| Total causal effect of a node on another node {MXM} | R Documentation |
Total causal effect of a node on another node
Description
Total causal effect of a node on another node.
Usage
ida(x, y, G, dataset)
Arguments
x |
A number between 1 and the number of variables (nodes) indicating the node whose total causal effect we want to estimate. This is the independent variable. See details for more on this. |
y |
A number between 1 and the number of variables (nodes) indicating the node who is the dependent variable. The goal is to estimate the total causal effect of x on y. |
G |
A square matrix representing a (partially) directed graph which contains 0s and 1s. If G[i, j] = 2 it means there is an arrow from node i to node j. If G[i, j] = 1, there is an undirected edge between nodes i and j and there is no edge between nodes i and j if G[i, j] = 0. |
dataset |
The dataset. This is a numerical matrix with data. |
Details
The total causal effect defined in Pearl's do-calculus is E(Y|do(X=z+1)) - E(Y|do(X=z)). As Pearl described it, he used linear regression, hence this funciton works for continuous data which are assumed to be Gaussian.
We estimate a set of possible total causal effects using linear regression. if y is a parent, or a descendant, of x in G, the estimated causal effect of x on y is zero. If y is not a parent of x, we take the regression coefficient of x in the regression lm(y ~ x + pa(x)), where pa(x) denotes the parents of x. This is repeated using all parents of x (including the empty set) and all possible parents values of x and their combinations.
One restriction to bear in mind. If a collider is created that combination of nodes is not used in the regression.
Value
A lis tincluding:
tc |
A matrix with 4 elements. The first columns one is the estimated beta coefficient, the second is its standard error, its t-value and the p-value for testing whether this is equal to 0. |
mess |
If the x node has no parents a message about this appears. Otherwise this is NULL. |
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr
References
M.H. Maathuis, M. Kalisch and P. Buehlmann (2009). Estimating high-dimensional intervention effects from observational data. Annals of Statistics 37, 3133-3164.
Pearl (2005). Causality. Models, reasoning and inference. Cambridge University Press, New York.
See Also
Examples
dataset <- rdag2(1000, p = 20, nei = 3)$x
mod <- pc.skel(dataset ,alpha = 0.01)
G <- pc.or(mod)$G
ida(10, 15, G, dataset)