Estimate graph from observed data

Estimates the graph of a linear SEM with assumed equal variance of the noise terms.

graph_est(X, method = "TD", measure = "deviance", which = "1se", ...)

Arguments

X	A matrix containing the observed variables
method	The estimation method. Possible choises are "TD", "BU", "HTD" and "HBU".
measure	Either "mse", "mae"
which	Either "min" or "1se"
...	Terms passed to the method specific estimation steps. If the method "HBU" is specified it is possible to specify a tuning parameter M to be used in the organic lasso. If the method "HTD" is specified it is posible to specify a max.degree and a search. The max.degree specifies the assumed maximal in-degree in the true causal graph. The parameter search may be set to either "full", "B&B" or "OMP" indicating how the algorithem should search for max.degree number of parameters to produce the lowest conditional variance. The "full" search method simply looks at all possible subsets of the current ansestreal set of size max.degree, the "B&B" method searches via a bound and branch method, and lastly "OMP" uses orthogonal matching pursuit (forward selection) to find max.degree variables from the ansestreal set.

Value

The graph_est function returns a vector top_order with the estimated topological ordering of the causal graph, a matrix G of the estimated causal graph, and lastly a matrix B of the estimated regression matrix.

Details

graph_est is a simple wrapper function which given data will fist estimate the topological ordering of the causal graph using the function top_order, and then estimate the causal graph itself using the function graph_from_top.

See also

graph_est is simply a wrapper functio for the two functions top_order and graph_from_top which givem data will estimate the topological ordering of the causal graph and estimates the causal graph itself given an ordering respectivly.

Examples

# we create some data from the graph B
n <- 1000
B <- matrix(c(0,1,0,1,
              0,0,2,0,
              0,0,0,1,
              0,0,0,0), ncol = 4, nrow = 4, byrow = TRUE)
X <- matrix(0, ncol = 4, nrow = n)
for (i in 1:4) {
  X[ ,i] <- X %*% B[ ,i] + rnorm(n)
}

# from the simulated data we etimate in two different way to illustrate
graph_est(X, method = "TD", measure = "deviance", which = "1se")
#> $top_order
#> [1] 1 2 3 4
#> 
#> $graph
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    0    0    1    0
#> [3,]    0    0    0    1
#> [4,]    0    0    0    0
#> 
#> $B
#>      [,1]      [,2]     [,3]      [,4]
#> [1,]    0 0.8276971 0.000000 1.0078577
#> [2,]    0 0.0000000 1.898111 0.0000000
#> [3,]    0 0.0000000 0.000000 0.9344701
#> [4,]    0 0.0000000 0.000000 0.0000000
#> 
#> attr(,"class")
#> [1] "graph_est"
graph_est(X, method = "HTD",
          measure = "deviance", which = "1se",
          max.degree = 2L, search = "full")
#> $top_order
#> [1] 1 2 3 4
#> 
#> $graph
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    1    0    1
#> [2,]    0    0    1    0
#> [3,]    0    0    0    1
#> [4,]    0    0    0    0
#> 
#> $B
#>      [,1]      [,2]     [,3]      [,4]
#> [1,]    0 0.8467335 0.000000 1.0428946
#> [2,]    0 0.0000000 1.898111 0.0000000
#> [3,]    0 0.0000000 0.000000 0.9458375
#> [4,]    0 0.0000000 0.000000 0.0000000
#> 
#> attr(,"class")
#> [1] "graph_est"