arXiv subjects

Geoffrey T. Wodtke

Publications and source records attributed to Geoffrey T. Wodtke.

4 recordsLinked to original sources

arXiv2025

Causal Mediation Analysis with Multiple Mediators: A Simulation Approach

Analyses of causal mediation often involve exposure-induced confounders or, relatedly, multiple mediators. In such applications, researchers aim to estimate a variety of different quantities, including interventional direct and indirect effects, multivariate natural direct and indirect effects, and/or path-specific effects. This study introduces a general approach to estimating all these quantities by simulating potential outcomes from a series of distribution models for each mediator and the outcome. Building on similar methods developed for analyses with only a single mediator (Imai et al. 2010), we first outline how to implement this approach with parametric models. The parametric implementation can accommodate linear and nonlinear relationships, both continuous and discrete mediators, and many different types of outcomes. However, it depends on correct specification of each model used to simulate the potential outcomes. To address the risk of misspecification, we also introduce an alternative implementation using a novel class of nonparametric models, which leverage deep neural networks to approximate the relevant distributions without relying on strict assumptions about functional form. We illustrate both methods by reanalyzing the effects of media framing on attitudes toward immigration (Brader et al. 2008) and the effects of prenatal care on preterm birth (VanderWeele et al. 2014).

stat.ME↗

arXiv2024

Deep Learning With DAGs

Social science theories often postulate causal relationships among a set of variables or events. Although directed acyclic graphs (DAGs) are increasingly used to represent these theories, their full potential has not yet been realized in practice. As non-parametric causal models, DAGs require no assumptions about the functional form of the hypothesized relationships. Nevertheless, to simplify the task of empirical evaluation, researchers tend to invoke such assumptions anyway, even though they are typically arbitrary and do not reflect any theoretical content or prior knowledge. Moreover, functional form assumptions can engender bias, whenever they fail to accurately capture the complexity of the causal system under investigation. In this article, we introduce causal-graphical normalizing flows (cGNFs), a novel approach to causal inference that leverages deep neural networks to empirically evaluate theories represented as DAGs. Unlike conventional approaches, cGNFs model the full joint distribution of the data according to a DAG supplied by the analyst, without relying on stringent assumptions about functional form. In this way, the method allows for flexible, semi-parametric estimation of any causal estimand that can be identified from the DAG, including total effects, conditional effects, direct and indirect effects, and path-specific effects. We illustrate the method with a reanalysis of Blau and Duncan's (1967) model of status attainment and Zhou's (2019) model of conditional versus controlled mobility. To facilitate adoption, we provide open-source software together with a series of online tutorials for implementing cGNFs. The article concludes with a discussion of current limitations and directions for future development.

stat.ML↗

arXiv2019

Residual Balancing: A Method of Constructing Weights for Marginal Structural Models

When making causal inferences, post-treatment confounders complicate analyses of time-varying treatment effects. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. To avoid such bias, researchers often use marginal structural models (MSMs) with inverse probability weighting (IPW). However, IPW requires models for the conditional distributions of treatment and is highly sensitive to their misspecification. Moreover, IPW is relatively inefficient, susceptible to finite-sample bias, and difficult to use with continuous treatments. We introduce an alternative method of constructing weights for MSMs, which we call "residual balancing." In contrast to IPW, it requires modeling the conditional means of the post-treatment confounders rather than the conditional distributions of treatment, and it is therefore easier to use with continuous exposures. Numeric simulations suggest that residual balancing is both more efficient and more robust to model misspecification than IPW and its variants. We illustrate the method by estimating (a) the cumulative effect of negative advertising on election outcomes and (b) the controlled direct effect of shared democracy on public support for war. Open source software is available for implementing the proposed method.

stat.AP↗

arXiv2018

Regression-with-residuals Estimation of Marginal Effects: A Method of Adjusting for Treatment-induced Confounders that may also be Moderators

Treatment-induced confounders complicate analyses of time-varying treatment effects and causal mediation. Conditioning on these variables naively to estimate marginal effects may inappropriately block causal pathways and may induce spurious associations between treatment and the outcome, leading to bias. Although several methods for estimating marginal effects avoid these complications, including inverse-probability-of-treatment-weighted (IPTW) estimation of marginal structural models (MSMs) as well as g- and regression-with-residuals (RWR) estimation of highly constrained structural nested mean models (SNMMs), each suffers from a set of nontrivial limitations. Specifically, IPTW estimation is inefficient, is difficult to use with continuous treatments or mediators, and may suffer from finite-sample bias, while g- and RWR estimation of highly constrained SNMMs for marginal effects are premised on the unrealistic assumption that there is no effect moderation. In this study, we adapt the method of RWR to estimate marginal effects with a set of moderately constrained SNMMs that accommodate several types of treatment-by-confounder and/or mediator-by-confounder interaction, thereby relaxing the assumption of no effect moderation. Through a series of simulation experiments and empirical examples, we show that this approach outperforms IPTW estimation of MSMs as well as both g- and RWR estimation of highly constrained SNMMs in which effect moderation is assumed away.

stat.AP↗