optPenaltyVARX1: Automatic penalty parameter selection for the VARX(1) model.
In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

Description Usage Arguments Value Author(s) References See Also Examples

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

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optPenaltyVARX1(Y, X, lambdaMin, lambdaMax, 
                lambdaInit=(lambdaMin+lambdaMax)/2, 
                optimizer="nlm", ...)

`Y`	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.
`X`	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{Ω}_{\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{Ω}_{\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{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 the `loglikLOOCVVARX1`-function.

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

Wessel N. van Wieringen <w.vanwieringen@vumc.nl>

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.

loglikLOOCVVARX1, ridgeVARX1.

# 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