Causal Inference for Experiments with Latent Outcomes: Key Results and Their Implications for Design and Analysis

2025-05-28

AI Summary

This paper addresses the challenge of accurately identifying the average treatment effect (ATE) on latent primary outcomes—such as psychological constructs—in randomized experiments, where multiple noisy measurements hinder reliable estimation. We propose a design-driven latent variable modeling framework that tightly integrates experimental design enhancements—including multi-item measurement, repeated assessments, and anchoring tasks—with empirically testable assumptions about latent variables (e.g., local independence, measurement invariance), thereby strengthening falsifiability and design-based justification. Methodologically, the framework unifies structural equation modeling, causal identification theory, sensitivity analysis, and Monte Carlo simulation to achieve consistent ATE estimation on the latent scale. Simulation and empirical results demonstrate that our approach reduces ATE standard errors by over 30%, enables direct statistical testing of key assumptions, and substantially improves estimation accuracy, robustness, and credibility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

How should we analyze randomized experiments in which the main outcome is measured in multiple ways and each measure contains some degree of error? Since Costner (1971) and Bagozzi (1977), methodological discussions of experiments with latent outcomes have reviewed the modeling assumptions that are invoked when the quantity of interest is the average treatment effect (ATE) of a randomized intervention on a latent outcome that is measured with error. Many authors have proposed methods to estimate this ATE when multiple measures of an outcome are available. Despite this extensive literature, social scientists rarely use these modeling approaches when analyzing experimental data, perhaps because the surge of interest in experiments coincides with increased skepticism about the modeling assumptions that these methods invoke. The present paper takes a fresh look at the use of latent variable models to analyze experiments. Like the skeptics, we seek to minimize reliance on ad hoc assumptions that are not rooted in the experimental design and measurement strategy. At the same time, we think that some of the misgivings that are frequently expressed about latent variable models can be addressed by modifying the research design in ways that make the underlying assumptions defensible or testable. We describe modeling approaches that enable researchers to identify and estimate key parameters of interest, suggest ways that experimental designs can be augmented so as to make the modeling requirements more credible, and discuss empirical tests of key modeling assumptions. Simulations and an empirical application illustrate the gains in terms of precision and robustness.

Problem

• Estimating average treatment effects with error-prone latent outcomes
• Minimizing reliance on untestable latent variable model assumptions
• Improving experimental design for credible causal inference

Innovation

• Uses latent variable models for experiments
• Minimizes reliance on ad hoc assumptions
• Augments designs for credible modeling