loglikLOOCVcontourVAR2: Contourplot of LOOCV log-likelihood of the VAR(2) model

Description

Evaluates the leave-one-out cross-validated log-likelihood of the estimated VAR(2) model over a grid of the ridge penalty parameters (\(\lambda_{a1}\) and \(\lambda_{a2}\)) for the lag one and lag two autoregression coefficient matrices \(\mathbf{A}_1\) and \(\mathbf{A}_2\) (respectively), while keeping \(\lambda_{\omega}\), the penalty parameter of the inverse error covariance matrix \(\mathbf{\Omega}_{\varepsilon} (=\mathbf{\Sigma_{\varepsilon}^{-1}})\), fixed at a user-specified value. 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(2)-process are assumed to have mean zero.

Usage

loglikLOOCVcontourVAR2(lambdaA1grid, lambdaA2grid, 
                       lambdaPgrid, Y, figure=TRUE, verbose=TRUE, ...)

Arguments

lambdaA1grid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to \(\lambda_{a1}\), the ridge penalty parameter for the lag one autoregression coefficient matrix \(\mathbf{A}_1\).

lambdaA2grid

A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to \(\lambda_{a2}\), the ridge penalty parameter for the lag two autoregression coefficient matrix \(\mathbf{A}_2\).

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 be 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 ridgeVAR2.

Value

A list-object with slots:

lambdaA1

A numeric with the grid points corresponding to \(\lambda_{a1}\) (the ridge penalty parameter for the lag one autoregression coefficient matrix \(\mathbf{A}_1\)).

lambdaA2

A numeric with the grid points corresponding to \(\lambda_{a2}\) (the ridge penalty parameter for the lag one autoregression coefficient matrix \(\mathbf{A}_2\)).

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 \(\lambda_{a1}\) and \(\lambda_{a2}\) values, respectively.

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 <- 12; T <- 10

# set model parameters
SigmaE <- diag(p)/4
A1 <- -createA(p, "clique", nCliques=1, nonzeroA=0.1)
A2 <- t(createA(p, "chain", nBands=1,   nonzeroA=0.1))

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

## plot contour of cross-validated likelihood
# }
# NOT RUN {
 lambdaA1grid <- seq(0.01, 1, length.out=20) 
# }
# NOT RUN {
 lambdaA2grid <- seq(0.01, 1000, length.out=20) 
# }
# NOT RUN {
 lambdaPgrid  <- seq(0.01, 1000, length.out=20) 
# }
# NOT RUN {
 loglikLOOCVcontourVAR2(lambdaA1grid, lambdaA2grid, lambdaPgrid, Y) 
# }
# NOT RUN {
## determine optimal values of the penalty parameters
# }
# NOT RUN {
optLambdas <- constrOptim(c(1,1,1), loglikLOOCVVAR2, gr=NULL, 
# }
# NOT RUN {
              ui=diag(3), ci=c(0,0,0), 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") 
# }