dda.indep: Direction Dependence Analysis: Independence Properties

Description

dda.indep evaluates asymmetries of predictor-error independence of causally competing models (y ~ x vs. x ~ y).

print returns DDA test statistics associated with dda.indep objects.

Usage

dda.indep(
  formula,
  pred = NULL,
  data = list(),
  nlfun = NULL,
  hetero = FALSE,
  hsic.method = "gamma",
  diff = FALSE,
  B = 200,
  boot.type = "perc",
  conf.level = 0.95,
  parallelize = FALSE,
  cores = 1
)
# S3 method for dda.indep
print(x, ...)

Value

An object of class dda.indep containing the results of independence tests of Direction Dependence Analysis.

Arguments

formula: Symbolic formula of the model to be tested or a lm object.
pred: A character indicating the variable name of the predictor which serves as the outcome in the alternative model.
data: An optional data frame containing the variables in the model (by default variables are taken from the environment which dda.indep is called from).
nlfun: Either a numeric value or a function of .Primitive type used for non-linear correlation tests. When nlfun is numeric the value is used in a power transformation.
hetero: A logical value indicating whether separate homoscedasticity tests (i.e., standard and robust Breusch-Pagan tests) should be computed.
hsic.method: A character indicating the inference method for the Hilbert-Schmidt Independence Criterion (HSIC). Must be one of the four specifications c("gamma", "eigenvalue", "bootstrap", "permutation"). hsic.method = "gamma"is the default.
diff: A logical value indicating whether differences in HSIC, Distance Correlation (dCor), and MI values should be computed. Bootstrap confidence intervals are computed using B bootstrap samples.
B: Number of permutations for separate dCor tests and number of resamples if hsic.method = c("bootstrap", "permutation") or diff = TRUE.
boot.type: A vector of character strings representing the type of bootstrap confidence intervals. Must be one of the two specifications c("perc", "bca").boot.type = "perc" is the default.
conf.level: Confidence level for bootstrap confidence intervals.
parallelize: A logical value indicating whether bootstrapping is performed on multiple cores. Only used if diff = TRUE.
cores: A numeric value indicating the number of cores. Only used if parallelize = TRUE.
x: An object of class dda.indep when using print.
...: Additional arguments to be passed to the function.

References

Wiedermann, W., & von Eye, A. (2025). Direction Dependence Analysis: Foundations and Statistical Methods. Cambridge, UK: Cambridge University Press.

Examples

Run this code


set.seed(123)
n <- 500
x <- rchisq(n, df = 4) - 4
e <- rchisq(n, df = 3) - 3
y <- 0.5 * x + e
d <- data.frame(x, y)

result <- dda.indep(y ~ x, pred = "x", data = d, parallelize = TRUE, cores = 2,
          nlfun = 2, B = 50, hetero = TRUE, diff = TRUE)


print(result)