Test normality of residuals from Direct LiNGAM

Calculate residuals (error terms) from the estimated adjacency matrix and test their normality. Since LiNGAM assumes non-Gaussian errors, rejecting normality (small p-value) supports the LiNGAM model assumption.

Usage

test_residual_normality(X, lingam_result, method = "shapiro", alpha = 0.05)

Arguments

X

original data matrix or data.frame

lingam_result

result from lingam_direct()

method

normality test method "shapiro" : Shapiro-Wilk test (default, n <= 5000) "ks" : Kolmogorov-Smirnov test (n > 5000) "ad" : Anderson-Darling test (requires nortest package) "lillie" : Lilliefors test (requires nortest package) "jb" : Jarque-Bera test (requires tseries package)

alpha

significance level (default: 0.05)

Value

data.frame with test results for each variable

Examples

# Load the sample data
LiNGAM_sample_1000 <- generate_lingam_sample_6()

# Run Direct LiNGAM
result <- lingam_direct(LiNGAM_sample_1000$data, reg_method = "ols")

# Shapiro-Wilk (default)
test_residual_normality(LiNGAM_sample_1000$data, result)
#> === Residual Normality Test ===
#> Method:         shapiro
#> Sample size:    1000
#> Significance:   0.050
#> Non-Gaussian:   6 / 6 variables
#> 
#>  variable statistic   p_value is_non_gauss skewness kurtosis
#>        x0    0.9526 < 2.2e-16         TRUE    0.063   -1.214
#>        x1    0.9533 < 2.2e-16         TRUE    0.026   -1.208
#>        x2    0.9557 < 2.2e-16         TRUE    0.083   -1.170
#>        x3    0.9578  2.25e-16         TRUE    0.025   -1.163
#>        x4    0.9556 < 2.2e-16         TRUE   -0.002   -1.205
#>        x5    0.9552 < 2.2e-16         TRUE   -0.044   -1.196
#> 
#> Interpretation:
#>   is_non_gauss = TRUE  -> rejects normality (supports LiNGAM assumption)
#>   is_non_gauss = FALSE -> cannot reject normality (LiNGAM may not fit)
#> 
#> All residuals are non-Gaussian. LiNGAM assumption is supported.