When a network is partially observed (here, NAs in the adjacency matrix rather than 1 or 0 due to missing information between node pairs), it is possible to account for the underlying process that generates those NAs. ‘missSBM’, presented in ‘Barbillon, Chiquet and Tabouy’ (2022) 10.18637/jss.v101.i12, adjusts the popular stochastic block model from network data sampled under various missing data conditions, as described in ‘Tabouy, Barbillon and Chiquet’ (2019) 10.1080/01621459.2018.1562934.
missSBM covers a variety of sampling designs for the missing dyads/nodes, split into two families depending on whether the sampling mechanism can be ignored:
"dyad", "node", "covar-dyad",
"covar-node", "snowball" — whether a dyad/node is observed does
not depend on the network itself, so a naive fit on the observed part
alone is already consistent."double-standard", "block-node",
"block-dyad", "degree" — the sampling depends on the underlying
block structure, the edge value, or the node degree, and must be
modeled jointly with the network to avoid biased inference.The last CRAN version is available via
install.packages("missSBM")
The development version is available via
# devtools::install_github("GrossSBM/missSBM")
install.packages("missSBM", repos = c('https://grosssbm.r-universe.dev', 'https://cloud.r-project.org'))
We illustrate missSBM on the French political blogosphere network
(frenchblog2007, bundled with the package): about 190 blogs, edges
standing for hyperlinks, each blog labeled by political party.
library(missSBM)
library(igraph)
data(frenchblog2007)
frenchblog2007 <- delete_vertices(frenchblog2007, which(degree(frenchblog2007) == 0))
adjacency <- as_adjacency_matrix(frenchblog2007, sparse = FALSE)
full_fit <- estimateMissSBM(adjacency, vBlocks = 1:10, sampling = "node",
control = missSBM_param(trace = FALSE))
plot(full_fit, "icl")
Real-world network data collection is rarely complete. We simulate a block-node sampling design (MNAR): blogs belonging to smaller political parties are less likely to have been surveyed than blogs in bigger ones, a mechanism tied to the very block structure we are trying to recover – exactly the kind of design a naive analysis of the observed part alone would get wrong.
set.seed(1234)
block_prop <- full_fit$bestModel$fittedSBM$blockProp
sampling_rate <- ifelse(block_prop < 0.1, 0.2, 0.8)
partial_network <- observeNetwork(adjacency, sampling = "block-node",
parameters = sampling_rate,
clusters = full_fit$bestModel$fittedSBM$memberships)
mean(is.na(partial_network)) # fraction of missing dyads
[1] 0.07891381
partial_fit <- estimateMissSBM(partial_network, vBlocks = 1:10, sampling = "block-node",
control = missSBM_param(trace = FALSE, iterates = 2))
plot(partial_fit, "icl")
Despite about 8% of the dyads missing under this informative design, missSBM recovers a block structure close to the one found on the fully observed network (Adjusted Rand Index, the closer to 1 the better):
aricode::ARI(full_fit$bestModel$fittedSBM$memberships, partial_fit$bestModel$fittedSBM$memberships)
[1] 0.8208973
par(mfrow = c(1, 2))
plot(full_fit$bestModel, "expected", dimLabels = list(row = "blogs", col = "blogs"))
plot(partial_fit$bestModel, "expected", dimLabels = list(row = "blogs", col = "blogs"))
See vignette("case_study_war_networks") and the JSS
article for a more comprehensive
tour, including covariates and further sampling designs.
Please cite our work using the following references:
Barbillon, P., Chiquet, J., & Tabouy, T. (2022). missSBM: An R Package for Handling Missing Values in the Stochastic Block Model. Journal of Statistical Software, 101(12), 1–32. DOI: 10.18637/jss.v101.i12
Timothée Tabouy, Pierre Barbillon & Julien Chiquet (2019) “Variational Inference for Stochastic Block Models from Sampled Data”, Journal of the American Statistical Association, DOI: 10.1080/01621459.2018.1562934