ragt2ridges (version 0.3.4)

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

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 (\(\mathbf{\Omega}_{\varepsilon}\), 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 (\(\mathbf{\Omega}_{\varepsilon}\), 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 (\(\mathbf{\Omega}_{\varepsilon}\), 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.

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

# NOT RUN {
# 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
# }