Ruling out Latent Time-Varying Confounders in Two-Variable Multi-Wave Studies

There has been considerable interest in estimating causal cross-lagged effects in two-variable, multi-wave designs. However, there does not currently exist a strategy for ruling out unmeasured time-varying covariates that may act as confounders. In this paper, we propose a new strategy for testing whether an unmeasured time-varying covariate explains all covariation between the two "causal" variables in the data. That model, called the Latent Time-Varying Covariate (LTVC) model, can be tested with observations for two variables assessed across three or more measurement waves. If the LTVC model fits well, then a time-varying covariate can explain the covariance structure, which undermines the plausibility of causal cross-lagged effects. Although the LTVC model tends to be underpowered when causal cross-lagged effects are small, if testable stationarity constraints on the LTVC model are imposed, adequate power can be achieved. We illustrate the LTVC approach with three examples from the literature. Additionally, we introduce the LTVC-CLPM model, which is identified given strong stationarity constraints. Also considered are multivariate and multi-factor models, the inclusion of measured time-invariant covariates in model, measurement of the stability of the LTVC, and the lag-lead model. These methods allow researchers to probe the assumption that an unmeasured time-varying confounder is the source of all the X-Y covariation. Our methods help researchers to rule out certain forms of confounding in two-variable, multi-wave designs.