Optimal Two-Time Point Longitudinal Models for Estimating Individual-Level Change: Asymptotic Insights and Practical Implications

Abstract

Based on findings from a simulation study, Parsons & McCormick (2024) argued that growth models with exactly two time points are poorly-suited to model individual differences in change in developmental studies. Their argument is based on an empirical investigation of the increase in precision to measure individual differences in change 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 change. 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

   University College London · Max Planck Society · MSB Medical School Berlin · Max Planck Institute for Human Development

   Affiliation as printed

   Center for Lifespan Psychology, Max Planck Institute for Human Development

   Department of Psychology, MSB Medical School Berlin

   Max Planck UCL Centre for Computational Psychiatry and Ageing Research

2. Ulman Lindenberger

   University College London · Max Planck Society · Max Planck Institute for Human Development

   Affiliation as printed

   Center for Lifespan Psychology , Max Planck Institute for Human Development

   Max Planck UCL Centre for Computational Psychiatry and Ageing Research

   Center for Lifespan Psychology, Max Planck Institute for Human Development

3. Ethan Michael McCormick corresponding Aachen Methodology and Statistics Department

   Leiden University · University of North Carolina at Chapel Hill

   Affiliation as printed

   University of North Carolina at Chapel Hill

   Methodology and Statistics Department, Leiden University