weightGraph {SEMgraph}

Graph weighting methods

Description

Add data-driven edge and node weights to the input graph.

Usage

weightGraph(graph, data, group = NULL, method = "r2z", limit = 10000, ...)

Arguments

graph

An igraph object.

data

A matrix or data.frame. Rows correspond to subjects, and columns to graph nodes.

group

Binary vector. This vector must be as long as the number of subjects. Each vector element must be 1 for cases and 0 for control subjects. By default, group = NULL. If group is not NULL, also node weighting is actived, and node weights correspond to the attribute: V(graph)$pv (P-value of the z-test = b/SE(b) from simple linear regression y ~ x, i.e., lm(node ~ group)) and V(graph)$sign (-1 if z<-2, +1 if z>2, 0 otherwise).

method

Edge weighting method. It can be one of the following:

1. "r2z", weight edges are defined using Fisher's r-to-z transform (Fisher, 1915) to test the correlation coefficient of pairs of interacting nodes, if group=NULL. Otherwise, the difference between group of the r-to-z trasform will be tested. Edge weights correspond to the attribute: E(graph)$pv (P-value of the z-test) and E(graph)$sign (-1 if z<-2, +1 if z>2, 0 otherwise).

2. "sem", edge weights are defined by a SEM model that implies testing the group effect simultaneously on source and sink nodes. A new parameter w is defined as the weighted sum of the total effect of the group on source and sink nodes, adjusted by node degree centrality. Edge weights correspond to the attribute: E(graph)$pv (P-value of the z-test = w/SE(w)) and E(graph)$sign (-1 if z<-2, +1 if z>2, 0 otherwise). Not available if group=NULL.

3. "cov", edge weights are defined by a new parameter w combining the group effect on the source node (mean group difference, adjusted by source degree centrality), the sink node (mean group difference, adjusted by sink degree centrality), and the source–sink interaction (correlation difference). Edge weights correspond to the attribute: E(graph)$pv (P-value of the z-test = w/SE(w) of the combined difference of the group over source node, sink node, and their connection) and E(graph)$sign (-1 if z<-2, +1 if z>2, 0 otherwise). Not available if group=NULL.

4. "cfa", edge weights are defined by a CFA1 model that implies testing the group effect, w on a latent variable (LV) with observed indicators two interacting nodes, fixing loading coefficients and residual variances for model identification. Edge weights correspond to the attribute: E(graph)$pv (P-value of the z-test = w/SE(w) of the group effect on the LV) and E(graph)$sign (-1 if z<-2, +1 if z>2, 0 otherwise). Not available if group=NULL.

limit

An integer value corresponding to the number of graph edges. Beyond this limit, multicore computation is enabled to reduce the computational burden. By default, limit = 10000.

...

Currently ignored.

Value

A weighted graph, as an igraph object.

Author(s)

Mario Grassi [e-mail]

References

Grassi M, Tarantino B (2023). [Supplementary material of] SEMtree: tree-based structure learning methods with structural equation models. Bioinformatics, 39 (6), 4829–4830 <https://doi.org/10.1093/bioinformatics/btad377>

Fisher RA (1915). Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population. Biometrika, 10(4), 507–521. <doi:10.2307/2331838>

Examples

# Graph weighting
G <- weightGraph(graph = sachs$graph,
                 data = log(sachs$pkc),
                 group = sachs$group,
                 method = "r2z")

# New edge attributes
head(E(G)$pv); summary(E(G)$pv)
head(E(G)$zsign); table(E(G)$zsign)

# New node attributes
head(V(G)$pv); summary(V(G)$pv)
head(V(G)$zsign); table(V(G)$zsign)