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.
Center for Lifespan Psychology, Max Planck Institute for Human Development, Germany; Max Planck UCL Centre for Computational Psychiatry and Ageing Research, Germany.
Dev Cogn Neurosci. 2024 Dec;70:101450. doi: 10.1016/j.dcn.2024.101450. Epub 2024 Sep 24.
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.
基于模拟研究的结果,Parsons 和 McCormick(2024)认为,在发展研究中,仅包含两个时间点的增长模型不太适合对线性斜率的个体差异进行建模。他们的论点基于对个体差异线性斜率测量精度提高的实证研究,如果研究通过在一个时间单位(例如一年)之后增加额外的测量机会逐步扩展,那么可以提高精度。他们得出的结论是,两个时间点模型不足以可靠地对个体水平的变化进行建模,这些模型应该侧重于组水平的效应。在这里,我们表明,可以通过解混淆研究持续时间的影响以及增加额外测量机会对估计线性斜率个体差异的精度的影响来解决这些限制。我们使用渐近结果来评估和比较代表不同研究设计的线性变化模型的精度,并表明主要是更长的时间跨度增加了精度,而不是额外的波次。此外,我们还展示了如何使用渐近结果来考虑不规则间隔以及计划和非计划缺失数据。总之,如果在进行研究之前进行仔细的研究设计规划,那么实际上仅用两个时间点就可以很好地捕捉真实的线性变化。