causaleffect {BCDAG}  R Documentation 
This function computes the total joint causal effect on variable response
consequent to an intervention on variables targets
for a given a DAG structure and parameters (D,L)
causaleffect(targets, response, L, D)
targets 
numerical vector with labels of target nodes 
response 
numerical label of response variable 
L 

D 

We assume that the joint distribution of random variables X_1, \dots, X_q
is zeromean Gaussian with covariance matrix Markov w.r.t. a Directed Acyclic Graph (DAG).
In addition, the allied Structural Equation Model (SEM) representation of a Gaussian DAGmodel allows to express the covariance matrix as a function of the (Cholesky) parameters (D,L)
,
collecting the conditional variances and regression coefficients of the SEM.
The total causal effect on a given variable of interest (response
) consequent to a joint intervention on a set of variables (targets
)
is defined according to Pearl's docalculus theory and under the Gaussian assumption can be expressed as a function of parameters (D,L)
.
The joint total causal effect, represented as a vector of same length of targets
Federico Castelletti and Alessandro Mascaro
J. Pearl (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge.
F. Castelletti and A. Mascaro (2021). Structural learning and estimation of joint causal effects among networkdependent variables. Statistical Methods and Applications, Advance publication.
P. Nandy, M.H. Maathuis and T. Richardson (2017). Estimating the effect of joint interventions from observational data in sparse highdimensional settings. Annals of Statistics 45(2), 647674.
# Randomly generate a DAG and the DAGparameters
q = 8
w = 0.2
set.seed(123)
DAG = rDAG(q = q, w = w)
outDL = rDAGWishart(n = 1, DAG = DAG, a = q, U = diag(1, q))
L = outDL$L; D = outDL$D
# Total causal effect on node 1 of an intervention on {5,6}
causaleffect(targets = c(6,7), response = 1, L = L, D = D)
# Total causal effect on node 1 of an intervention on {5,7}
causaleffect(targets = c(5,7), response = 1, L = L, D = D)