A collection of tests to analyze the causal direction of dependence in linear models (Wiedermann, W., & von Eye, A., 2025, ISBN: 9781009381390). The package includes functions to perform Direction Dependence Analysis for variable distributions, residual distributions, and independence properties of predictors and residuals in competing causal models. In addition, the package contains functions to test the causal direction of dependence in conditional models (i.e., models with interaction terms) For more information see < https://www.ddaproject.com>.
Direction Dependence Analysis (Package: \code{dda}) provides framework for analyzing competing linear models. A target model \code{y ~ x} is compared to an alternate (causally reversed) model \code{x ~ y} through a series of diagnostic tests. DDA framework supports causal model exploration and potential confounding detection through diagnostics with higher-order moments.
cdda.indep() conditional (moderation) independence property tests, including non‐linear correlation tests, Breusch–Pagan homoscedasticity tests, and the HSIC testcdda.vardist() conditional (moderation) variable distribution‐based tests, including D'Agostino and Anscombe–Glynn tests and bootstrap CIs on higher moment differencesdda.indep() independence property tests, including non‐linear correlation tests, Breusch–Pagan homoscedasticity tests, and the HSIC testdda.resdist() residual distribution tests, including D'Agostino and Anscombe–Glynn tests and bootstrap CIs on higher moment differencesdda.vardist() variable distribution‐based tests, including D'Agostino and Anscombe–Glynn tests and bootstrap CIs on higher moment differencesIf you are new to Direction Dependence Analysis (DDA) concepts, the best place to start is the Direction Dependence in Statistical Modeling: Methods of Analysis text.
The dda development version can be installed from GitHub:
remotes::install_github("wwiedermann/dda")
library(dda)
n <- 1000
### generate moderator
z <- sort(rnorm(n))
z1 <- z[z <= 0]; z2 <- z[z > 0]
### x -> y when m <= 0
x1 <- rchisq(length(z1), df = 4) - 4
e1 <- rchisq(length(z1), df = 3) - 3
y1 <- 0.5 * x1 + e1
### y -> x when m > 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)
dat <- data.frame(x,y,z)
m <- lm(y ~ x*z, data = dat)
##summary(m)
mean.indep <- cdda.indep(m, pred = "x", mod = "z", data = dat, nlfun = 2,
modval = "mean", diff = TRUE, hetero = TRUE)
summary(mean.indep, hsic.diff = TRUE, dcor.diff = TRUE, mi.diff = TRUE)
plot.cddaindep(mean.indep, stat = "hsic.diff")
point.vardist <- cdda.vardist(m, pred = "x", mod = "z", data = dat,
modval = c(-1, 0, 1))
summary(point.vardist, coskew = TRUE, cokurt = TRUE)
plot(mean.vardist, stat = "rhs", ylim = c(-0.2, 0.3))
If you encounter a clear bug, please file an issue with a minimal reproducible example on GitHub. For questions and other discussion, please contact the package maintainer.