node_relevance_plot function

Produces a node relevance plot, which compares the impact each node has on the network autocorrelation once a model order has been chosen.

Produces a node relevance plot based on the node relevance index c("$\\mathrm{globindex}(X_{i, t}) := \\bigg (\\sum_{j = 1}^{d} [\\mathbf{W} \\odot \\mathbf{S}]_{j i} \\bigg )\n$", "$\\bigg \\{ \\underset{l \\in \\mathcal{K}}{\\max} \\bigg ( \\sum_{j = 1}^{d} [\\mathbf{W} \\odot \\mathbf{S}]_{j l} \\bigg ) \\bigg \\}^{-1},$") which computes the ratio between nodes $i$ column sum for nodes in neighbourhood regressions. Nodes are ordered according to the relative contribution eahc has to the autocovariance. The nodes are ordered in ascending order.

node_relevance_plot(network, r_star, node_names, node_label_size = 2)

Arguments

• network: GNAR network object, which is the underlying network for the time series under study.
• r_star: Maximum active r-stage depth for neighbourhood regression.
• node_names: Names corresponding to each, this makes identifying nodes in the plot easier. If this argument is NULL, then the plot links to each node a number.
• node_label_size: Text size when producing the plot. Default is 2, however, depending on the number of nodes it might be necessary to adjust the size.

Returns

Data Frame consisting of two variable, the node name and the node relevance value.

Author(s)

Daniel Salnikov and Guy Nason.

References

Nason, G.P., Salnikov, D. and Cortina-Borja, M. (2023) New tools for network time series with an application to COVID-19 hospitalisations. https://arxiv.org/abs/2312.00530

Examples

#
# Produces a node relevance plot with respect to a stationary GNAR process 
# with underlying network fiveNet
#
# GNAR simulation
gnar_simulation <- GNARsim(n = 100, net=fiveNet, alphaParams = list(rep(0.25, 5), rep(0.12, 5)), 
        betaParams = list(c(0.25, 0.13), c(0.20)), sigma=1)
# Node relevance plot without names
node_relevance_plot(network = fiveNet, r_star = 2, node_label_size = 10)
#
# Node relevance plot with names
#
node_relevance_plot(network = fiveNet, r_star = 2, node_names = c("A", "B", "C", "D", "E"), 
        node_label_size = 10)