Longitudinal Principal Component Analysis with an Application to Marketing Data

We propose a longitudinal principal component analysis method for multivariate longitudinal data using a random-effects eigen-decomposition, where the eigen-decomposition utilizes 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.