Optimal two-time point longitudinal models for estimating individual-level change: Asymptotic insights and practical implications

Developmental Cognitive Neuroscience, vol. 70, pp. 101450

Abstract

Based on findings from a simulation study, Parsons and McCormick (2024) argued that growth models with exactly two time points are poorly-suited to model individual differences in linear slopes in developmental studies. Their argument is based on an empirical investigation of the increase in precision to measure individual differences in linear slopes if studies are progressively extended by adding an extra measurement occasion after one unit of time (e.g., year) has passed. They concluded that two-time point models are inadequate to reliably model change at the individual level and that these models should focus on group-level effects. Here, we show that these limitations can be addressed by deconfounding the influence of study duration and the influence of adding an extra measurement occasion on precision to estimate individual differences in linear slopes. We use asymptotic results to gauge and compare precision of linear change models representing different study designs, and show that it is primarily the longer time span that increases precision, not the extra waves. Further, we show how the asymptotic results can be used to also consider irregularly spaced intervals as well as planned and unplanned missing data. In conclusion, we like to stress that true linear change can indeed be captured well with only two time points if careful study design planning is applied before running a study.

Authors 3

1. Andreas M. Brandmaier

   MSB Medical School Berlin · Max Planck Institute for Human Development

   Affiliation as printed

   Department of Psychology, MSB Medical School Berlin, Germany; Center for Lifespan Psychology, Max Planck Institute for Human Development, Germany; Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Germany

2. Ulman Lindenberger

   Max Planck Institute for Human Development

   Affiliation as printed

   Center for Lifespan Psychology, Max Planck Institute for Human Development, Germany; Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Germany

3. Ethan Michael McCormick corresponding Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Methodology and Statistics Department, Leiden University, The Netherlands. Electronic address: e.m.mccormick@fsw.leidenuniv.nl