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Summarize the goodness-of-fit of a Direct LiNGAM model at once

Source: R/summary_lingam.r
summary_lingam.Rd

For a fitted Direct LiNGAM model, this verifies how well the two main assumptions on which LiNGAM relies (mutual independence of residuals and non-Gaussianity of residuals) hold, all at once, and displays the results together. Internally it calls get_error_independence_p_values() and test_residual_normality().

Usage

summary_lingam(
  X,
  lingam_result,
  independence_method = "spearman",
  normality_method = "shapiro",
  alpha = 0.05
)

Arguments

X

The original data (matrix or data.frame), the one used to estimate lingam_result.

lingam_result

The return value of lingam_direct() (a LingamResult object)

independence_method

The type of correlation coefficient used in the residual independence test ("spearman", "pearson", "kendall"). Passed to get_error_independence_p_values().

normality_method

The method for the residual normality test ("shapiro", "ks", "ad", "lillie", "jb"). Passed to test_residual_normality().

alpha

Significance level (default: 0.05)

Value

A list of class lingam_summary, containing the following elements:

  • n_variables, n_samples: Number of variables / number of observations

  • causal_order: Causal order (variable-name labels)

  • n_edges: Number of nonzero elements in the adjacency matrix (number of estimated edges)

  • independence_p_values: Matrix of p-values from the independence test between residuals

  • n_dependent_pairs, n_pairs: Number of pairs with p < alpha / total number of pairs

  • min_independence_p: Minimum p-value of the independence test

  • normality: Result of the normality test (a lingam_normality_test object)

  • n_non_gaussian: Number of variables judged to be non-Gaussian

  • alpha, independence_method, normality_method: The settings used

Details

Gaussian-likelihood-based criteria such as BIC/AIC are not included because they are theoretically inconsistent with LiNGAM's assumption that "the errors are non-Gaussian". Instead, the verification results of the assumptions themselves are summarized.

Examples

LiNGAM_sample_1000 <- generate_lingam_sample_6()

model <- lingam_direct(LiNGAM_sample_1000$data, reg_method = "ols")

summary_lingam(LiNGAM_sample_1000$data, model)
#> === Direct LiNGAM Model Summary ===
#> Variables:    6
#> Observations: 1000
#> Edges:        15
#> Causal order: x3 -> x2 -> x0 -> x4 -> x5 -> x1
#> 
#> --- Assumption 1: Independence of residuals ---
#> Method:           spearman
#> Dependent pairs:  0 / 15  (p < 0.050)
#> Min p-value:      0.9187
#> => Residuals appear mutually independent (assumption supported).
#> 
#> --- Assumption 2: Non-Gaussianity of residuals ---
#> Method:           shapiro
#> Non-Gaussian:     6 / 6  (p <= 0.050)
#> => All residuals are non-Gaussian (assumption supported).