Longitudinal Principal Component Analysis With an Application to Marketing Data

Christopher Kinson, Xiwei Tang, Zhen Zuo, Annie Qu

Research output: Contribution to journalArticlepeer-review


We propose a longitudinal principal component analysis method for multivariate longitudinal data using a random-effects eigen-decomposition, where the eigen-decomposition uses longitudinal information through nonparametric splines and the multivariate random effects incorporate significant store-wise heterogeneity. Our method can effectively analyze large marketing data containing sales information for products from hundreds of stores over an 11-year time period. The proposed method leads to more accurate estimation and interpretation compared to existing approaches. We illustrate our method through simulation studies and an application to marketing data from IRI. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)335-350
Number of pages16
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Apr 2 2020


  • Marketing data
  • Multivariate longitudinal data
  • Nonparametric spline
  • Principal component analysis
  • Random-effects model
  • Time-varying covariance matrix

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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