Allow sim_mv to simulate DAGs with cycles

[stefaneng]

Example:

library(GWASBrewer)

G <- matrix(
  c(0, 0, 0.1, 0,
    0.4, 0, 0, 0,
    0, 0, 0,  0.1,
    0, -0.5, 0.2, 0),
  nrow = 4,
  byrow = 4
)

dat <- sim_mv(
    G = G,
    N = 20000,
    J = 5000,
    h2 = 0.2,
    pi =  0.1,
    est_s = TRUE,
    restrict_dag = FALSE
)

mvmr_res <- nesmr_complete_mvmr(
    beta_hat = dat$beta_hat,
    se_beta_hat = dat$s_estimate,
    pval_select = NULL,
    alpha = alpha
)

print("--- leave-one-out MVMR ---")
print(round(mvmr_res$beta_hat, 2))
print(sprintf("RMSE: %.3f", sqrt(mean((mvmr_res$beta_hat - G)^2))))

#> [1] "--- leave-one-out MVMR ---"
#>       [,1]  [,2]  [,3]  [,4]
#> [1,]  0.00 -0.01  0.10 -0.02
#> [2,]  0.28  0.00 -0.01 -0.05
#> [3,]  0.00  0.01  0.00  0.08
#> [4,] -0.05 -0.46  0.23  0.00
#> [1] "RMSE: 0.036"

nc_res <- nesmr_complete(
    beta_hat = dat$beta_hat,
    se_beta_hat = dat$s_estimate,
    pval_select = NULL,
    alpha = alpha
)

print("--- NESMR Complete ---")
print(round(nc_res$beta_hat, 2))
print(sprintf("RMSE: %.3f", sqrt(mean((nc_res$beta_hat - G)^2))))

#> [1] "--- NESMR Complete ---"
#>       [,1]  [,2] [,3]  [,4]
#> [1,]  0.00 -0.02 0.10 -0.02
#> [2,]  0.28  0.00 0.00 -0.05
#> [3,]  0.01  0.02 0.00  0.18
#> [4,] -0.07 -0.48 0.09  0.00
#> [1] "RMSE: 0.051"