
all.equal(
    solve(prec(g2, theta = c(0, 0)))[1:n3, 1:n3],
    solve(prec(g3, theta = c(0, 0)))[1:n3, 1:n3]
)

vcov(g2, theta = c(0,0))
vcov(g3, theta = c(0,0))