# loglikLOOCVVAR1: Leave-one-out (minus) cross-validated log-likelihood of... In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

## Description

Evaluation of the (minus) leave-one-out cross-validated log-likelihood of the VAR(1) model for given choices 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 functions also works with a (possibly) unbalanced experimental set-up. The VAR(1)-process is assumed to have mean zero.

## Usage

 1 loglikLOOCVVAR1(lambdas, Y, unbalanced=matrix(nrow=0, ncol=2), ...) 

## Arguments

 lambdas A numeric of length two, comprising positive values only. It contains the ridge penalty parameters to be used in the estimation of \mathbf{A} and the precision matrix of the errors, respectively. 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. unbalanced A matrix with two columns, indicating the unbalances in the design. Each row represents a missing design point in the (time x individual)-layout. The first and second column indicate the time and individual (respectively) specifics of the missing design point. ... Other arguments to be passed to ridgeVAR1.

## Value

A numeric of length one: the minus (!) LOOCV log-likelihood.

## Note

The minus LOOCV log-likelihood is returned as standard optimization procedures in R like nlminb and constrOptim minimize (rather then maximize). Hence, by providing the minus LOOCV log-likelihood the function loglikLOOCVVAR1 can directly used by these optimization procedures.

## 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.

ridgeP and ridgeVAR1.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 # 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) ## 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))$par # ridge ML estimation of the VAR(1) parameter estimates with # optimal penalty parameters optLambdas <- c(0.1, 0.1) ridgeVAR1(Y, optLambdas[1], optLambdas[2])$A