pcalg (version 2.7-12)

LINGAM: Linear non-Gaussian Acyclic Models (LiNGAM)

Description

Fits a Linear non-Gaussian Acyclic Model (LiNGAM) to the data and returns the corresponding DAG.

For details, see the reference below.

Usage

lingam(X, verbose = FALSE)
## For back-compatibility; this is *deprecated*
LINGAM(X, verbose = FALSE)

Value

lingam() returns an R object of (S3) class "LINGAM", basically a list with components

Bpruned

a \(p \times p\) matrix \(B\) of linear coefficients, where \(B_{i,j}\) corresponds to a directed edge from \(j\) to \(i\).

stde

a vector of length \(p\) with the standard deviations of the estimated residuals

ci

a vector of length \(p\) with the intercepts of each equation
..................

LINGAM() --- deprecated now --- returns a list with components

Adj

a \(p \times p\) 0/1 adjacency matrix \(A\). A[i,j] == 1 corresponds to a directed edge from i to j.

B

\(p \times p\) matrix of corresponding linear coefficients. Note it corresponds to the transpose of Adj, i.e., identical( Adj, t(B) != 0 ) is true.

Arguments

X

n x p data matrix (n: sample size, p: number of variables).

verbose

logical or integer indicating that increased diagnostic output is to be provided.

Author

Of LINGAM() and the underlying functionality, Patrik Hoyer <[e-mail]>, Doris Entner <[e-mail]>, Antti Hyttinen <[e-mail]> and Jonas Peters <[e-mail]>.

References

S. Shimizu, P.O. Hoyer, A. Hyv\"arinen, A. Kerminen (2006) A Linear Non-Gaussian Acyclic Model for Causal Discovery; Journal of Machine Learning Research 7, 2003--2030.

See Also

fastICA from package fastICA is used.

Examples

##################################################
## Exp 1
##################################################
set.seed(1234)
n <- 500
eps1 <- sign(rnorm(n)) * sqrt(abs(rnorm(n)))
eps2 <- runif(n) - 0.5

x2 <- 3 + eps2
x1 <- 0.9*x2 + 7 + eps1

#truth: x1 <- x2
trueDAG <- cbind(c(0,1),c(0,0))

X <- cbind(x1,x2)
res <- lingam(X)

cat("true DAG:\n")
show(trueDAG)

cat("estimated DAG:\n")
as(res, "amat")

cat("\n true constants:\n")
show(c(7,3))
cat("estimated constants:\n")
show(res$ci)

cat("\n true (sample) noise standard deviations:\n")
show(c(sd(eps1), sd(eps2)))
cat("estimated noise standard deviations:\n")
show(res$stde)


##################################################
## Exp 2
##################################################
set.seed(123)
n <- 500
eps1 <- sign(rnorm(n)) * sqrt(abs(rnorm(n)))
eps2 <- runif(n) - 0.5
eps3 <- sign(rnorm(n)) * abs(rnorm(n))^(1/3)
eps4 <- rnorm(n)^2

x2 <-                eps2
x1 <-   0.9*x2     + eps1
x3 <-   0.8*x2     + eps3
x4 <- -x1  -0.9*x3 + eps4

X <- cbind(x1,x2,x3,x4)

trueDAG <- cbind(x1 = c(0,1,0,0),
                 x2 = c(0,0,0,0),
                 x3 = c(0,1,0,0),
                 x4 = c(1,0,1,0))
## x4 <- x3 <- x2 -> x1 -> x4
## adjacency matrix:
## 0 0 0 1
## 1 0 1 0
## 0 0 0 1
## 0 0 0 0

res1 <- lingam(X, verbose = TRUE)# details on LINGAM
res2 <- lingam(X, verbose = 2)   # details on LINGAM and fastICA
## results are the same, of course:
stopifnot(identical(res1, res2))
cat("true DAG:\n")
show(trueDAG)

cat("estimated DAG:\n")
as(res1, "amat")