Generate Paradoxical Data Where DirectLiNGAM Struggles
Source:R/generate_lingam_sample.r
generate_lingam_paradox_data.RdGenerates a synthetic dataset designed to favor ICA-LiNGAM (due to standardized scales)
while challenging DirectLiNGAM (due to heavy measurement noise on the root variable,
which triggers error propagation). The true causal structure is a serial chain:
x0 -> x1 -> x2 -> x3 (each coefficient 0.8).
Value
list(data, true_adjacency)
data: a data frame with 4 standardized variables (x0,x1,x2,x3); each column has a mean of 0 and a standard deviation of 1.true_adjacency: the 4x4 true adjacency matrix of the data-generating chain, following them[row = to, col = from]convention and holding the structural coefficients (0.8) on the latent, pre-standardization scale.
Details
This function intentionally injects strong measurement error into the root (causal upstream)
variable x0. This noise corrupts the independence tests performed at the initial step
of DirectLiNGAM, frequently causing it to misidentify the root variable and leading to
a cascading failure (error propagation) throughout the causal ordering.
On the other hand, the output data is completely standardized using the scale() function.
This eliminates any differences in scale among the variables, thereby neutralizing the major
weakness of ICA-LiNGAM (scale-dependence) and allowing it to perform relatively better.
Because the data are standardized and the root carries measurement error, the coefficients
estimated by lingam_direct() will not exactly match the 0.8 values stored in
true_adjacency.
Examples
# Generate the dataset
paradox <- generate_lingam_paradox_data(n = 1000, seed = 123)
# Verify the dataset
head(paradox$data)
#> x0 x1 x2 x3
#> 1 -0.98832138 -1.063113 -1.4745460 -1.8068974
#> 2 1.61196747 1.065200 0.1778246 1.0019652
#> 3 0.08506249 -0.909761 -1.3731009 -1.3846494
#> 4 1.75854498 1.845430 1.4870297 1.4747061
#> 5 0.47914188 2.009083 1.5757889 0.6862838
#> 6 -1.99217282 -1.410370 -0.8932110 -0.4404976
sapply(paradox$data, sd)
#> x0 x1 x2 x3
#> 1 1 1 1
# True data-generating structure
paradox$true_adjacency
#> x0 x1 x2 x3
#> x0 0.0 0.0 0.0 0
#> x1 0.8 0.0 0.0 0
#> x2 0.0 0.8 0.0 0
#> x3 0.0 0.0 0.8 0