Causal inference methods for treatment effect estimation usually assume independent experimental units. However, this assumption is often questionable because experimental units may interact. We develop augmented inverse probability weighting (AIPW) for estimation and inference of causal treatment effects on dependent observational data. Our framework covers very general cases of spillover effects induced by units interacting in networks. We use plugin machine learning to estimate infinite-dimensional nuisance components leading to a consistent treatment effect estimator that converges at the parametric rate and asymptotically follows a Gaussian distribution.

The linear coefficient in a partially linear model with confounding variables can be estimated using double machine learning (DML). However, this DML estimator has a two-stage least squares (TSLS) interpretation and may produce overly wide confidence intervals. To address this issue, we propose a regularization and selection scheme, regsDML, which leads to narrower confidence intervals. It selects either the TSLS DML estimator or a regularization-only estimator depending on whose estimated variance is smaller. The regularization-only estimator is tailored to have a low mean squared error. The regsDML estimator is fully data driven. The regsDML estimator converges at the parametric rate, is asymptotically Gaussian distributed, and asymptotically equivalent to the TSLS DML estimator, but regsDML exhibits substantially better finite sample properties. The regsDML estimator uses the idea of k-class estimators, and we show how DML and k-class estimation can be combined to estimate the linear coefficient in a partially linear endogenous model. Empirical examples demonstrate our methodological and theoretical developments. Software code for our regsDML method is available in the R-package dmlalg.

Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed‐effects model for repeated measurements. Using machine learning algorithms allows us to incorporate complex interaction structures, nonsmooth terms, and high‐dimensional variables. The linear variables and the response are adjusted nonparametrically for the nonlinear variables, and these adjusted variables satisfy a linear mixed‐effects model in which the linear coefficient can be estimated with standard linear mixed‐effects methods. We prove that the estimated fixed effects coefficient converges at the parametric rate, is asymptotically Gaussian distributed, and semiparametrically efficient. Two simulation studies demonstrate that our method outperforms a penalized regression spline approach in terms of coverage. We also illustrate our proposed approach on a longitudinal dataset with HIV‐infected individuals. Software code for our method is available in the R‐package dmlalg.