optPenaltyVAR2: Automatic penalty parameter selection for the VAR(2) model.

Description

Automatic penalty parameter selection for the VAR(2) model through maximization of the leave-one-out cross-validated (LOOCV) log-likelihood.

Usage

optPenaltyVAR2(Y, lambdaMin, lambdaMax, 
               lambdaInit=(lambdaMin+lambdaMax)/2, 
               optimizer="nlm", ...)

Arguments

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

lambdaMin

A numeric of length three, containing the minimum values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \(\mathbf{A}_1\), the matrix with lag one autoregression coefficients, the second to matrix \(\mathbf{A}_2\) containing the lag two autoregression coefficients, while the third parameter relates to the penalty on \(\mathbf{\Omega}_{\varepsilon}\), the precision matrix of the errors.

lambdaMax

A numeric of length three, containing the maximum values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \(\mathbf{A}_1\), the matrix with lag one autoregression coefficients, the second to matrix \(\mathbf{A}_2\) containing the lag two autoregression coefficients, while the third parameter relates to the penalty on \(\mathbf{\Omega}_{\varepsilon}\), the precision matrix of the errors.

lambdaInit

A numeric of length three, containing the initial values of ridge penalty parameters to be considered. The first element is the ridge parameter corresponding to the penalty on \(\mathbf{A}_1\), the matrix with lag one autoregression coefficients, the second to matrix \(\mathbf{A}_2\) containing the lag two autoregression coefficients, while the third 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 loglikLOOCVVAR2.

Value

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

References

Miok, V., Wilting, S.M., Van Wieringen, W.N. (2019), ``Ridge estimation of network models from time-course omics data'', Biometrical Journal, 61(2), 391-405.

Examples

Run this code

# NOT RUN {
# set dimensions (p=covariates, n=individuals, T=time points)
p <- 3; n <- 4; T <- 10

# set model parameters
SigmaE <- diag(p)/4
A1 <- createA(p, topology="clique", nonzeroA=0.1, nClique=1)
A2 <- createA(p, topology="hub", nonzeroA=0.1, nHubs=1)

# generate data
Y <- dataVAR2(n, T, A1, A2, SigmaE)

# determine the optimal penalty parameter
optLambda <- optPenaltyVAR2(Y, rep(10^(-10), 3), rep(1000, 3), 
                            optimizer="nlm")

# fit VAR(2) model
ridgeVAR2(Y, optLambda[1], optLambda[2], optLambda[3])
# }