backbone (version 2.0.0)

osdsm: 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,
  trials = 1000,
  alpha = NULL,
  signed = FALSE,
  fwer = "none",
  class = "original",
  narrative = FALSE
)

Arguments

B

An ordinally weighted bipartite graph, as: (1) an incidence matrix in the form of a matrix, sparse Matrix, or dataframe; (2) an edgelist in the form of a three-column matrix, sparse Matrix, or dataframe; (3) an igraph object; (4) a network object. Any rows and columns of the associated bipartite matrix that contain only zeros or only ones are automatically removed before computations.

trials

integer: Number of random bipartite graphs generated

alpha

real: significance level of hypothesis test(s)

signed

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

fwer

string: type of familywise error rate 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", "sparseMatrix", "igraph", "network", "edgelist"). If "original", the backbone graph returned is of the same class as B.

narrative

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

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, fwer, class, and narrative parameters are ignored.

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.

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.

References

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. 10.1177/0308518X16631339

Examples

# NOT RUN {
#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, class = "igraph") #An oSDSM backbone...
plot(bb) #...is sparse with clear communities
# }