xtifedml

Double Machine Learning for Panel Models with Interactive Fixed Effects

The xtifedml package implements Double Machine Learning for partially linear regression models for panel data with interactive fixed effects (panel DML-IFE), as in Binzhi et al. (2026).

The package follows the object-oriented architecture of DoubleML (Bach et al., 2024) and is built on top of xtdml (Polselli, 2025), which handles additive one-way fixed effects. It uses the mlr3 ecosystem for nuisance-function estimation, keeping the same R6-style API.

The Partially Linear Panel Regression Model with Interactive Fixed Effects

xtifedml estimates the structural (causal) parameter from panel data models of the form

$$ Y_{it} = \theta_0 V_{it} + l_0(X_{it}) + \lambda_i' f_t + U_{it}, $$

$$ D_{it} = m_0(X_{it}) + \gamma_i' f_t + V_{it}, $$

$$ X_{it} = \Gamma_i' f_t + E_{it}, $$

where

• $Y_{it}$ is the outcome, $D_{it}$ the treatment, $X_{it}$ the high-dimensional covariates;
• $\theta_0$ is the structural (causal) parameter to estimate;
• $l_0$ and $m_0$ are (possibly nonlinear) nuisance functions to learn from the data;
• $\lambda_i' f_t$, $\gamma_i' f_t$, and $\Gamma_i' f_t$ are interactive (factor-structures) fixed effects, with unobserved individual loadings ${\lambda_i,\gamma_i, \Gamma_i}$ interacted with unobserved common time factors $f_t$;
• $U_{it}$, $V_{it}$, and $E_{it}$ are disturbances.

Note: The model is written using the 'partialled-out' approach of Robinson (1988) with $V_{it}$ rather than $D_{it}$ representing the orthogonalised treatment. The PLPR model can be specified using the alternative `IV approach', i.e.,

$$ Y_{it} = \theta_0 D_{it} + g_0(Xit) + \lambda_i^\prime f_t +U_{it}, $$

where $g_0(\cdot)\neq l_0(\cdot)$, which is less attractive because model fitting generally requires iterating between learning $g_0(\cdot)$ and estimating $\theta_0$ until convergence.

What the user controls

The user can run the estimator directly on a panel data.frame; no manual data preparation is required. The two main choices are:

1. Panel-data approach: approach = "pcce" (Pooled Common Correlated Effects), implements a projection-based defactorisation following Pesaran (2006), as adapted by Rucker (2025), which approximates the factor space using cross-sectional averages before applying DML; or approach = "pooled", which does not transform the data.

2. Covariate transformation: transformX = c("no", "minmax", "poly"), default "no".

   • "no" leaves $X$ untransformed — recommended for tree-based learners.
   • "minmax" applies min–max normalization $x' = (x - x_{\min})/(x_{\max} - x_{\min})$ — recommended for neural networks.
   • "poly" adds polynomials up to order three and pairwise/three-way interactions — recommended for Lasso.

Note Two orthogonal scores are available via the score argument of xtifedml_plr$new(): "orth-PO" (partialling-out, requires ml_l and ml_m) and "orth-IV" (IV-type orthogonal score, additionally requires ml_g).

Installation

Install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("POLSEAN/xtifedml")

Quick start

A minimal end-to-end example using a regression tree (rpart) as the nuisance learner:

library(xtifedml)
library(mlr3)
library(rpart)
library(mlr3misc)
library(mlr3tuning)

set.seed(1234)

# 1. Simulate panel data with interactive fixed effects
data <- make_plpr_data(n_obs = 100, t_per = 5, dim_x = 10, theta = 1,
                        r = 2, rho = 0.6, dgp = "discontinuous")

x_cols <- paste0("X", 1:10)

# 2. Build the xtifedml data backend
obj_xtifedml_data <- xtifedml_data_df(
  data,
  x_cols   = x_cols,
  y_col    = "y",
  d_cols   = "d",
  panel_id = "id",
  time_id  = "time",
  approach = "pcce"
)

# 3. Learners
ml_l <- lrn("regr.rpart")
ml_m <- lrn("regr.rpart")

# 4. Set DML estimation environment
xtifedml_obj <- xtifedml_plr$new(obj_xtifedml_data,
                                  ml_l = ml_l, ml_m = ml_m,
                                  n_folds = 5, score = "orth-PO")

# 5. Tune and fit
param_grid <- list(
  "ml_l" = ps(cp = p_dbl(0.001, 0.1), minsplit = p_int(5, 30)),
  "ml_m" = ps(cp = p_dbl(0.001, 0.1), minsplit = p_int(5, 30))
)

tune_settings <- list(
  n_folds_tune = 5,
  rsmp_tune    = mlr3::rsmp("cv", folds = 5),
  terminator   = mlr3tuning::trm("evals", n_evals = 10),
  tuner        = mlr3tuning::tnr("grid_search", resolution = 10)
)

xtifedml_obj$tune(param_set = param_grid, tune_settings = tune_settings)
xtifedml_obj$fit()

# 6. Print estimated objects
xtifedml_obj$print()
xtifedml_obj$summary()

Inspecting the results

After fitting, the main quantities are available as fields and methods on the xtifedml_plr object:

Field / method	Meaning
coef_theta	Point estimate of the structural parameter $\theta_0$
se_theta	Standard error of $\hat\theta$
pval_theta	Two-sided $p$-value
confint()	Confidence interval (default 95%)
model_rmse	Overall model RMSE
rmses	RMSE of each nuisance learner (ml_l, ml_m, ml_g)
params	Tuned hyperparameters
get_panel_info()	Stored panel data information (n_obs, n_subjects, n_groups)

Main functions

Function	Purpose
xtifedml_plr	R6 class implementing DML for partially linear panel models with interactive fixed effects.
xtifedml_data	Constructor for the data backend used by the estimator.
xtifedml_data_df()	Wrapper that builds an xtifedml_data object directly from a data.frame.
make_plpr_data()	Simulates panel data from a partially linear regression model with interactive fixed effects.

Full documentation is available via ?xtifedml_plr, ?xtifedml_data_df, etc.

Dependencies

xtifedml requires R (>= 3.5.0) and imports R6 (>= 2.4.1), data.table (>= 1.12.8), mlr3 (>= 1.3.0), mlr3tuning (>= 1.5.0), mlr3learners (>= 0.13.0), mlr3misc (>= 0.19.0), mvtnorm, clusterGeneration, magrittr, dplyr, MLmetrics, checkmate. Suggested: rpart, mlr3pipelines, bbotk (>= 1.8.0).

References

• Bach, P., Chernozhukov, V., Kurz, M. S., Spindler, M., and Klaassen, S. (2024). DoubleML — An Object-Oriented Implementation of Double Machine Learning in R. Journal of Statistical Software, 108(3), 1–56. doi:10.18637/jss.v108.i03
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1–C68.
• Clarke S. P., and Polselli A., (2026). Double machine learning for static panel models with fixed effects, The Econometrics Journal, Volume 29, Issue 1, January 2026, Pages 69–86. https://doi.org/10.1093/ectj/utaf011
• Polselli, A. (2025). xtdml: Double Machine Learning Estimation to Static Panel Data Models with Fixed Effects in R. arXiv preprint arXiv:2512.15965.
• Rücker, M., Vogt, M., Linton, O., and Walsh, C. (2025). Estimation and inference in high- dimensional panel data models with interactive fixed effects. Quantitative Economics, 16(4):1457–1509.