fdapace {fdapace}

fdapace: Functional Data Analysis and Empirical Dynamics

Description

fdapace is 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.

Details

Links for fdapace/PACE: Matlab version of pace at http://anson.ucdavis.edu/~mueller/data/pace.html Papers and background at http://anson.ucdavis.edu/~mueller/ and http://www.stat.ucdavis.edu/~wang/

PACE is based on the idea that observed functional data are generated by a sample of underlying (but usually not fully observed) random trajectories that are realizations of a stochastic process. It does not rely on pre-smoothing of trajectories, which is problematic if functional data are sparsely sampled.

The functional principal components can be used for further statistical analysis depending on the demands of a user, for example if one has densely sampled functional predictors and a generalized response, such as in a GLM, the predictor functions can be replaced by their first couple of principal component scores that will then be used as predictors; one can also easily fit polynomial functional models by using powers (usually squares) and interactions of functional principal components among the predictors for a scalar response.

fdapace is a comprehensive package that directly implements fitting of the following models:

• functional linear regression

• functional additive regression

• functional covariance and correlation (via dynamic correlation)

• functional clustering

• concurrent (varying coefficient) regression models for sparse and dense designs

• varying coefficient additive models

• multivariate functional data analysis (normalization and functional singular component analysis)

• variance processes and volatility processes (the latter of interest in finance)

• optimal designs for longitudinal data analysis (for trajectory prediction and for functional linear regression)

• stringing, a method to convert high-dimensional data into functional data

• quantile regression, with functions as predictors

Author(s)

Maintainer: Yidong Zhou [e-mail] (ORCID)

Authors:

• Han Chen

• Su I Iao

• Poorbita Kundu

• Hang Zhou

• Satarupa Bhattacharjee

• Cody Carroll (ORCID)

• Yaqing Chen

• Xiongtao Dai

• Jianing Fan

• Alvaro Gajardo

• Pantelis Z. Hadjipantelis

• Kyunghee Han

• Hao Ji

• Changbo Zhu

• Hans-Georg Müller [e-mail] [copyright holder, thesis advisor]

• Jane-Ling Wang [e-mail] [copyright holder, thesis advisor]

Other contributors:

• Paromita Dubey [contributor]

• Shu-Chin Lin [contributor]

References

• Wang, J.L., Chiou, J., Müller, H.G. (2016). Functional data analysis. Annual Review of Statistics and Its Application 3, 257–295;

• Chen, K., Zhang, X., Petersen, A., Müller, H.G. (2017). Quantifying infinite-dimensional data: Functional Data Analysis in action. Statistics in Biosciences 9, 582–-604.

See Also

Useful links:

• https://github.com/functionaldata/tPACE

• Report bugs at https://github.com/functionaldata/tPACE/issues

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