Type:	Package
Title:	Models for Correlation Matrices Based on Graphs
Version:	0.1.12
Maintainer:	Elias 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:10.48550/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.
Additional_repositories:	https://inla.r-inla-download.org/R/testing
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	yes
Depends:	R (≥ 4.3), Matrix, graph, numDeriv
Imports:	methods, stats, utils, Rgraphviz
Suggests:	INLA (≥ 24.02.09)
BuildVignettes:	true
Packaged:	2025-04-27 14:15:31 UTC; eliask
Author:	Elias 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:	2025-04-27 23:20:02 UTC

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(graph)

## Default S3 method:
Laplacian(graph)

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

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

Precision matrix parametrization helper functions.

Description

Precision matrix parametrization helper functions.

Usage

Lprec(theta, p, ilowerL)

fillLprec(L, lfi)

theta2Lprec2C(theta, p, ilowerL)

Arguments

Details

The precision matrix definition consider m parameters for the lower part of L. If Q is dense, then m = p(p-1)/2, else m = length(ilowerL). Then the precision is defined as Q(\theta) = L(\theta)L(\theta)^T

Value

matrix as the Cholesky factor of a precision matrix as the inverse of a correlation

a matrix whose elements at the lower triangle are the filled in elements of the Cholesky decomposition of a precision matrix and diagonal elements as 1:p.

Functions

• fillLprec(): Function to fill-in a Cholesky matrix

• theta2Lprec2C(): Internal function to build C

Examples

theta1 <- c(1, -1, -2)
Lprec(theta1)
theta2 <- c(0.5, -0.5, -1, -1)
Lprec(theta2, 4, c(2,4,7,12))

Build an inla.cgeneric object to implement the LKG prior for the correlation matrix.

Description

Build an inla.cgeneric object to implement the LKG prior for the correlation matrix.

Usage

cgeneric_LKJ(n, eta, debug = FALSE, useINLAprecomp = TRUE, libpath = NULL)

Arguments

Details

The parametrization uses the hypershere decomposition, as proposed in Rapisarda, Brigo and Mercurio (2007). consider \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 from \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 compute x[k] = pi/(1+exp(-theta[k])) organize it as a lower triangle of a n \times n matrix

| cos(x[i,j]) , j=1

B[i,j] = | cos(x[i,j])prod_{k=1}^{j-1}sin(x[i,k]), 2 <= j <= i-1

| prod_{k=1}^{j-1}sin(x[i,k]) , j=i

| 0 , j+1 <= j <= n

Result

\gamma[i,j] = -log(sin(x[i,j]))

KLD(R) = \sqrt(2\sum_{i=2}^n\sum_{j=1}^{i-1} \gamma[i,j]

Value

a inla.cgeneric, cgeneric() object.

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>

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

Description

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

Usage

cgeneric_Wishart(
  n,
  dof,
  R,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = 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 inla.cgeneric, cgeneric() object.

Build an inla.cgeneric to implement a model whose precision has a conditional precision parameter. See details. This uses the cgeneric interface that can be used as a model in a INLA f() model component.

Description

Build an inla.cgeneric to implement a model whose precision has a conditional precision parameter. See details. This uses the cgeneric interface that can be used as a model in a INLA f() model component.

Usage

cgeneric_generic0(
  R,
  param,
  constr = TRUE,
  scale = TRUE,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = NULL
)

cgeneric_iid(
  n,
  param,
  constr = FALSE,
  scale = TRUE,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = NULL
)

Arguments

Details

The precision matrix is defined as

Q = \tau R

where the structure matrix R is supplied by the user and \tau is the precision parameter. Following Sørbie and Rue (2014), if scale = TRUE the model is scaled so that

Q = \tau s R

where s is the geometric mean of the diagonal elements of the generalized inverse of R.

s = \exp{\sum_i \log((R^{-})_{ii})/n}

If the model is scaled, the geometric mean of the marginal variances, the diagonal of Q^{-1}, is one. Therefore, when the model is scaled, \tau is the marginal precision, otherwise \tau is the conditional precision.

Value

a inla.cgeneric, cgeneric() object.

Functions

• cgeneric_iid(): The cgeneric_iid() uses the cgeneric_generic0 with the structure matrix as the identity.

References

Sigrunn Holbek Sørbye and Håvard Rue (2014). Scaling intrinsic Gaussian Markov random field priors in spatial modelling. Spatial Statistics, vol. 8, p. 39-51.

Build an inla.cgeneric for a graph, see graphpcor()

Description

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

Usage

cgeneric_graphpcor(
  graph,
  lambda,
  base,
  sigma.prior.reference,
  sigma.prior.probability,
  params.id,
  low.params.fixed,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = NULL
)

Arguments

Value

a inla.cgeneric, cgeneric() object.

Build an inla.cgeneric to implement the PC prior, proposed on Simpson et. al. (2007), for the correlation matrix parametrized from the hypershere decomposition, see details.

Description

Build an inla.cgeneric to implement the PC prior, proposed on Simpson et. al. (2007), for the correlation matrix parametrized from the hypershere decomposition, see details.

Usage

cgeneric_pc_correl(
  n,
  lambda,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = NULL
)

Arguments

Details

The hypershere decomposition, as proposed in Rapisarda, Brigo and Mercurio (2007) consider \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 compute x[k] = pi/(1+exp(-\theta[k])) organize it as a lower triangle of a n \times n matrix

B[i,j] = \left\{\begin{array}{cc} cos(x[i,j]) & j=1 \\ cos(x[i,j])prod_{k=1}^{j-1}sin(x[i,k]) & 2 <= j <= i-1 \\ prod_{k=1}^{j-1}sin(x[i,k]) & j=i \\ 0 & j+1 <= j <= n \end{array}\right.

Result

\gamma[i,j] = -log(sin(x[i,j]))

KLD(R) = \sqrt(2\sum_{i=2}^n\sum_{j=1}^{i-1} \gamma[i,j]

Value

a inla.cgeneric, cgeneric() object.

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>

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

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

Description

Build an inla.cgeneric 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,
  libpath = NULL
)

Arguments

Details

The precision matrix parametrization step 1:

Q0 = \left[ \begin{array}{ccccc} 1 & & & & \\ \theta_1 & 1 & & & \\ \theta_2 & \theta_n & & & \\ \vdots & & \ldots & \ddots & \\ \theta_{n-1} & \theta_{2n-3} \ldots & \theta_m & 1 \end{array} \right]

step 2: V = Q0^{-1}

step 3: S = diag(V)^{1/2}

step 4: C = SVS

step 5: Q = C^{-1}

p(Q|\lambda) = p(\theta[1:m] | lambda) =

p_C(C(Q)) | Jacobian C(Q) |

where p_C is the PC-prior for correlation, see section 6.2 of Simpson et. al. (2017), which is based on the hypersphere decomposition.

The hypershere decomposition, as proposed in Rapisarda, Brigo and Mercurio (2007) consider \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 compute x[k] = pi/(1+exp(-theta[k])) organize it as a lower triangle of a n \times n matrix

B[i,j] = \left\{\begin{array}{cc} cos(x[i,j]) & j=1 \\ cos(x[i,j])prod_{k=1}^{j-1}sin(x[i,k]) & 2 <= j <= i-1 \\ prod_{k=1}^{j-1}sin(x[i,k]) & j=i \\ 0 & j+1 <= j <= n \end{array}\right.

Result

\gamma[i,j] = -log(sin(x[i,j]))

KLD(R) = \sqrt(2\sum_{i=2}^n\sum_{j=1}^{i-1} \gamma[i,j]

Value

a inla.cgeneric, cgeneric() object.

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>

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

Build an cgeneric for treepcor())

Description

This set the necessary data to implement the penalized complexity prior for a correlation matrix considering a three as proposed in Sterrantino et. al. 2025

Usage

cgeneric_treepcor(
  graph,
  lambda,
  sigma.prior.reference,
  sigma.prior.probability,
  debug = FALSE,
  useINLAprecomp = TRUE,
  libpath = NULL
)

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

a inla.cgeneric, cgeneric() object.

See Also

treepcor() and 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

The graphpcor generic method for graphpcor

Description

The graphpcor generic method for graphpcor

Usage

graphpcor(...)

Arguments

Value

a graphpcor object

Set a graph whose nodes and edges represent variables and conditional distributions, respectively.

Description

Set a graph whose nodes and edges represent variables and conditional distributions, respectively.

Usage

## 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(graph)

## S4 method for signature 'graphpcor'
chol(x, ...)

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

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

Arguments

Details

The terms in the formula do represent the nodes. The ~ is taken as link.

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

• chol(graphpcor): Build the unite diagonal lower triangle matrix

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

Functions

• graphpcor(formula): A graphpcor is a graph where a node represents a variable and an edge a conditional distribution.

• 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'

Examples

g1 <- graphpcor(x ~ y, y ~ v, v ~ z, z ~ x)
g1
summary(g1)
plot(g1)
prec(g1)

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

Examples

g <- graphpcor(x1 ~ x2 + x3, x2 ~ x4, x3 ~ x4)
ne <- dim(g)
gH0 <- hessian(g, rep(-1, ne[2]))
## alternatively
C0 <- vcov(g, theta = rep(c(0,-1), ne))
all.equal(hessian(g, C0), gH0)

inla.cgeneric class, short cgeneric, to define a INLA::cgeneric() latent model

Description

This organize data needed on the C interface for building latent models, which are characterized from a given model parameters \theta and the the following model elements.

• graph to define the non-zero precision matrix pattern. only the upper triangle including the diagonal is needed. The order should be by line.

• Q vector where the

  • first element (N) is the size of the matrix,

  • second element (M) is the number of non-zero elements in the upper part (including) diagonal

  • the remaining (M) elements are the actual precision (upper triangle plus diagonal) elements whose order shall follow the graph definition.

• mu the mean vector,

• initial vector with

  • first element as the number of the parameters in the model

  • remaining elements should be the initials for the model parameters.

• log.norm.const log of the normalizing constant.

• log.prior log of the prior for the model parameters.

See details in INLA::cgeneric()

Usage

cgeneric(model, ...)

## Default S3 method:
cgeneric(model, debug = FALSE, useINLAprecomp = TRUE, libpath = NULL, ...)

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

cgeneric_get(
  model,
  cmd = c("graph", "Q", "initial", "mu", "log_prior"),
  theta,
  optimize = TRUE
)

initial(model)

## S3 method for class 'inla.cgeneric'
initial(model)

mu(model, theta)

## S3 method for class 'inla.cgeneric'
mu(model, theta)

prior(model, theta)

## S3 method for class 'inla.cgeneric'
prior(model, theta)

graph(model, ...)

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

Q(model, ...)

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

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

## S4 method for signature 'inla.cgeneric,inla.cgeneric'
kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)

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

Arguments

Value

a inla.cgeneric, cgeneric() object.

depends on cmd

Methods (by class)

• cgeneric(default): This calls INLA::inla.cgeneric.define()

• cgeneric(character): Method for when model is a character. E.g. cgeneric(model = "generic0") calls cgeneric_generic0

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

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

Functions

• cgeneric_get(): cgeneric_get is an internal function used by graph, prec, initial, mu or prior methods for inla.cgeneric

• initial(): Retrieve the initial model parameter(s).

• initial(inla.cgeneric): Retrive the initial parameter(s) of an inla.cgeneric model.

• mu(): Evaluate the mean.

• mu(inla.cgeneric): Evaluate the mean for an inla.cgeneric model.

• prior(): Evaluate the log-prior.

• prior(inla.cgeneric): Evaluate the prior for an inla.cgeneric model

• graph(): Retrieve the graph

• graph(inla.cgeneric): Retrieve the graph of an inla.cgeneric object

• Q(): Evaluate prec() on a model

• prec(inla.cgeneric): Evaluate prec() on an inla.cgeneric object

• kronecker(X = inla.cgeneric, Y = inla.cgeneric): Kronecker (product) between two inla.cgeneric models as a method for kronecker()

See Also

INLA::cgeneric()

inla.rgeneric class, short rgeneric, to define a INLA::rgeneric() latent model

Description

inla.rgeneric class, short rgeneric, to define a INLA::rgeneric() latent model

Define rgeneric methods.

The rgeneric default method.

Usage

## S4 method for signature 'inla.cgeneric,inla.rgeneric'
kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)

## S4 method for signature 'inla.rgeneric,inla.cgeneric'
kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)

## S4 method for signature 'inla.rgeneric,inla.rgeneric'
kronecker(X, Y, FUN = "*", make.dimnames = FALSE, ...)

rgeneric(model, debug = FALSE, compile = TRUE, optimize = TRUE, ...)

## Default S3 method:
rgeneric(model, debug = FALSE, compile = TRUE, optimize = TRUE, ...)

## S3 method for class 'inla.rgeneric'
graph(model, ...)

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

## S3 method for class 'inla.rgeneric'
initial(model)

## S3 method for class 'inla.rgeneric'
mu(model, theta)

## S3 method for class 'inla.rgeneric'
prior(model, theta)

Arguments

Value

a inla.rgeneric object.

Functions

• kronecker(X = inla.cgeneric, Y = inla.rgeneric): Kronecker (product) between a inla.cgeneric model and a inla.rgeneric model as a method for kronecker()

• kronecker(X = inla.rgeneric, Y = inla.cgeneric): Kronecker (product) between a inla.rgeneric model and a inla.cgeneric model as a method for kronecker()

• kronecker(X = inla.rgeneric, Y = inla.rgeneric): Kronecker (product) between a inla.rgeneric model and a inla.rgeneric model as a method for kronecker()

• graph(inla.rgeneric): The graph method for 'inla.rgeneric'

• prec(inla.rgeneric): The precision method for an inla.rgeneric object.

• initial(inla.rgeneric): The initial method for 'inla.rgeneric'

• mu(inla.rgeneric): The mu method for 'inla.rgeneric'

• prior(inla.rgeneric): The prior metho for 'inla.rgeneric'

Define the is.zero method

Description

Define the is.zero method

Usage

is.zero(x, ...)

## Default S3 method:
is.zero(x, ...)

## S3 method for class 'matrix'
is.zero(x, ...)

Arguments

Value

logical

Methods (by class)

• is.zero(default): The is.zero.default definition

• is.zero(matrix): The is.zero.matrix definition

The prec method

Description

The prec method

Usage

prec(model, ...)

## Default S3 method:
prec(model, ...)

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

Arguments

Value

a precision matrix

Functions

• prec(default): The default precision method computes the inverse of the variance

• prec(inla): Define the prec method for an inla output object

Functions for the mapping between spherical and Euclidean coordinates.

Description

Functions for the mapping between spherical and Euclidean coordinates.

Usage

rphi2x(rphi)

x2rphi(x)

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

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

KLD10(C1, C0)

theta2H(theta)

Arguments

Details

see N-sphere/Euclidian

compute C1 using 'theta2C' on theta with

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

Functions

• x2rphi(): Tranform from Euclidian coordinates to spherical

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

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

• KLD10(): Compute the KLD with respect to a base model

• theta2H(): Compute the hessian, its svd and some elements

Build the correlation matrix parametrized from the hypershere decomposition, see details.

Description

Build the correlation matrix parametrized from the hypershere decomposition, see details.

Usage

theta2correl(theta, fromR = TRUE)

theta2gamma2L(theta, fromR = TRUE)

rcorrel(p, lambda)

Arguments

Details

The hypershere decomposition, as proposed in Rapisarda, Brigo and Mercurio (2007) consider \theta[k] \in [0, \infty], k=1,...,m=n(n-1)/2 compute x[k] = pi/(1+exp(-theta[k])) organize it as a lower triangle of a n \times n matrix

| cos(x[i,j]) , j=1

B[i,j] = | cos(x[i,j])prod_{k=1}^{j-1}sin(x[i,k]), 2 <= j <= i-1

| prod_{k=1}^{j-1}sin(x[i,k]) , j=i

| 0 , j+1 <= j <= n

Result

\gamma[i,j] = -log(sin(x[i,j]))

KLD(R) = \sqrt(2\sum_{i=2}^n\sum_{j=1}^{i-1} \gamma[i,j]

Value

a correlation matrix

Lower triangular n x n matrix

Functions

• theta2gamma2L(): Build a lower triangular matrix from a parameter vector. See details.

• rcorrel(): Drawn a random sample correlation matrix

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>

Simspon 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>

Define a tree used to model correlation matrices using a shared latent variables method represented by a tree, whose nodes represent the two kind of variables: children and parent. See treepcor.

Description

Define a tree used to model correlation matrices using a shared latent variables method represented by a tree, whose nodes represent the two kind of variables: children and parent. See treepcor.

Usage

treepcor(...)

Arguments

Details

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 variables are identified as p1, ..., pm, where the m is the number of parent variables. The main parent (fist) should be identified as p1. Parent variables (except p1) have an ancestor, which is a parent variable.

Value

a treepcor object

Examples

g1 <- treepcor(p1 ~ c1 + c2 - c3)
g1
summary(g1)
plot(g1)
prec(g1)
prec(g1, theta = 0)

g2 <- treepcor(p1 ~ c1 + c2 + p2,
          p2 ~ c3 - c4)
g2
summary(g2)
plot(g2)
prec(g2)
prec(g2, theta = c(0, 0))

g3 <- treepcor(p1 ~ -p2 + c1 + c2,
          p2 ~ c3)
g3
summary(g3)
plot(g3)
prec(g3)
prec(g3, theta = c(0,0))

Set a tree whose nodes represent the two kind of variables: children and parent.

Description

Set a tree whose nodes represent the two kind of variables: children and parent.

Usage

## 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)

Arguments

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

• 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.