# loglikLOOCVcontourVAR1: Contourplot of LOOCV log-likelihood of VAR(1) model In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

## Description

Evaluates the leave-one-out cross-validated log-likelihood of the VAR(1) model for a given grid of the ridge penalty parameters (λ_a and λ_{ω}) for the autoregression coefficient matrix \mathbf{A} and the inverse error covariance matrix \mathbf{Ω}_{\varepsilon} (=\mathbf{Σ_{\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

 1 2 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 λ_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 λ_{ω} (the penalty parameters for the inverse error covariance matrix \mathbf{Ω}_{\varepsilon} (=\mathbf{Σ_{\varepsilon}^{-1}})). Y 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 λ_a (the penalty parameter for the autoregression coefficient matrix \mathbf{A}). lambdaP A numeric with the grid points corresponding to λ_{ω} (the penalty parameter for the inverse error covariance matrix \mathbf{Ω}_{\varepsilon} (=\mathbf{Σ_{\varepsilon}^{-1}})). llLOOCV A matrix of leave-one-out cross-validated log-likelihoods. Rows and columns correspond to λ_a and λ_{ω} values, respectively.

## Note

Internally, this function calls the loglikLOOCVVAR1-function, which evaluates the minus (!) LOOCV log-likelihood (for practical reasons). For interpretation purposes loglikLOOCVcontourVAR1 provides the regular LOOCV log-likelihood (that is, without the minus).

## Author(s)

Wessel N. van Wieringen <[email protected]>

## 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.

loglikLOOCVVAR1.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # 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) ## 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 ## add point of optimum ## Not run: points(optLambdas[1], optLambdas[2], pch=20, cex=2, ## Not run: col="red")