loglikLOOCVcontourVARX1: Contourplot of the LOOCV log-likelihood of VARX(1) model
In ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes

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

View source: R/loglikLOOCVcontourVARX1.r

Evaluates the leave-one-out cross-validated log-likelihood of the VARX(1) model over a grid of the ridge penalty parameters (λ_a and λ_b) for the autoregression and time-varying covariate regression coefficient matrices \mathbf{A} and \mathbf{B}, respectively, 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 VARX(1)-process is assumed to have mean zero.

1 2	loglikLOOCVcontourVARX1(lambdaAgrid, lambdaBgrid, lambdaPgrid, Y, X, lagX=0, 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 lag one autoregression coefficient matrix \mathbf{A}).
`lambdaBgrid`	A `numeric` of length larger than one, comprising positive numbers only. It contains the grid points corresponding to the λ_b (the penalty parameters for the regression coefficient matrix \mathbf{B} of the time-varying covariates.
`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 be centered variate-wise.
`X`	Three-dimensional `array` containing the time-varying covariates. The first, second and third dimensions correspond to covariates, time and samples, respectively. The data are assumed to be centered covariate-wise.
`lagX`	An `integer`, either `0` or 1, specifying whether \mathbf{X}_t or \mathbf{X}_{t-1} affects \mathbf{Y}_t, respectively.
`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 `ridgeVARX1`.

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}).
`lambdaB`	A `numeric` with the grid points corresponding to λ_b (the penalty parameter for time-varying covariate regression coefficient matrix \mathbf{B}.
`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_{b} values, respectively.

When lambdaAgrid, lambdaBgrid and lambdaPgrid are all vectors of length exceeding one, the contour is determined for the grid formed by the Cartesius product of lambdaAgrid and lambdaBgrid meanwhile restricting lambdaPgrid to its first element.

Internally, this function calls the loglikLOOCVVARX1-function, which evaluates the minus (!) LOOCV log-likelihood (for practical reasons). For interpretation purposes loglikLOOCVcontourVARX1 provides the regular LOOCV log-likelihood (that is, without the minus).

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

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.

loglikLOOCVcontourVAR1, loglikLOOCVcontourVAR1fused.

# set dimensions (p=covariates, n=individuals, T=time points)
p <- 3; n <- 12; T <- 10

# set model parameters
SigmaE <- diag(p)/4
Ax     <- createA(3, "chain")

# generate time-varying covariate data
X <- dataVAR1(n, T, Ax, SigmaE)

# regression parameter matrices of VARX(1) model
A <- createA(p, topology="clique", nonzeroA=0.1, nClique=1)
B <- createA(p, topology="hub", nonzeroA=0.1, nHubs=1)

# generate data
Y <- dataVARX1(X, A, B, SigmaE, lagX=0)

## plot contour of cross-validated likelihood
## Not run:  lambdaAgrid <- seq(0.01, 1, length.out=20) 
## Not run:  lambdaBgrid <- seq(0.01, 1000, length.out=20) 
## Not run:  lambdaPgrid <- seq(0.01, 1000, length.out=20) 
## Not run:  loglikLOOCVcontourVARX1(lambdaAgrid, lambdaBgrid, lambdaPgrid, Y, X) 

## determine optimal values of the penalty parameters
## Not run: optLambdas <- constrOptim(c(1,1,1), loglikLOOCVVARX1, gr=NULL, 
## Not run:               ui=diag(3), ci=c(0,0,0), Y=Y, X=X,
## 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")