Model-based causal feature selection for general response types

Package tramicp [1] implements invariant causal prediction (ICP) [2] for transformation models [3], including binary logistic regression, Weibull regression, the Cox model, linear regression and many others. Methods for other generalized linear models are also provided. The aim of ICP is to discover the direct causes of a response given data from heterogeneous experimental settings and a potentially large pool of candidate predictors. Methodological details are described in the paper.

Installation

The development version of tramicp package can be installed via:

# install.packages("remotes")
remotes::install_github("LucasKook/tramicp")

A stable version is available on CRAN:

install.packages("tramicp")

Using package tramicp

Consider the following data simulated from a structural causal model:

set.seed(-42)
n <- 5e2
E <- sample(0:1, n, TRUE)
X1 <- -E + rnorm(n)
Y <- as.numeric(0.5 * X1 > rlogis(n))
X2 <- Y + 0.8 * E + rnorm(n)
df <- data.frame(Y = Y, X1 = X1, X2 = X2, E = E)

The response Y is governed by a logistic regression model with parent X1, X2 is a child and both X1 and X2 are influenced by a binary environment indicator E. tramicp can discover the parent of Y by testing whether the score residuals for the models Y ~ X1, Y ~ X2, and Y ~ X1 + X2 are uncorrelated with (a residualized version of) E. Under the correctly specified model, Y ~ X1, this correlation will be zero. To obtain an estimator for the parent set, ICP takes the intersection over all sets for which the invariance hypothesis is failed to be rejected.

The code chunk below shows how to use TRAMICP on the data above.

icp <- glmICP(Y ~ X1 + X2, data = df, env = ~ E, family = "binomial",
              test = "gcm.test", verbose = FALSE)
pvalues(icp, "set")

       Empty           X1           X2        X1+X2 
1.818449e-02 5.096300e-01 4.541276e-09 2.219956e-03 

Indeed, the only set which is not rejected is X1.

Here, glmICP() with family = "binomial" is used. The formula Y ~ X1 + X2 specifies the response (LHS) and all candidate predictors (RHS). The environments are also specified as a formula (RHS only). Details on the test and other options can be found in the manuscript and documentation of the package.

General usage

In full generality, TRAMICP is implemented in the dicp() function, which takes the argument modFUN (model function). For instance, the glmICP call from above is equivalent to dicp(..., modFUN = glm, family = "binomial").

Implemented model classes

Instead of using dicp(), tramicp directly implements several model classes with an alias, as shown in the table below.

Function alias	Corresponding modFUN
BoxCoxICP()	tram::BoxCox()
ColrICP()	tram::Colr()
cotramICP()	cotram::cotram()
CoxphICP()	tram::Coxph()
coxphICP()	survival::coxph()
glmICP()	stats::glm()
LehmannICP()	tram::Lehmann()
LmICP()	tram::Lm()
lmICP()	stats::lm()
PolrICP()	tram::Polr()
polrICP()	MASS::polr()
SurvregICP()	tram::Survreg()
survregICP()	survival::survreg()

Other implementations, such as additive TRAMs in tramME, can still be used via the dicp() function, for instance, after loading tramME, dicp(..., modFUN = "BoxCoxME") can be used.

Nonparametric ICP via the GCM test [4] and random forests for the two regressions is implemented in the alias rangerICP(). Survival forests are supported for right-censored observations and implemented in survforestICP().

Replication materials

This repository contains the code for reproducing the results in [1] in the inst directory. Please follow the instructions in the README to run the code.

References

[1] Kook L., Saengkyongam S., Lundborg A., Hothorn T., Peter J. (2023) Model-based causal feature selection for general response types. arXiv preprint. doi:10.48550/arXiv.2309.12833

[2] Peters, J., Bühlmann, P., & Meinshausen, N. (2016). Causal inference by using invariant prediction: identification and confidence intervals. Journal of the Royal Statistical Society Series B: Statistical Methodology, 78(5), 947-1012. doi:10.1111/rssb.12167

[3] Hothorn, T., Möst, L., & Bühlmann, P. (2018). Most likely transformations. Scandinavian Journal of Statistics, 45(1), 110-134. doi:10.1111/sjos.12291

[4] Shah, R. D., & Peters, J. (2020). The hardness of conditional independence testing and the generalised covariance measure. doi:10.1214/19-aos1857