# ridgePathVAR1: Visualize the ridge regularization paths of the parameters of... In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

## 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

 1 2 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 autoregression 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 <[email protected]>.

ridgePathS, ridgeP, ridgeVAR1.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 # 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")