Regression Discontinuity Analysis with Latent Variables.

Area of Science:

• Econometrics
• Psychometrics
• Social Sciences

Background:

• Regression discontinuity (RD) designs are crucial for causal inference when randomization is not feasible.
• Conventional RD analysis using observed scores limits the examination of local average treatment effect (ATE) heterogeneity and generalization.

Purpose of the Study:

• To propose a novel latent regression discontinuity (RD) framework for enhanced causal inference.
• To enable the analysis of latent constructs underlying the running variable in RD designs.
• To allow for the examination of ATE heterogeneity and generalization away from the cutoff.

Main Methods:

• The proposed latent RD framework utilizes multiple indicator variables (raw item responses) of the latent construct.
• An explicit measurement model is specified to link latent constructs to observed indicators.
• This approach allows defining the local ATE conditional on the latent construct.

Main Results:

• The latent RD framework facilitates disentangling the heterogeneity of the local ATE.
• It enables the generalization of the local ATE to scores away from the cutoff.
• Proof-of-concept simulations demonstrate good parameter recovery under practical conditions.

Conclusions:

• The latent RD framework offers a significant methodological advancement for causal inference with latent variables.
• This approach improves the ability to study treatment effects in a more nuanced and generalizable manner.
• Researchers can gain deeper insights into causal relationships when dealing with unobserved constructs.