optPenaltyVAR1: Automatic penalty parameter selection for the VAR(1) model.

In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

Description

Automatic penalty parameter selection for the VAR(1) model through maximization of the leave-one-out cross-validated (LOOCV) log-likelihood.

Usage

optPenaltyVAR1(Y, lambdaMin, lambdaMax, 
               lambdaInit=(lambdaMin+lambdaMax)/2, 
               optimizer="nlm", ...)

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 centered covariate-wise.
lambdaMin	A numeric of length two, containing the minimum values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \mathbf{A}, the matrix with autoregression coefficients, while the second parameter relates to the penalty on (\mathbf{Ω}_{\varepsilon}, the precision matrix of the errors.
lambdaMax	A numeric of length two, containing the maximum values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \mathbf{A}, the matrix with autoregression coefficients, while the second parameter relates to the penalty on (\mathbf{Ω}_{\varepsilon}, the precision matrix of the errors.
lambdaInit	A numeric of length two, containing the initial values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \mathbf{A}, the matrix with autoregression coefficients, while the second parameter relates to the penalty on (\mathbf{Ω}_{\varepsilon}, the precision matrix of the errors.
optimizer	A character (either nlm (default) or optim) specifying which optimization function should be used: nlminb (default) or constrOptim?
...	Additional arguments passed on to loglikLOOCVVAR1.

Value

A numeric with the LOOCV optimal choice for the ridge penalty parameter.

Author(s)

Wessel N. van Wieringen <[e-mail]>

References

Miok, V., Wilting, S.M., Van Wieringen, W.N. (2017), “Ridge estimation of the VAR(1) model and its time series chain graph from multivariate time-course omics data”, Biometrical Journal, 59(1), 172-191.

See Also

loglikLOOCVVAR1, ridgeVAR1.

Examples

# set dimensions (p=covariates, n=individuals, T=time points)
p <- 3; n <- 4; T <- 10

# set model parameters
SigmaE <- diag(p)/4
A      <- createA(3, "chain")

# generate data
Y <- dataVAR1(n, T, A, SigmaE)

# determine the optimal penalty parameter
optLambda <- optPenaltyVAR1(Y, rep(10^(-10), 2), rep(1000, 2))

# fit VAR(1) model
ridgeVAR1(Y, optLambda[1], optLambda[2])$A

ragt2ridges documentation built on Jan. 28, 2020, 5:08 p.m.