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Identifying Unmeasured Confounders in Panel Causal Models: A Two-Stage LM-Wald Approach

Bang Quan Zheng

TL;DR

This paper tackles the problem that panel causal inferences rest on sequential ignorability, which is threatened by time-varying unmeasured confounders. It develops the Two-Stage LM-Wald (2SLW) diagnostic, combining the local LM test with a forward Wald test to identify where unmodeled latent structure may bias within-person cross-lag effects in RI-CLPMs, without attempting to recover the hidden confounders. Through Monte Carlo simulations across three confounding scenarios and an empirical application to longitudinal political attitudes, 2SLW demonstrates reliable detection of misspecification and meaningful changes in substantive parameters when residual dependencies are incorporated. The approach, implemented in lavaan, offers a practical, theory-grounded tool to augment robustness checks in panel SEMs and can generalize to broader longitudinal designs beyond RI-CLPM. It emphasizes diagnostic rather than confirmatory inference, advocating integration with formal sensitivity analyses to quantify the potential impact of unmeasured confounding on causal conclusions.

Abstract

Panel data are widely used in political science to draw causal inferences. However, these models often rely on the strong and untested assumption of sequential ignorability--that no unmeasured variables influence both the independent and outcome variables across time. Grounded in psychometric literature on latent variable modeling, this paper introduces the Two-Stage LM-Wald (2SLW) approach, a diagnostic tool that extends the Lagrange Multiplier (LM) and Wald tests to detect violations of this assumption in panel causal models. Using Monte Carlo simulations within the Random Intercept Cross-Lagged Panel Model (RI-CLPM), which separates within and between person effects, I demonstrate the 2SLW's ability to detect unmeasured confounding across three key scenarios: biased corrections, distorted direct effects, and altered mediation pathways. I also illustrate the approach with an empirical application to real-world panel data. By providing a practical and theoretically grounded diagnostic, the 2SLW approach enhances the robustness of causal inferences in the presence of potential time-varying confounders. Moreover, it can be readily implemented using the R package lavaan.

Identifying Unmeasured Confounders in Panel Causal Models: A Two-Stage LM-Wald Approach

TL;DR

This paper tackles the problem that panel causal inferences rest on sequential ignorability, which is threatened by time-varying unmeasured confounders. It develops the Two-Stage LM-Wald (2SLW) diagnostic, combining the local LM test with a forward Wald test to identify where unmodeled latent structure may bias within-person cross-lag effects in RI-CLPMs, without attempting to recover the hidden confounders. Through Monte Carlo simulations across three confounding scenarios and an empirical application to longitudinal political attitudes, 2SLW demonstrates reliable detection of misspecification and meaningful changes in substantive parameters when residual dependencies are incorporated. The approach, implemented in lavaan, offers a practical, theory-grounded tool to augment robustness checks in panel SEMs and can generalize to broader longitudinal designs beyond RI-CLPM. It emphasizes diagnostic rather than confirmatory inference, advocating integration with formal sensitivity analyses to quantify the potential impact of unmeasured confounding on causal conclusions.

Abstract

Panel data are widely used in political science to draw causal inferences. However, these models often rely on the strong and untested assumption of sequential ignorability--that no unmeasured variables influence both the independent and outcome variables across time. Grounded in psychometric literature on latent variable modeling, this paper introduces the Two-Stage LM-Wald (2SLW) approach, a diagnostic tool that extends the Lagrange Multiplier (LM) and Wald tests to detect violations of this assumption in panel causal models. Using Monte Carlo simulations within the Random Intercept Cross-Lagged Panel Model (RI-CLPM), which separates within and between person effects, I demonstrate the 2SLW's ability to detect unmeasured confounding across three key scenarios: biased corrections, distorted direct effects, and altered mediation pathways. I also illustrate the approach with an empirical application to real-world panel data. By providing a practical and theoretically grounded diagnostic, the 2SLW approach enhances the robustness of causal inferences in the presence of potential time-varying confounders. Moreover, it can be readily implemented using the R package lavaan.

Paper Structure

This paper contains 24 sections, 35 equations, 9 figures, 22 tables.

Table of Contents

  1. Introduction
  2. Panel Causal Inference & Unmeasured Confounding
  3. From Static Measurement Models to Panel Causal Models
  4. Challenges in Sensitivity Analysis
  5. Research Strategy
  6. LM and Wald Tests as the Statistical Basis of 2SLW
  7. The LM Test and Expected Parameter Change (EPC)
  8. The Wald Test
  9. Complementarity of LM and Wald Tests
  10. Monte Carlo Simulation
  11. Population Models
  12. Population Models & Specification
  13. Model Variants
  14. Baseline Model Specification and Validity
  15. The Two-Stage Process for Confounder Searches
  16. ...and 9 more sections

Figures (9)

  • Figure 1: Diagrams of a 3-Wave RI-CLPM
  • Figure 2: Diagrams of Population Models
  • Figure 3: Diagram of the RI-CLPM
  • Figure A1: 5-Wave RI-CLPM with 2 Indicators (Correlation)
  • Figure A2: 5-Wave RI-CLPM with 2 Indicators (Direct Effect)
  • ...and 4 more figures