Functional Data Analysis and Empirical Dynamics

A versatile package that provides implementation of various methods of Functional Data Analysis (FDA) and Empirical Dynamics. The core of this package is Functional Principal Component Analysis (FPCA), a key technique for functional data analysis, for sparsely or densely sampled random trajectories and time courses, via the Principal Analysis by Conditional Estimation (PACE) algorithm. This core algorithm yields covariance and mean functions, eigenfunctions and principal component (scores), for both functional data and derivatives, for both dense (functional) and sparse (longitudinal) sampling designs. For sparse designs, it provides fitted continuous trajectories with confidence bands, even for subjects with very few longitudinal observations. PACE is a viable and flexible alternative to random effects modeling of longitudinal data. There is also a Matlab version (PACE) that contains some methods not available on fdapace and vice versa. Updates to fdapace were supported by grants from NIH Echo and NSF DMS-1712864 and DMS-2014626. Please cite our package if you use it (You may run the command citation("fdapace") to get the citation format and bibtex entry). References: Wang, J.L., Chiou, J., Müller, H.G. (2016) ; Chen, K., Zhang, X., Petersen, A., Müller, H.G. (2017) .


Current version

New functionality:

  • Added functional additive models (MultiFAM, TVAMSBFitting, SBFitting).
  • Added stringing (Stringing).
  • Added functonal linear regression with functional response (FPCReg).


  • Dropped argument k from SelectK.
  • Vignette in HTML.
  • FClust functionality uses EMCluster instead Rmixmod.
  • Multiple minor bug fixes.

fdapace v0.3.0 (Release date: 25-Jan-2017)

New functionality:

  • Added obsOnly option to CreatePathPlot.
  • Added derivative estimators (FPCAder, fitted.FPCAder)
  • Added functional concurrent correlation (FCCor).
  • Added pairwise curve synchronization for functional data (WFDA).
  • Added optimal designs for longitudinal or functional data (FOptDes).
  • Miscellaneous update to utility functions (CreateBasis, MakeSparseGP)


  • Covariance GCV bandwidth is modified to prevent oversmoothing.
  • "Diagnostic plots" are renamed.
  • GetNormalisedSample now uses fitted covariance.

fdapace v0.2.5 (Release date: 14-Jul-2016)


  • K is used for specifying the number of components in functions such as SelectK, fitted, CreatePathPlot, CreateFuncBoxPlot, etc, instead of k.
  • GetCrCovYX is sped up.


  • Improved the legend placing in CreateDesignPlot.
  • Plot functions no longer show warnings.
  • Changed clustering example in vignettes.


  • Improved the legend placing in CreateDesignPlot.
  • Plot functions no longer show warnings.

fdapace v0.2.0 (Release date: 17-Jun-2016)

New functionality:

  • Addition of Functional Variance Process Analysis (FVPA.R), Functional Clustering (FClust.R) and Functional Singular Value Decomposition (FSVD.R) functionality.


  • Minor changes to the interface of functions FPCA.R and FCReg.R.
  • New internal C++ smoother used.
  • General improvements and bug fixes.
  • Vignette with knitr.

fdapace v0.1.1 (Release data: 15-Mar-2016)

  • Initial release

Reference manual

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0.5.8 by Alvaro Gajardo, 2 months ago

Report a bug at

Browse source code at

Authors: Alvaro Gajardo [aut, cre] , Satarupa Bhattacharjee [aut] , Cody Carroll [aut] , Yaqing Chen [aut] , Xiongtao Dai [aut] , Jianing Fan [aut] , Pantelis Z. Hadjipantelis [aut] , Kyunghee Han [aut] , Hao Ji [aut] , Changbo Zhu [aut] , Shu-Chin Lin [ctb] , Paromita Dubey [ctb] , Hans-Georg Müller [cph, ths, aut] , Jane-Ling Wang [cph, ths, aut]

Documentation:   PDF Manual  

Task views: Functional Data Analysis

BSD_3_clause + file LICENSE license

Imports Rcpp, Hmisc, MASS, Matrix, pracma, numDeriv

Suggests plot3D, rgl, aplpack, mgcv, ks, gtools, knitr, rmarkdown, EMCluster, minqa, testthat

Linking to Rcpp, RcppEigen

Imported by KFPCA, SLFPCA, WRI, fdaPOIFD, fdadensity, fdapaceShiny, fgm, frechet, ftsa.

Depended on by LCox.

Suggested by mistat.

See at CRAN