optPenaltyVARX1: Automatic penalty parameter selection for the VARX(1) model.

Description

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

Usage

optPenaltyVARX1(Y, X, 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.

Three-dimensional array containing the time-varying covariate data. The first, second and third dimensions correspond to covariates, 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 \(\mathbf{A}\), the matrix with autoregression coefficients, the second to matrix \(\mathbf{B}\) containing the regression coefficients of the time-varying covariates, 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 \(\mathbf{A}\), the matrix with autoregression coefficients, the second to matrix \(\mathbf{B}\) containing the regression coefficients of the time-varying covariates, 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 \(\mathbf{A}\), the matrix with autoregression coefficients, the second to matrix \(\mathbf{B}\) containing the regression coefficients of the time-varying covariates, 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 the loglikLOOCVVARX1-function.

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
Ax     <- createA(3, "chain")

# generate time-varying covariate data
X <- dataVAR1(n, T, Ax, SigmaE)

# (auto)regression parameter matrices of VARX(1) model
A <- createA(p, topology="clique", nonzeroA=0.1, nClique=1)
B <- createA(p, topology="hub", nonzeroA=0.1, nHubs=1)

# generate data
Y <- dataVARX1(X, A, B, SigmaE, lagX=0)

# determine the optimal penalty parameter
optLambda <- optPenaltyVARX1(Y, X, rep(10^(-10), 3), rep(1000, 3), 
                             optimizer="nlm", lagX=0)

# fit VAR(1) model
ridgeVARX1(Y, X, optLambda[1], optLambda[2], optLambda[3], lagX=0)$A
# }