osdsm {backbone}R Documentation

Extract backbone using the Ordinal Stochastic Degree Sequence Model

Description

osdsm extracts the backbone of a bipartite projection using the Ordinal Stochastic Degree Sequence Model.

Usage

osdsm(
  B,
  alpha = 0.05,
  trials = NULL,
  signed = FALSE,
  mtc = "none",
  class = "original",
  narrative = FALSE
)

Arguments

B

An ordinally weighted bipartite graph, as: (1) an incidence matrix in the form of a matrix or sparse Matrix; (2) an edgelist in the form of a three-column dataframe; (3) an igraph object. Any rows and columns of the associated bipartite matrix that contain only zeros or only ones are automatically removed before computations.

alpha

real: significance level of hypothesis test(s)

trials

integer: the number of bipartite graphs generated to approximate the edge weight distribution. If NULL, the number of trials is selected based on alpha (see details)

signed

boolean: TRUE for a signed backbone, FALSE for a binary backbone (see details)

mtc

string: type of Multiple Test Correction to be applied; can be any method allowed by p.adjust.

class

string: the class of the returned backbone graph, one of c("original", "matrix", "Matrix", "igraph", "edgelist"). If "original", the backbone graph returned is of the same class as B.

narrative

boolean: TRUE if suggested text & citations should be displayed.

Details

The osdsm function compares an edge's observed weight in the projection B*t(B) to the distribution of weights expected in a projection obtained from a random bipartite network where both the rows and the columns contain approximately the same number of each value. The edges in B must be integers, and are assumed to represent an ordinal-level measure such as a Likert scale that starts at 0.

When signed = FALSE, a one-tailed test (is the weight stronger) is performed for each edge with a non-zero weight. It yields a backbone that perserves edges whose weights are significantly stronger than expected in the chosen null model. When signed = TRUE, a two-tailed test (is the weight stronger or weaker) is performed for each every pair of nodes. It yields a backbone that contains positive edges for edges whose weights are significantly stronger, and negative edges for edges whose weights are significantly weaker, than expected in the chosen null model. NOTE: Before v2.0.0, all significance tests were two-tailed and zero-weight edges were evaluated.

The p-values used to evaluate the statistical significance of each edge are computed using Monte Carlo methods. The number of trials performed affects the precision of these p-values, and the confidence that a given p-value is less than the desired alpha level. Because these p-values are proportions (i.e., the proportion of times an edge is weaker/stronger in the projection of a random bipartite graphs), evaluating the statistical significance of an edge is equivalent to comparing a proportion (the p-value) to a known proportion (alpha). When trials = NULL, the power.prop.test function is used to estimate the required number of trials to make such a comparison with a alpha type-I error rate, (1-alpha) power, and when the riskiest p-value being evaluated is at least 5% smaller than alpha. When any mtc correction is applied, for simplicity this estimation is based on a conservative Bonferroni correction.

Value

If alpha != NULL: Binary or signed backbone graph of class class.

If alpha == NULL: An S3 backbone object containing three matrices (the weighted graph, edges' upper-tail p-values, edges' lower-tail p-values), and a string indicating the null model used to compute p-values, from which a backbone can subsequently be extracted using backbone.extract(). The signed, mtc, class, and narrative parameters are ignored.

References

package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. PLOS ONE, 17, e0269137. doi: 10.1371/journal.pone.0269137

osdsm: Neal, Z. P. (2017). Well connected compared to what? Rethinking frames of reference in world city network research. Environment and Planning A, 49, 2859-2877. doi: 10.1177/0308518X16631339

Examples

#A weighted binary bipartite network of 20 agents & 50 artifacts; agents form two communities
B <- rbind(cbind(matrix(sample(0:3, 250, replace = TRUE, prob = ((1:4)^2)),10),
                 matrix(sample(0:3, 250, replace = TRUE, prob = ((4:1)^2)),10)),
           cbind(matrix(sample(0:3, 250, replace = TRUE, prob = ((4:1)^2)),10),
                 matrix(sample(0:3, 250, replace = TRUE, prob = ((1:4)^2)),10)))

P <- B%*%t(B) #An ordinary weighted projection...
plot(igraph::graph_from_adjacency_matrix(P, mode = "undirected",
                                         weighted = TRUE, diag = FALSE)) #...is a dense hairball

bb <- osdsm(B, alpha = 0.05, narrative = TRUE,  #An oSDSM backbone...
            class = "igraph", trials = 100)
plot(bb) #...is sparse with clear communities

[Package backbone version 2.1.0 Index]