# Linear non-Gaussian Acyclic Models (LiNGAM) Fits a Linear non-Gaussian Acyclic Model (LiNGAM) to the data and returns the corresponding DAG. For details, see the reference below. ```r lingam(X, verbose = FALSE) ## For back-compatibility; this is *deprecated* LINGAM(X, verbose = FALSE) ``` ## 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. ## Returns `lingam()` returns an object of (S3) class `"LINGAM"`, basically a `list` with components - **Bpruned**: a $p x p$ 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 $p x p$ 0/1 adjacency matrix $A$. `A[i,j] == 1` corresponds to a directed edge from i to j. - **B**: $p x p$ matrix of corresponding linear coefficients. Note it corresponds to the **transpose** of `Adj`, i.e., `identical( Adj, t(B) != 0 )` is true. ## 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. ## Author(s) Of `LINGAM()` and the underlying functionality, Patrik Hoyer , Doris Entner , Antti Hyttinen and Jonas Peters . ## See Also `fastICA` from package `fastICA` is used. ## Examples ```r ################################################## ## 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") ```

LINGAM function