pcalg (version 2.7-12)

rmvDAG: Generate Multivariate Data according to a DAG

Description

Generate multivariate data with dependency structure specified by a (given) DAG (Directed Acyclic Graph) with nodes corresponding to random variables. The DAG has to be topologically ordered.

Usage

rmvDAG(n, dag,
       errDist = c("normal", "cauchy", "t4", "mix", "mixt3", "mixN100"),
       mix = 0.1, errMat = NULL, back.compatible = FALSE,
       use.node.names = !back.compatible)

Value

A \(n*p\) matrix with the generated data. The \(p\) columns correspond to the nodes (i.e., random variables) and each of the

\(n\) rows correspond to a sample.

Arguments

n

number of samples that should be drawn. (integer)

dag

a graph object describing the DAG; must contain weights for all the edges. The nodes must be topologically sorted. (For topological sorting use tsort from the RBGL package.)

errDist

string specifying the distribution of each node. Currently, the options "normal", "t4", "cauchy", "mix", "mixt3" and "mixN100" are supported. The first three generate standard normal-, t(df=4)- and cauchy-random numbers. The options containing the word "mix" create standard normal random variables with a mix of outliers. The outliers for the options "mix", "mixt3", "mixN100" are drawn from a standard cauchy, t(df=3) and N(0,100) distribution, respectively. The fraction of outliers is determined by the mix argument.

mix

for the "mix*" error distributuion, mix specifies the fraction of “outlier” samples (i.e., Cauchy, \(t_3\) or \(N(0,100)\)).

errMat

numeric \(n * p\) matrix specifiying the error vectors \(e_i\) (see Details), instead of specifying errDist (and maybe mix).

back.compatible

logical indicating if the data generated should be the same as with pcalg version 1.0-6 and earlier (where wgtMatrix() differed).

use.node.names

logical indicating if the column names of the result matrix should equal nodes(dag), very sensibly, but new, hence the default.

Author

Markus Kalisch () and Martin Maechler.

Details

Each node is visited in the topological order. For each node \(i\) we generate a \(p\)-dimensional value \(X_i\) in the following way: Let \(X_1,\ldots,X_k\) denote the values of all neighbours of \(i\) with lower order. Let \(w_1,\ldots,w_k\) be the weights of the corresponding edges. Furthermore, generate a random vector \(E_i\) according to the specified error distribution. Then, the value of \(X_i\) is computed as $$X_i = w_1*X_1 + \ldots + w_k*X_k + E_i.$$ If node \(i\) has no neighbors with lower order, \(X_i = E_i\) is set.

See Also

randomDAG for generating a random DAG; skeleton and pc for estimating the skeleton and the CPDAG of a DAG that corresponds to the data.

Examples

## generate random DAG
p <- 20
rDAG <- randomDAG(p, prob = 0.2, lB=0.1, uB=1)

if (require(Rgraphviz)) {
## plot the DAG
plot(rDAG, main = "randomDAG(20, prob = 0.2, ..)")
}

## generate 1000 samples of DAG using standard normal error distribution
n <- 1000
d.normMat <- rmvDAG(n, rDAG, errDist="normal")

## generate 1000 samples of DAG using standard t(df=4) error distribution
d.t4Mat <- rmvDAG(n, rDAG, errDist="t4")

## generate 1000 samples of DAG using standard normal with a cauchy
## mixture of 30 percent
d.mixMat <- rmvDAG(n, rDAG, errDist="mix",mix=0.3)

require(MASS) ## for mvrnorm()
Sigma <- toeplitz(ARMAacf(0.2, lag.max = p - 1))
dim(Sigma)# p x p
## *Correlated* normal error matrix "e_i" (against model assumption)
eMat <- mvrnorm(n, mu = rep(0, p), Sigma = Sigma)
d.CnormMat <- rmvDAG(n, rDAG, errMat = eMat)