Functional Data Analysis for Sparse Longitudinal Data

Yao, Fang; Müller, Hans‐Georg; Wang, Jane-Ling

doi:10.1198/016214504000001745

Cited by 1,304 publications

(1,923 citation statements)

References 26 publications

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“…However, in general, E{y i (t)} = µ(t), thereforeȳ(t) is not a consistent estimator of µ(t). Similar considerations extend to estimators associated with more ambitious statistical analyses, including functional PCA (Rice and Silverman 1991) and functional regression (Guo 2002;Yao et al 2005).…”

Section: Phase Variability and Curve Registrationmentioning

confidence: 99%

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

Telesca

2015

Nonparametric Bayesian Inference in Biostatistics

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This manuscript reviews the use of Bayesian hierarchical curve registration in Biostatistics and Bioinformatics. Several models allowing for unit-specific random time scales are discussed and applied to longitudinal data arising in biomedicine, pharmacokinetics and time-course genomics. We consider representations of random functionals based on P-spline priors. Under this framework, straightforward posterior simulation strategies are outlined for inference. Beyond curve registration, we discuss joint regression modeling of both random effects and population level functional quantities. Finally, the use of mixture priors is discussed in the setting of differential expression analysis.

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Section: Phase Variability and Curve Registrationmentioning

confidence: 99%

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

Telesca

2015

Nonparametric Bayesian Inference in Biostatistics

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“…One can obtain a consistent estimator for σ by taking the difference between a smoother that uses only the diagonal elements and the diagonal estimate obtained from smoothing step (13). We refer to Yao et al (2005a) for more details.…”

Section: A1 Estimation Proceduresmentioning

confidence: 99%

“…We follow the procedures introduced in Yao et al (2005a) and extended in Yao et al (2005b). In order to overcome the limitations of sparse designs, we borrow strength across subjects by pooling the data to achieve estimates of µ(t) and G(s, t).…”

Section: A1 Estimation Proceduresmentioning

confidence: 99%

A stickiness coefficient for longitudinal data

Gottlieb

Müller

2012

Computational Statistics & Data Analysis

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In this paper, we introduce the stickiness coefficient, a summary statistic for time-course and longitudinal data, which is designed to characterize the time dynamics of such data. The stickiness coefficient provides a simple, intuitive and informative measure that captures key information contained in time-course data. Under the assumption that the data are generated by the trajectories of a smooth underlying stochastic process, the stickiness coefficient illuminates the relationship between the value of the process at one time with the value it assumes at another time via a single numeric measure. In particular, the stickiness coefficient summarizes the extent to which deviations from the mean trajectory tend to co-vary over time. The estimation scheme we propose will allow for estimation even in the case that the longitudinal data are sparsely observed at irregular times and may be corrupted by noise. We demonstrate an estimation procedure for the stickiness coefficient and establish asymptotic consistency as well as asymptotic convergence rates. We illustrate the resulting stickiness coefficient with some theoretical calculations as well as several economic and health related data examples.

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“…We provide a review of a recently developed version of functional principal component analysis (Yao et al, 2005), which is geared towards sparse, irregularly observed and noisy data, the principal analysis through conditional expectation (PACE) method.…”

Section: Introductionmentioning

confidence: 99%

“…For nearly identical products that are auctioned repeatedly, one may view the price history of each of these auctions as realization of an underlying smooth stochastic process, the price process. While the traditional Functional Data Analysis (FDA) approach requires that entire trajectories of the underlying process are observed without noise, this assumption is not satisfied for typical auction data.We provide a review of a recently developed version of functional principal component analysis (Yao et al, 2005), which is geared towards sparse, irregularly observed and noisy data, the principal analysis through conditional expectation (PACE) method.The PACE method borrows and pools information from the sparse data in all auctions.This allows the recovery of the price process even in situations where only few bids are observed. In a modified approach, we adapt PACE to summarize the bid history for varying current times during an ongoing auction through time-varying principal component scores.…”

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confidence: 99%

Functional Data Analysis for Sparse Auction Data

Liu

Müller

2008

Statistical Methods in E‐Commerce Research

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Bid arrivals of eBay auctions often exhibit "bid sniping", a phenomenon where "snipers" place their bids at the last moments of an auction. This is one reason why bid histories for eBay auctions tend to have sparse data in the middle and denser data both in the beginning and at the end of the auction. Time spacing of the bids is thus irregular and sparse. For nearly identical products that are auctioned repeatedly, one may view the price history of each of these auctions as realization of an underlying smooth stochastic process, the price process. While the traditional Functional Data Analysis (FDA) approach requires that entire trajectories of the underlying process are observed without noise, this assumption is not satisfied for typical auction data.We provide a review of a recently developed version of functional principal component analysis (Yao et al., 2005), which is geared towards sparse, irregularly observed and noisy data, the principal analysis through conditional expectation (PACE) method.The PACE method borrows and pools information from the sparse data in all auctions.This allows the recovery of the price process even in situations where only few bids are observed. In a modified approach, we adapt PACE to summarize the bid history for varying current times during an ongoing auction through time-varying principal component scores. These scores then serve as time-varying predictors for the closing price. We study the resulting time-varying predictions using both linear regression and generalized additive modelling, with current scores as predictors. These methods will be illustrated with a case study for 157 Palm M515 PDA auctions from e-Bay, and the proposed methods are seen to work reasonably well. Other related issues will also be discussed.

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Functional Data Analysis for Sparse Longitudinal Data

Cited by 1,304 publications

References 26 publications

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

Bayesian Analysis of Curves Shape Variation Through Registration and Regression

A stickiness coefficient for longitudinal data

Functional Data Analysis for Sparse Auction Data

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