We propose a new method for estimating subject-specific mean functions from longitudinal data. We aim to do this in a flexible manner (without restrictive assumptions about the shape of the subject-specific mean functions), while exploiting similarities in the mean functions between different subjects. Functional principal components analysis fulfils both requirements, and methods for functional principal components analysis have been developed for longitudinal data. However, we find that these existing methods sometimes give fitted mean functions which are more complex than needed to provide a good fit to the data. We develop a new penalised likelihood approach to flexibly model longitudinal data, with a penalty term to control the balance between fit to the data and smoothness of the subject-specific mean curves. We run simulation studies to demonstrate that the new method substantially improves the quality of inference relative to existing methods across a range of examples, and apply the method to data on changes in body composition in adolescent girls.

翻译：本文提出了一种从纵向数据中估计受试者特定均值函数的新方法。我们的目标是在灵活（无需对受试者特定均值函数形状施加严格假设）的同时，利用不同受试者间均值函数的相似性。函数主成分分析可满足这两个要求，且针对纵向数据的函数主成分分析方法已有发展。然而，我们发现这些现有方法有时会给出比数据良好拟合所需的更复杂的拟合均值函数。为此，我们开发了一种新的惩罚似然方法来灵活建模纵向数据，通过惩罚项控制数据拟合度与受试者特定均值曲线平滑度之间的平衡。通过模拟研究证明，该方法在一系列示例中相比现有方法显著提升了推断质量，并应用于青少年女性身体成分变化的数据分析。