[Paper Review] Longitudinal Mediation Analysis with Latent Growth Curves

Adam Sullivan, Douglas Gunzler+2 more|arXiv (Cornell University)|Mar 9, 2021

Advanced Causal Inference Techniques20 references4 citations

TL;DR

This paper introduces a counterfactual framework for longitudinal mediation analysis using latent growth curve models to estimate natural direct and indirect effects when exposure, mediator, and outcome are modeled as latent growth trajectories. It provides estimators and standard errors for these effects, enabling causal inference in longitudinal studies with continuous, time-varying mediators and outcomes under sequential ignorability assumptions.

ABSTRACT

The paper considers mediation analysis with longitudinal data under latent growth curve models within a counterfactual framework. Estimators and their standard errors are derived for natural direct and indirect effects when the mediator, the outcome, and possibly also the exposure can be modeled by an underlying latent variable giving rise to a growth curve. Settings are also considered in which the exposure is instead fixed at a single point in time.

Motivation & Objective

• To develop a causal inference framework for mediation analysis in longitudinal studies with time-varying exposures, mediators, and outcomes.
• To model exposure, mediator, and outcome as latent growth curves to capture individual trajectories over time.
• To derive estimators and standard errors for natural direct and indirect effects under a counterfactual framework.
• To extend mediation analysis to settings where exposure is fixed at a single time point while mediators and outcomes are longitudinal.
• To ensure methodological rigor through identification assumptions such as sequential ignorability and conditional independence of potential outcomes.

Proposed method

• Uses latent growth curve models (LGCMs) to represent the underlying trajectories of exposure, mediator, and outcome as latent variables with intercept and slope factors.
• Applies a counterfactual framework to define natural direct and indirect effects in terms of potential outcomes under different exposure and mediator conditions.
• Derives estimators for natural direct and indirect effects based on structural equation modeling (SEM) with latent variables.
• Derives standard errors for the estimators using the delta method or robust variance estimation under multivariate normality.
• Implements the model within a structural equation modeling (SEM) framework to estimate path coefficients and indirect effects via product-of-paths.
• Relies on assumptions such as sequential ignorability, conditional independence of potential outcomes, and correct model specification of latent growth trajectories.

Experimental results

Research questions

• RQ1 How can natural direct and indirect effects be estimated in longitudinal mediation models with time-varying mediators and outcomes?
• RQ2 What is the appropriate counterfactual framework for defining direct and indirect effects when exposure is fixed at a single time point?
• RQ3 How can latent growth curve models be used to represent individual trajectories of exposure, mediator, and outcome in mediation analysis?
• RQ4 What are the identification conditions required for valid estimation of natural direct and indirect effects in this framework?
• RQ5 How do the proposed estimators and standard errors perform under realistic longitudinal data structures with measurement error and missing data?

Key findings

• The paper successfully derives closed-form estimators for natural direct and indirect effects in longitudinal mediation models using latent growth curve structures.
• Standard errors for the estimators are derived using the delta method, enabling statistical inference under multivariate normality.
• The method allows for the estimation of indirect effects even when the exposure is fixed at a single time point, extending applicability to observational studies.
• The approach supports the decomposition of total effects into natural direct and indirect components under sequential ignorability.
• The framework enables the modeling of individual differences in growth trajectories, improving power and precision compared to traditional repeated-measures approaches.
• The methodological framework is implemented within a structural equation modeling (SEM) context, allowing for model fit assessment and parameter estimation with standard software.