Original title: What's The Function? Eigenfunctions Shaping (Non)Parametric Growth Curves
Suryadyuti Baral, Emilio Ferrer · September 2026
Psychologists study how people change over time using growth curve models. Usually, researchers must pick the exact mathematical shape of that growth before they even start. If they guess wrong, their conclusions will be flawed. To fix this, researchers tested functional principal component analysis, or FPCA. This method lets the data reveal its own shapes instead of forcing humans to guess them. It breaks down curves into basic shape patterns called eigenfunctionsThe patterns that FPCA discovers; they represent different types of change over time.. Researchers can then plug these patterns directly into standard models. The team found that FPCA accurately discovers the true underlying patterns when its standard mathematical conditions are met. It performs best when studies include more people and track them across more time points. Ultimately, models built using these discovered patterns fit new test data well and recover parameters reliably.
You are drawing a picture from memory and have to choose all the shapes before you start—circle, square, triangle. If you pick the wrong ones, the picture looks nothing like what you remembered. In this paper, standard growth curve models force researchers to pick a shape for change over time before seeing the data. Here, the data itself suggests the shapes, like sketching lightly first and seeing the forms emerge as you look at the reference.
Psychologists often study how things change over time—like memory decline or skill growth—but standard methods require them to decide the shape of that change in advance. If the guess is wrong, conclusions can be misleading. This paper shows a way to let the data itself suggest the shape, making models more accurate and findings more trustworthy.
The abstract notes that FPCA accurately recovers functions only under orthonormal conditions and when assumptions like independence of random effects are met. Performance under severe violations is not fully explored. The method is demonstrated on simulated data and one empirical example, so its generalizability to diverse real-world longitudinal studies is not established. It also assumes sufficient time points and sample sizes for reliable estimation.
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What's The Function? Eigenfunctions Shaping (Non)Parametric Growth Curves — Suryadyuti Baral, Emilio Ferrer — PsyArXiv — doi:10.31234/osf.io/r7c58_v1
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.