loglikLOOCVcontourVAR1fused: Contourplot of LOOCV log-likelihood of multiple VAR(1) models

In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

Description

Evaluates the leave-one-out cross-validated log-likelihood of multiple jointly estimated VAR(1) models over a grid of the (fused) ridge penalty parameters (λ_a and λ_{f}) for the autoregression coefficient matrices \mathbf{A}_g, while keeping λ_{ω}, the penalty parameter of the inverse error covariance matrix \mathbf{Ω}_{\varepsilon} (=\mathbf{Σ_{\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(1)-processes are assumed to have mean zero.

Usage

loglikLOOCVcontourVAR1fused(lambdaAgrid, lambdaFgrid, Y, id, 
                            lambdaP, figure=TRUE, verbose=TRUE, ...)

Arguments

lambdaAgrid	A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to λ_a, the ridge penalty parameter for the autoregression coefficient matrices \mathbf{A}_g.
lambdaFgrid	A numeric of length larger than one, comprising positive numbers only. It contains the grid points corresponding to λ_{f}, the fused ridge penalty parameter for the autoregression coefficient matrices \mathbf{A}_g.
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 be centered covariate-wise.
id	A vector with group indices comprising of integers only. First group is represented by '0', the next by '1', and so on until the last.
lambdaP	A numeric specifying the value at which λ_{ω} should be fixed.
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 ridgeVAR1fused.

Value

A list-object with slots:

lambdaA	A numeric with the grid points corresponding to λ_a (the ridge penalty parameter for the autoregression coefficient matrices \mathbf{A}_g).
lambdaF	A numeric with the grid points corresponding to λ_{f} (the fused ridge penalty parameter for the autoregression coefficient matrices \mathbf{A}_g.
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 <[e-mail]>, Viktorian Miok.

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.

See Also

loglikLOOCVcontourVAR1, loglikLOOCVcontourVARX1.

Examples

# 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") 

ragt2ridges documentation built on Jan. 28, 2020, 5:08 p.m.