fdapace

fdapace is an open‑source R package designed for functional data analysis, with a focus on sparse and irregularly observed functional data. It implements methods based on the Principal Analysis by Conditional Estimation (PACE) framework, enabling nonparametric estimation of mean and covariance surfaces, as well as functional principal component analysis (FPCA). The package supports recovering underlying trajectories and predicting future values for individual subjects from sparsely observed time points.

Key features include mean and covariance estimation from sparsely sampled data, smoothing of observed curves through local linear and kernel methods, and incorporation of measurement error in the estimation process. It provides procedures for deriving eigenfunctions and associated eigenvalues, computing subject-specific FPCA scores, and reconstructing individual trajectories using a truncated FPCA expansion. The approach is designed to handle irregular observation times, missing data, and varying observation counts across subjects, making it suitable for longitudinal and longitudinal-like functional data.

Typical usage involves organizing data into a structure that records subject identifiers, observation times, and observed values, then applying the package’s FPCA and covariance estimation routines. Users can select the number of FPCA components, assess smoothing parameters, and generate predictions or reconstructed trajectories for new or existing subjects. The workflow emphasizes data-driven estimation of the mean, covariance, and functional basis, followed by applications such as trajectory reconstruction, clustering, or functional regression tasks that depend on the estimated functional components.

fdapace is available on CRAN and is accompanied by documentation and vignettes that illustrate common workflows. It is widely used in statistical practice and research for analyzing functional data observed under sparsity and irregular timing, aligning with the broader PACE literature in functional data analysis.