Causal Inference for Latent Markov Models Using the Parametric G-Formula

The parametric g-formula can be used to estimate causal effects of time-varying exposures on observable outcomes. It resolves intermediate confounding in such settings by specifying several parametric models, one each for every time-varying variable, and by performing micro-simulations. However, its restriction to applications with observable outcomes limits its usability for social sciences where variables of interest are often unobservable constructs. In such cases, measurement models are needed. We propose a new approach utilizing bias-adjusted three-step latent Markov models (LMMs) within the parametric g-formula. LMMs estimate the probability of membership in an unobservable state conditional on observed indicator variables. By replacing the parametric models in the g-formula with LMMs, micro-simulations are performed as usual to estimate a causal effect of the time-varying exposure. We illustrate this new approach by estimating the average treatment effect of unemployment on several unobservable mental health states utilizing longitudinal data from the Longitudinal Internet studies for the Social Sciences panel.