loglikLOOCVcontourVAR1: Contourplot of LOOCV log-likelihood of VAR(1) model

Description

Evaluates the leave-one-out cross-validated log-likelihood of the VAR(1) model for a given grid of the ridge penalty parameters (\(\lambda_a\) and \(\lambda_{\omega}\)) for the autoregression coefficient matrix \(\mathbf{A}\) and the inverse error covariance matrix \(\mathbf{\Omega}_{\varepsilon} (=\mathbf{\Sigma_{\varepsilon}^{-1}})\), respectively). The result is plotted as a contour plot, which facilitates the choice of optimal penalty parameters. The function also works with a (possibly) unbalanced experimental set-up. The VAR(1)-process is assumed to have mean zero.

Usage

loglikLOOCVcontourVAR1(lambdaAgrid, lambdaPgrid, Y, figure=TRUE, 
                       verbose=TRUE, ...)

Arguments

lambdaAgrid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to the \(\lambda_a\) (the penalty parameter for the autoregression coefficient matrix \(\mathbf{A}\)).

lambdaPgrid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to the \(\lambda_{\omega}\) (the penalty parameters for the inverse error covariance matrix \(\mathbf{\Omega}_{\varepsilon} (=\mathbf{\Sigma_{\varepsilon}^{-1}})\)).

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.

figure

A logical, indicating whether the contour plot should be generated.

verbose

A logical indicator: should intermediate output be printed on the screen?

...

Other arguments to be passed on (indirectly) to ridgeVAR1.

Value

A list-object with slots:

lambdaA

A numeric with the grid points corresponding to \(\lambda_a\) (the penalty parameter for the autoregression coefficient matrix \(\mathbf{A}\)).

lambdaP

A numeric with the grid points corresponding to \(\lambda_{\omega}\) (the penalty parameter for the inverse error covariance matrix \(\mathbf{\Omega}_{\varepsilon} (=\mathbf{\Sigma_{\varepsilon}^{-1}})\)).

llLOOCV

A matrix of leave-one-out cross-validated log-likelihoods. Rows and columns correspond to \(\lambda_a\) and \(\lambda_{\omega}\) values, respectively.

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.

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
A <- createA(p, "chain")

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

## plot contour of cross-validated likelihood
# }
# NOT RUN {
 lambdaAgrid <- seq(0.01, 1, length.out=20) 
# }
# NOT RUN {
 lambdaPgrid <- seq(0.01, 1000, length.out=20) 
# }
# NOT RUN {
 loglikLOOCVcontourVAR1(lambdaAgrid, lambdaPgrid, Y) 
# }
# NOT RUN {
## determine optimal values of the penalty parameters
# }
# NOT RUN {
optLambdas <- constrOptim(c(1,1), loglikLOOCVVAR1, gr=NULL, 
# }
# NOT RUN {
              ui=diag(2), ci=c(0,0), Y=Y, 
# }
# NOT RUN {
              control=list(reltol=0.01))$par 
# }
# NOT RUN {
## add point of optimum
# }
# NOT RUN {
 points(optLambdas[1], optLambdas[2], pch=20, cex=2, 
# }
# NOT RUN {
 col="red") 
# }