RAPSEM: Identifying Latent Mediators Without Sequential Ignorability via a Rank-Preserving Structural Equation Model

The identification of latent mediator variables is typically conducted using standard structural equation models (SEMs). When SEM is applied to mediation analysis with a causal interpretation, valid inference relies on the strong assumption of no unmeasured confounding, that is, all relevant covariates must be included in the analysis. This assumption is often violated in empirical applications, leading to biased estimates of direct and indirect effects. We address this limitation by weakening the causal assumptions and proposing a procedure that combines g-estimation with a two-stage method of moments to incorporate latent variables, thereby enabling more robust mediation analysis in settings common to the social sciences. We establish consistency and asymptotic normality of the resulting estimator. Simulation studies demonstrate that the estimator is unbiased across a wide range of settings, robust to violations of its underlying no-effect-modifier assumption, and achieves reasonable power to detect medium to large effects for sample sizes above 500, with power increasing as the strength of treatment-covariate interactions grows.