A Dynamic Approach to Control for Cohort Differences in Maturation Speed Using Accelerated Longitudinal Designs

Abstract

Accelerated longitudinal designs (ALD) allow studying developmental processes usually spanning multiple years in a much shorter time framework by including participants from different age cohorts, which are assumed to share the same population parameters. However, different cohorts may have been exposed to dissimilar contextual factors, resulting in different developmental trajectories. If such differences are not accounted for, the generating process will not be adequately characterized. In this paper, we propose a continuous-time latent change score model as an approach to capture cohort differences affecting the speed of maturation of psychological processes in ALDs. This approach fills an important gap in the literature because, until now, no method existed for this goal. Using a Monte-Carlo simulation study, we show that the proposed model detects cohort differences adequately, regardless of their size in the population. Our proposed model can help developmental researchers control for cohort effects in the context of ALDs.

Keywords:

• Accelerated longitudinal designs
• cohort differences
• continuous time models
• latent change score models
• speed of maturation
• state space models

Disclosure statement

The authors report there are no competing interests to declare.

Notes

1 Quadratic and higher order components are also sometimes interpreted a rate of acceleration (e.g., Finkel et al., 2007; Gerstorf et al., 2011).

2 Further within-individual variability could be incorporated into the model in the form of prediction errors (i.e., innovation or dynamic error) at the latent level (Oravecz et al., 2011; Voelkle et al., 2012; Voelkle & Oud, 2015). This specification, however, is very uncommon in the LCS framework.

3 LCS models are also capable of capturing exponential trajectories of accelerated (instead of decelerated) change, which are defined by a positive self-feedback. In such scenarios, scores further from the initial level lead to larger subsequent changes, resulting in a pattern of “explosive” change, where even small increases in time lead to dramatic changes in the variable of interest.

4 When the latent level of y is measured by multiple indicators, Equation 9 can be extended to include them. In that case, the dimensions of the vector of observed variables, the matrix of factor loadings, and the vector of measurement errors are rescaled according to the number of indicators.

5 Note that the dual LCS model described in previous sections and the LCS model with moderators from Equations (10)–(12) differ in the interpretation of some parameters. In the former, the parameters β, µ_a, and σ_a describe the trajectories of the whole sample of participants, whereas in our model they refer to participants with a value of zero in the cohort variable (i.e., when coh_k = 0).

6 When cohort effects are null (d = 0), the parameters λ_β, λ_µa, and λ_σa have populational values of zero (θ = 0), and thus computing the RB would imply dividing by zero. In such conditions, RB was computed by dividing the absolute bias by the minimum value for θ in our study, that is, the population value of λ_β, λ_µa, and λ_σa in conditions with small cohort differences (d = .1).

Additional information

Funding

This work was funded by the Ministry of Science and Innovation of Spain [ref. PID2019-107570GA-I00/AEI/ doi: 10.13039/501100011033, granted to EE].