tskeleton {tpc}

Estimate the Skeleton of a DAG while Accounting for a Partial Ordering

Description

Like pcalg::skeleton, but takes a user-specified partial node ordering into account. The conditional independence between x and y given S is not tested if any variable in S lies in the future of both x and y.

Usage

tskeleton(
  suffStat,
  indepTest,
  alpha,
  labels,
  p,
  method = c("stable", "original"),
  m.max = Inf,
  fixedGaps = NULL,
  fixedEdges = NULL,
  NAdelete = TRUE,
  tiers = NULL,
  verbose = FALSE
)

Arguments

suffStat

A list of sufficient statistics, containing all necessary elements for the conditional independence decisions in the function indepTest.

indepTest

Predefined function for testing conditional independence. It is internally called as indepTest(x,y,S,suffStat), and tests conditional independence of x and y given S. Here, x and y are variables, and S is a (possibly empty) vector of variables (all variables are denoted by their (integer) column positions in the adjacency matrix). suffStat is a list, see the argument above. The return value of indepTest is the p-value of the test for conditional independence.

alpha

Significance level (number in (0,1) for the individual conditional independence tests.

labels

(optional) character vector of variable (or "node") names. Typically preferred to specifying p.

p

(optional) number of variables (or nodes). May be specified if labels are not, in which case labels is set to 1:p.

method

Character string specifying method; the default, "stable" provides an order-independent skeleton, see 'Details' below.

m.max

Maximal size of the conditioning sets that are considered in the conditional independence tests.

fixedGaps

logical symmetric matrix of dimension p*p. If entry [i,j] is true, the edge i-j is removed before starting the algorithm. Therefore, this edge is guaranteed to be absent in the resulting graph.

fixedEdges

a logical symmetric matrix of dimension p*p. If entry [i,j] is true, the edge i-j is never considered for removal. Therefore, this edge is guaranteed to be present in the resulting graph.

NAdelete

logical needed for the case indepTest(*) returns NA. If it is true, the corresponding edge is deleted, otherwise not.

tiers

Numeric vector specifying the tier / time point for each variable. Must be of length 'p', if specified, or have the same length as 'labels', if specified. A smaller number corresponds to an earlier tier / time point. Conditional independence testing is restricted such that if x is in tier t(x) and y is in t(y), only those variables are allowed in the conditioning set whose tier is not larger than t(x).

verbose

if TRUE, detailed output is provided.

Details

See pcalg::skeleton for further information on the skeleton algorithm.

Value

An object of class "pcAlgo" (see pcalg::pcAlgo) containing an estimate of the skeleton of the underlying DAG, the conditioning sets (sepset) that led to edge removals and several other parameters.

Author(s)

Original code by Markus Kalisch, Martin Maechler, Alain Hauser and Diego Colombo. Modifications by Janine Witte.

Examples

# load simulated cohort data
data("dat_sim")
n <- nrow(dat_sim)
lab <- colnames(dat_sim)
# estimate skeleton without taking background information into account
tskel.fit <- tskeleton(suffStat = list(C = cor(dat_sim), n = n),
                       indepTest = gaussCItest, alpha = 0.01, labels = lab)
skel.fit <- pcalg::skeleton(suffStat = list(C = cor(dat_sim), n = n),
                            indepTest = gaussCItest, alpha = 0.01, labels = lab)
                            identical(skel.fit@graph, tskel.fit@graph) # TRUE

# estimate skeleton with temporal ordering as background information
tiers <- rep(c(1,2,3), times=c(3,3,3))
tskel.fit2 <- tskeleton(suffStat = list(C = cor(dat_sim), n = n),
                       indepTest = gaussCItest, alpha = 0.01, labels = lab, tiers = tiers)

# in this case, the skeletons estimated with and without
# background knowledge are identical, but fewer conditional
# independence tests were performed when background
# knowledge was taken into account
identical(tskel.fit@graph, tskel.fit2@graph) # TRUE
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