cdda.vardist: Conditional Directional Dependence Analysis: Variable Distributions

Description

cdda.vardist evaluates variable distributions of competing conditional models (y ~ x * m vs.x ~ y * m with m being a continuous or categorical moderator).

print returns the output of standard linear model coefficients for competing target and alternative models.

plot returns graphs for results of cdda.vardist.

summary returns test statistics from the cdda.vardist class object.

Usage

cdda.vardist(
  formula,
  pred = NULL,
  mod = NULL,
  data = list(),
  modval = NULL,
  B = 200,
  boot.type = "perc",
  conf.level = 0.95
)
# S3 method for cdda.vardist
print(x, ...)
# S3 method for cdda.vardist
plot(x, stat = NULL, ylim = NULL, ...)
# S3 method for cdda.vardist
summary(object, skew = TRUE, coskew = FALSE, kurt = TRUE, cokurt = FALSE, ...)

Value

An object of class cdda.vardist containing the results of conditional direction dependence tests of variable distributions.

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.
mod: A character indicating the variable name of the moderator.
data: A required data frame containing the variables in the model.
modval: Characters or a numeric sequence specifying the moderator values used in post-hoc probing. Possible characters include c("mean", "median", "JN"). modval = "mean" tests the interaction effect at the moderator values M - 1SD, M, and M + 1SD; modval = "median" uses Q1, Md, and Q3. The Johnson-Neyman approach is applied when modval = "JN" with conditional effects being evaluated at the boundary values of the significance regions. When a numeric sequence is specified, the pick-a-point approach is used for the selected numeric values.
B: Number of bootstrap samples.
boot.type: A character indicating the type of bootstrap confidence intervals. Must be one of the two values c("perc", "bca"). boot.type = "bca" is the default.
conf.level: Confidence level for bootstrap confidence intervals.
x: An object of class cdda.vardist when using print or plot.
...: Additional arguments to be passed to the function.
stat: A character indicating the statistic to be plotted, default is "rhs", with options c("coskew", "cokurt", "rhs", "rcc", "rtanh").
ylim: A numeric vector of length 2 indicating the y-axis limits. If NULL, the function will set the limits automatically.
object: An object of class cdda.vardist when using summary.
skew: A logical value indicating whether skewness differences and separate D'Agostino skewness tests should be returned when using summary, default is TRUE.
coskew: A logical value indicating whether co-skewness differences should be returned when using summary, default is FALSE.
kurt: A logical value indicating whether excess kurtosis differences and Anscombe-Glynn kurtosis tests should be returned when using summary, default is TRUE.
cokurt: A logical value indicating whether co-kurtosis differences should be returned when using summary, default is FALSE.

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(321)
n <- 700

## --- generate moderator

z <- sort(rnorm(n))
z1 <- z[z <= 0]
z2 <- z[z > 0]

## --- x -> y when z <= 0

x1 <- rchisq(length(z1), df = 4) - 4
e1 <- rchisq(length(z1), df = 3) - 3
y1 <- 0.5 * x1 + e1

## --- y -> x when m z > 0

y2 <- rchisq(length(z2), df = 4) - 4
e2 <- rchisq(length(z2), df = 3) - 3
x2 <- 0.25 * y2 + e2

y <- c(y1, y2); x <- c(x1, x2)

d <- data.frame(x, y, z)

m <- lm(y ~ x * z, data = d)

result <- cdda.vardist(m, pred = "x", mod = "z", B = 50,
                      modval = c(-1, 1), data = d)

print(result)

plot(result, stat = "rtanh", ylim = c(-0.05, 0.05))

summary(result, skew = FALSE, kurt = FALSE, coskew = TRUE)