causal.influence: Identifying causally influential units on social network
In netchain: Inferring Causal Effects on Collective Outcomes under Interference

Description Usage Arguments Value Author(s) Examples

This function calculates probability associated with counterfactual collective outcome(s) P(Y(a_j) = y) as a measure of influence of unit j, where a_j indicates the sole intervention of unit j.

causal.influence(
  targetoutcome = "mean",
  Avalues,
  inputY,
  inputA,
  listC,
  R.matrix,
  E.matrix,
  edgeinfo = NULL,
  n.obs = 1000,
  n.burn = 100,
  optim.method = "L-BFGS-B"
)

`targetoutcome`	is a targeted couterfactual outcome of probability is in our interest, having different forms depending on the context of influence : a vector of length `m` a vector specifies every element of y. a `[q x m]` matrix a collection of y_1, y_2, ..., y_q of which we want to derive the probability. an integer the number of 1's in y (0 ≥ & ≤ m). 'mean' when we want derive E(Y(a)) (default).
`Avalues`	distinct treatment values of which maximum indicates intervention. Defaults to `(0,1)`.
`inputY`	a `[n x m]` matrix of `n` independent outcomes for `m` units.
`inputA`	a `[n x m]` matrix of `n` independent treatment assignments assigned to `m` units.
`listC`	is either a matrix, list or `NULL`: a `[n x m]` matrix a matrix of `n` independent confounders for `m` units under single confounder. a list of `[n x m]` matrices a collection of `n` independent confounders for `m` units under multiple confounders. `NULL` no confounders.
`R.matrix`	a `[m x m]` relational symmetric matrix where R.matrix_ij = 1 indicates Y_i and Y_j are adjacent.
`E.matrix`	a `[m x m]` matrix where E.matrix_ij = 1 indicates A_i has a direct causal effect on Y_j. Defaults to diagonal matrix, which indicates no interference.
`edgeinfo`	a list of matrix specifying additional directed edges (from confounders or treatment to the outcomes) information. Defaults to `NULL`. first column: `"Y"` indicates outcomes; `"A"` indicates treatment; `"C"` indicates confounders. Under multiple confounders, `"C1"`, `"C2"`, ... indicate each confounder. second column: an index for unit corresponding to the variable in the first column, `i=1,2,...m`.
`n.obs`	the number of Gibbs samplers except for burn-in sample.
`n.burn`	the number of burn-in sample in Gibbs sampling.
`optim.method`	the method used in `optim()`. Defaults to `"L-BFGS-B"`.

returns "noconvergence" in case of failure to converence or a list with components :

`influence`
`n.par`	the number of parameters estimated in conditional log-linear model.
`par.est`	the estimated parameters.

Youjin Lee

library(netchain)
set.seed(1234)
weight.matrix <- matrix(c(0.5, 1, 0, 1, 0.3, 0.5, 0, 0.5, -0.5), 3, 3)
simobs <- simGibbs(n.unit = 3, n.gibbs = 100, n.sample = 5, 
                  weight.matrix,
                  treat.matrix = 0.5*diag(3), cov.matrix= (-0.3)*diag(3) )
inputY <- simobs$inputY                   
inputA <- simobs$inputA   
inputC <- simobs$inputC 
R.matrix <- ifelse(weight.matrix==0, 0, 1)
diag(R.matrix) <- 0
edgeinfo <- list(rbind(c("Y", 1), c("C", 1)), rbind(c("Y", 2), c("C", 2)), 
           rbind(c("Y", 3), c("C", 3)))   
# implement a function (take > 10 seconds)
# result <- causal.influence(targetoutcome = "mean", Avalues = c(1,0), inputY, inputA, 
# listC = inputC, R.matrix, E.matrix = diag(3), edgeinfo = edgeinfo)