Controlling for cohort effects in accelerated longitudinal designs using continuous- and discrete-time dynamic models.

Abstract

Accelerated longitudinal designs (ALDs) allow examining developmental changes over a period of time longer than the duration of the study. In ALDs, participants enter the study at different ages (i.e., different cohorts), and provide measures during a time frame shorter than the total study. They key assumption is that participants from the different cohorts come from the same population and, therefore, can be assumed to share the same general trajectory. The consequences of not meeting that assumption have not been examined systematically. In this paper, we propose an approach to detect and control for cohort differences in ALDs using Latent Change Score models in both discrete and continuous time. We evaluated the effectiveness of such a method through a Monte Carlo study. Our results indicate that, in a broad set of empirically relevant conditions, both LCS specifications can adequately estimate cohort effects ranging from very small to very large, with slightly better performance of the continuous-time version. Across all conditions, cohort effects on the asymptotic level (dAs) caused much larger bias than on the latent initial level (d0). When cohort differences were present, including them in the model led to unbiased estimates. In contrast, not including them led to tenable results only when such differences were not large (d0 ≤ 1 and dAs ≤ 0.2). Among the sampling schedules evaluated, those including at least three measurements per participant over 4 years or more led to the best performance. Based on our findings, we offer recommendations regarding study designs and data analysis.

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

“…In the empirical and methodological literature, this parameter is described as the extent to which the state of a process at any given time t is determined by its previous state at t−1. However, to the best of our knowledge, no previous empirical studies have used it as an indicator of the speed of maturation, and very few methodological papers have acknowledged it as such (see Cáncer et al, 2021;Estrada et al, 2021). Furthermore, and to our best knowledge, the model proposed in this manuscript is the first approach to controlling for cohort differences in the speed of maturation.…”

“…In a recent study, Estrada et al (2021) proposed using LCS models as a dynamic approach to the study of cohort differences. In fact, they proposed an extension of these models that successfully captured cohort differences in the initial and maximum level of the trajectories.…”

“…Furthermore, and to our best knowledge, the model proposed in this manuscript is the first approach to controlling for cohort differences in the speed of maturation. Therefore, although cohort differences in the so-called rate of change (i.e., overall change, typically captured with linear and higher order components in multilevel and growth models) have been widely reported in the literature (e.g., Cole, 2000Cole, , 2003Drewelies et al, 2018;Estrada et al, 2021;Finkel et al, 2007;Gerstorf et al, 2011;Vainikainen & Hautamäki, 2022;Zhang et al, 2020), it is hardly possible to find empirical examples of cohort differences in the speed of maturation specifically. This does not mean, however, that such differences do not exist at all (see, for example, Eckert-Lind et al, 2020).…”

“…In the context of ALDs, where each individual provides only few observations and time intervals can differ widely across individuals, CT models are a more adequate approach. In fact, previous studies comparing LCS models in discrete and continuous time with data from ALDs found that CT models provide a much better recovery of the generating parameters when the observations are unevenly spaced (see Estrada et al, 2021;).…”

“…In a previous study, Estrada et al (2021) found that only 125 participants were required to recover cohort effects in the mean latent initial level and asymptote of the trajectories using LCS models. Here we included the following three sample sizes: 125, 200, and 500 individuals per sample.…”