In Selbosh/scrooge: Statistical modelling of heterogeneous citation networks

Suppose each player, (i), belongs to a community, (c_i). Then we may wish to fit the following model. [\operatorname{logit}\mathbb{P}(i~\text{cites}~j) = \alpha_i(c_j) - \alpha_j(c_i)]

That is, in each game, player (i)'s ability depends on the community of player (j) and vice versa.

To implement this in R, try the following (based on this Gist).

modelcommunities <- function(C, groups) {
  n <- nrow(C)
  ngroups <- length(unique(groups))
  Y <- as.matrix(cbind(win1 = t(C)[lower.tri(C)],
                       win2 = C[lower.tri(C)]))
  npairs <- nrow(Y)
  X <- matrix(0, npairs, n * ngroups)
  X[cbind(
      1:npairs,
      col(C)[lower.tri(C)] + n * (groups[row(C)[lower.tri(C)]] - 1)
      )] <- 1
  X[cbind(
      1:npairs,
      row(C)[lower.tri(C)] + n * (groups[col(C)[lower.tri(C)]] - 1)
      )] <- -1
  colnames(X) <- varNames <- c(outer(colnames(C), paste0('G', 1:ngroups), paste, sep = '_'))
  X <- X[, -1] # remove a redundant column

  glm(Y ~ 0 + X, family = binomial)
}

Here is an example of using such code.

library(scrooge)
data(citations)
G <- sample.int(4, nrow(citations), replace = TRUE) # 4 random communities
modelcommunities(citations, G)

Selbosh/scrooge documentation built on May 5, 2019, 8 p.m.