ida: Total causal effect of a node on another node

In MXM: Feature Selection (Including Multiple Solutions) and Bayesian Networks

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 [e-mail]

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

plotnetwork, nei, pc.or

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)

MXM documentation built on Aug. 25, 2022, 9:05 a.m.