SEMace {SEMgraph}

Compute the Average Causal Effect (ACE) for a given source-sink pair

Description

Compute total effects as ACEs of variables X on variables Y in a directed acyclic graph (DAG). The ACE will be estimated as the path coefficient of X (i.e., theta) in the linear equation Y ~ X + Z. The set Z is defined as the adjustment (or conditioning) set of Y over X, applying various adjustement sets. Standard errors (SE), for each ACE, are computed following the lm standard procedure or a bootstrap-based procedure (see boot for details).

Usage

SEMace(
  graph,
  data,
  group = NULL,
  type = "parents",
  effect = "all",
  method = "BH",
  alpha = 0.05,
  boot = NULL,
  ...
)

Arguments

graph

An igraph object.

data

A matrix or data.frame. Rows correspond to subjects, and columns to graph nodes (variables).

group

A binary vector. This vector must be as long as the number of subjects. Each vector element must be 1 for cases and 0 for control subjects. If group = NULL (default), group influence will not be considered.

type

character Conditioning set Z. If "parents" (default) the Pearl's back-door set (Pearl, 1998), "minimal" the dagitty minimal set (Perkovic et al, 2018), or "optimal" the O-set with the smallest asymptotic variance (Witte et al, 2020) are computed.

effect

character X to Y effect. If "all" (default) all effects from X to Y, "source2sink" only effects from source X to sink Y, or "direct" only direct effects from X to Y are computed.

method

Multiple testing correction method. One of the values available in p.adjust. By default, method = "BH" (i.e., FDR multiple test correction).

alpha

Significance level for ACE selection (by default, alpha = 0.05).

boot

The number of bootstrap samplings enabling bootstrap computation of ACE standard errors. If NULL (default), bootstrap is disabled.

...

Currently ignored.

Value

A data.frame of ACE estimates between network sources and sinks.

Author(s)

Mario Grassi [e-mail]

References

Pearl J (1998). Graphs, Causality, and Structural Equation Models. Sociological Methods & Research, 27(2):226-284. <https://doi.org/10.1177/0049124198027002004>

Perkovic E, Textor J, Kalisch M, Maathuis MH (2018). Complete graphical characterization and construction of adjustment sets in Markov equivalence classes of ancestral graphs. Journal of Machine Learning Research, 18:1-62. <http://jmlr.org/papers/v18/16-319.html>

Witte J, Henckel L, Maathuis MH, Didelez V (2020). On efficient adjustment in causal graphs. Journal of Machine Learning Research, 21:1-45. <http://jmlr.org/papers/v21/20-175.htm>

Examples

# ACE without group, O-set, all effects:
ace1 <- SEMace(graph = sachs$graph, data = log(sachs$pkc),
               group = NULL, type = "optimal", effect = "all",
               method = "BH", alpha = 0.05, boot = NULL)
print(ace1)

# ACE with group perturbation, Pa-set, direct effects:
ace2 <- SEMace(graph = sachs$graph, data = log(sachs$pkc),
               group = sachs$group, type = "parents", effect = "direct",
               method = "none", alpha = 0.05, boot = NULL)
print(ace2)