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Activity Number: 508
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #319294
Title: Longitudinal Principal Component Analysis
Author(s): Christopher Kinson* and Xiwei Tang and Annie Qu
Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
Keywords: estimating equation ; marketing data ; random effects ; splines ; time-varying ; PCA

We propose the longitudinal principal component analysis (PCA) which incorporates time-varying associations among variables. Our method can effectively analyze large marketing data which contain weekly sales information for selected products from thousands of stores. Time-varying associations among store products provide important information which allows us to capture changes in consumer behavior. Existing methods mainly estimate a component-wise covariance matrix which could be restrictive if the dimension of that covariance matrix becomes large. We propose two approaches to address this problem. First, an estimating equation eigen-analysis (EE) method is proposed by adapting PCA under the generalized estimating equations framework. The EE method utilizes longitudinal information over time to model time-varying eigenvalues and eigenvectors of the corresponding covariance matrices using splines. Second, the estimating equation eigen-analysis with random effects (EERE) approach is capable of incorporating heterogeneity among different stores which leads to less biased estimation. We illustrate our method through simulation studies and an application of the IRI marketing data.

Authors who are presenting talks have a * after their name.

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