Visualize the ridge regularization paths of the parameters of the VAR(1) model

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Description

Function that visualizes the regularization paths of the parameters of the VAR(1) model. The elements of the ridge ML estimate of either \mathbf{A} or (possibly standardized, inverse of) \mathbf{Σ}_{\varepsilon} are plotted against a specified range of their penalty parameter (keeping the other penalty parameter fixed).

Usage

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ridgePathVAR1(Y, lambdaAgrid, lambdaPgrid, pathType="A", 
plotTypeSigmaE="pcor", diag=FALSE, verbose=TRUE, ...)

Arguments

Y

Three-dimensional array containing the data. The first, second and third dimensions correspond to covariates, time and samples, respectively. The data are assumed to be centered covariate-wise.

lambdaAgrid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to the λ_a (the penalty parameter for the regression coefficient matrix \mathbf{A}).

lambdaPgrid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to the λ_{ω} (the penalty parameters for the inverse error covariance matrix \mathbf{Ω}_{\varepsilon} (=\mathbf{Σ_{\varepsilon}^{-1}})).

pathType

A character indicating of which parameter to plot its ridge regularization paths. Either "A" or "SigmaE".

plotTypeSigmaE

A character indicating the type of element for which a visualization of the regularization paths (of \mathbf{Σ}_{\varepsilon}) is desired. Must be one of: "pcor", "cor", "cov", "prec".

diag

A logical indicating if the diagonal elements should be retained for visualization of the regularization path of \mathbf{Σ}_{\varepsilon}.

verbose

A logical indicator: should intermediate output be printed on the screen?

...

Other arguments to be passed to ridgeVAR1.

Details

If pathType="A", the regularization paths of \mathbf{A} will be evaluated for λ_{ω} equal to the minimum value of lambdaPgrid. If pathType="SigmaE", the regularization paths of (inverse of / possibly standardarized) \mathbf{Σ}_{\varepsilon} will be evaluated for λ_a equal to the minimum value of lambdaAgrid.

Regularization paths may be visualized for (partial) correlations, covariances and precision elements. The type of element for which a visualization of the regularization paths is desired can be indicated by the argument plotType.

The arguments diag and plotTypeSigmaE are ignored when pathType="A".

Author(s)

Wessel N. van Wieringen <w.vanwieringen@vumc.nl>.

See Also

ridgePathS, ridgeP, ridgeVAR1.

Examples

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# set dimensions (p=covariates, n=individuals, T=time points)
p <- 3; n <- 4; T <- 10
     
# set model parameters
SigmaE <- diag(p)/4
A <- createA(p, "chain")
     
# generate data
Y <- dataVAR1(n, T, A, SigmaE)

## Visualize regularization paths
lambdaAgrid <- seq(0.01, 1, length.out=20) 
lambdaPgrid <- seq(0.01, 1, length.out=20) 
ridgePathVAR1(Y, lambdaAgrid, lambdaPgrid, pathType="A")

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