# Visualize the ridge regularization paths of the parameters of the VAR(1) model

### Description

Function that visualizes the regularization paths of the parameters of the VAR(1) model. The elements of the ridge ML estimate of either *\mathbf{A}* or (possibly standardized, inverse of)
*\mathbf{Σ}_{\varepsilon}* are plotted against a specified range of their penalty parameter (keeping the other penalty parameter fixed).

### Usage

1 2 | ```
ridgePathVAR1(Y, lambdaAgrid, lambdaPgrid, pathType="A",
plotTypeSigmaE="pcor", diag=FALSE, verbose=TRUE, ...)
``` |

### Arguments

`Y` |
Three-dimensional |

`lambdaAgrid` |
A |

`lambdaPgrid` |
A |

`pathType` |
A |

`plotTypeSigmaE` |
A |

`diag` |
A |

`verbose` |
A |

`...` |
Other arguments to be passed to |

### Details

If `pathType="A"`

, the regularization paths of *\mathbf{A}* will be evaluated for *λ_{ω}* equal to the minimum value of `lambdaPgrid`

. If `pathType="SigmaE"`

, the regularization paths of (inverse of / possibly standardarized) *\mathbf{Σ}_{\varepsilon}* will be evaluated for *λ_a* equal to the minimum value of `lambdaAgrid`

.

Regularization paths may be visualized for (partial) correlations, covariances and precision elements. The type of element for which a visualization of the regularization paths is desired can be indicated by the argument `plotType`

.

The arguments `diag`

and `plotTypeSigmaE`

are ignored when `pathType="A"`

.

### Author(s)

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

### See Also

`ridgePathS`

, `ridgeP`

, `ridgeVAR1`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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)
## Visualize regularization paths
lambdaAgrid <- seq(0.01, 1, length.out=20)
lambdaPgrid <- seq(0.01, 1, length.out=20)
ridgePathVAR1(Y, lambdaAgrid, lambdaPgrid, pathType="A")
``` |