logit {backbone}

Logit-based probabilities for SDSM

Description

logit estimates cell probabilities under the logit model

Usage

logit(M)

Arguments

M

matrix

Details

Given a matrix M, the logit model returns a valued matrix B in which Bij is the approximate probability that Mij = 1 in the space of all binary matrices with the same row and column marginals as M.

The Bipartite Configuration Model (BiCM), which is available using bicm is faster and yields slightly more accurate probabilities (Neal et al., 2021). Therefore, it is the default used in sdsm. However, the BiCM it requires the assumption that any cell in M can take a value of 0 or 1.

In contrast, the logit model allows constraints on specific cells. If M represents a bipartite graph, these constraints are equivalent to structural 0s (an edge that can never be present) and structural 1s (an edge that must always be present). To impose such constraints, M should be binary, except that structural 0s are represented with Mij = 10, and structural 1s are represented with Mij = 11.

Value

a matrix of probabilities

References

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

logit model: Neal, Z. P. (2014). The backbone of bipartite projections: Inferring relationships from co-authorship, co-sponsorship, co-attendance and other co-behaviors. Social Networks, 39, 84-97. doi:10.1016/j.socnet.2014.06.001

logit model with constraints: Neal, Z. P. and Neal, J. W. (2024). Stochastic Degree Sequence Model with Edge Constraints (SDSM-EC) for Backbone Extraction. Proceedings of the 12th International Conference on Complex Networks and their Applications. Springer.

Examples

M <- matrix(c(0,0,1,0,1,0,1,0,1),3,3)  #A binary matrix
logit(M)
M <- matrix(c(0,10,1,0,1,0,1,0,11),3,3)  #A binary matrix with structural values
logit(M)