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

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

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.

1 2	loglikLOOCVcontourVAR1(lambdaAgrid, lambdaPgrid, Y, figure=TRUE, verbose=TRUE, ...)

`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`.

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.

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).

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

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.

# 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")