Effectiveness of the Deterministic and Stochastic Bivariate Latent Change Score Models for Longitudinal Research

Abstract

The Bivariate Latent Change Score (BLCS) model is a popular framework for the study of dynamics in longitudinal research. Despite its popularity, there is little evidence of the ability of this model to recover latent dynamics when the latent trajectories are affected by stochastic innovations (i.e., dynamic error). The deterministic specification of the BLCS model does not account for the effect of these innovations in the system. In contrast, the stochastic specification of the BLCS model includes parameters that capture the effect of such innovations at the latent level. Through Monte Carlo simulation, we generated two developmental processes and examined the recovery of the parameters in the deterministic and stochastic BLCS models under a broad range of empirically relevant conditions. Based on our findings, we provide specific guidelines and recommendations for the application of BLCS models in developmental research.

Estimation of planned and unplanned missing individual scores in longitudinal designs using continuous-time state-space models.

“…Equation 1 includes no prediction error (i.e., the change at time t is perfectly predicted by the level at t − 1 and the time-invariant additive component y a ). It is possible to include dynamic error variance, capturing the effect of random shock on the trajectory, which would lead to a stochastic LCS model (e.g., Cáncer & Estrada, 2023). However, to the best of our knowledge, such a model is rarely used in applied research.…”

“…In the present study, we worked with a deterministic system, and therefore these innovations were fixed to zero. For more details about stochasticity in dynamic models, see Cáncer and Estrada (2023), Oud and Delsing (2010), Schuurman et al (2015), Voelkle et al (2018), or Zyphur et al (2020).…”

The Base-Rate and Longer-Term Relevance of Year-to-Year Change in Personality Traits

“…In the stochastic LSCM, so-called innovations are added as time-specific residuals to the latent change score variables. These innovations differ from measurement error in that they are carried over to subsequent time points via autocorrelations, impacting the latent process also later (Cáncer & Estrada, 2023). Hence, the innovation factors reflect (a) reliable, timespecific (i.e., year-to-year) effects that (b) are not captured by the estimated longer-term trajectories including linear and lagged effects, and yet (c) propagate to later instances in the latent process via autocorrelation.…”