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Percentile

Enumerates sets of covariates that (asymptotically) allow unbiased estimation of causal effects from observational data, assuming that the input causal graph is correct.

##### Usage
adjustmentSets(x, exposure = NULL, outcome = NULL, type = c("minimal", "canonical", "all"), effect = c("total", "direct"))
##### Arguments
x
the input graph, a DAG, MAG, PDAG, or PAG.
exposure
name(s) of the exposure variable(s). If not given (default), then the exposure variables are supposed to be defined in the graph itself.
outcome
name(s) of the outcome variable(s), also taken from the graph if not given.
type
which type of adjustment set(s) to compute. If type="minimal", then only minimal sufficient adjustment sets are returned (default). For type="all", all valid adjustment sets are returned. For type="canonical", a single adjustment set is returned that consists of all (possible) ancestors of exposures and outcomes, minus (possible) descendants of nodes on proper causal paths. This canonical adjustment set is always valid if any valid set exists at all.
effect
which effect is to be identified. If effect="total", then the total effect is to be identified, and the adjustment criterion by Perkovic et al (2015; see also van der Zander et al., 2014), an extension of Pearl's back-door criterion, is used. Otherwise, if effect="direct", then the average direct effect is to be identified, and Pearl's single-door criterion is used (Pearl, 2009). In a structural equation model (Gaussian graphical model), direct effects are simply the path coefficients.
##### Details

If the input graph is a MAG or PAG, then it must not contain any undirected edges (=hidden selection variables).

##### References

J. Pearl (2009), Causality: Models, Reasoning and Inference. Cambridge University Press.

B. van der Zander, M. Liskiewicz and J. Textor (2014), Constructing separators and adjustment sets in ancestral graphs. In Proceedings of UAI 2014.

E. Perkovic, J. Textor, M. Kalisch and M. H. Maathuis (2015), A Complete Generalized Adjustment Criterion. In Proceedings of UAI 2015.

##### Examples
# The M-bias graph showing that adjustment for
# pre-treatment covariates is not always valid
g <- dagitty( "dag{ x -> y ; x <-> m <-> y }" )
adjustmentSets( g, "x", "y" ) # empty set
# Generate data where true effect (=path coefficient) is .5
set.seed( 123 ); d <- simulateSEM( g, .5, .5 )
confint( lm( y ~ x, d ) )["x",] # includes .5
confint( lm( y ~ x + m, d ) )["x",] # does not include .5

# Adjustment sets can also sometimes be computed for graphs in which not all
# edge directions are known
g <- dagitty("pdag { x[e] y[o] a -- {i z b}; {a z i} -> x -> y <- {z b} }")