Plausible Values for Within-Person Moderation in Dynamic Structural Equation Models

Dynamic structural equation models (DSEMs) are a popular method for modeling intensive longitudinal data. DSEM performs a latent decomposition, which converts observed variables into two orthogonal latent variables: the person mean and the momentary deviation from the person mean. A complication following this process is that the within-person model consists solely of latent variables. Therefore, any questions regarding within-person moderation require latent interactions. Speyer et al. proposed a two-stage method to address this issue. The first stage creates factor scores for within-person latent variables; the second stage treats the factor scores as observed. A potential caveat is that the uncertainty in the factor scores may not propagate to the second stage. We discuss how taking multiple plausible value draws for the latent variable – rather than a single factor score – can account for uncertainty. Although more principled, plausible values significantly increase computational time, so a practical question is whether plausible values meaningfully improve performance. Empirical examples and simulations show that latent variable posterior distributions tend to be quite tight given that intensive longitudinal data have many observations, so the added benefit of plausible values is relatively small. The factor score approach is therefore computationally expedient while also being low risk.