Functional Multiple-Outcome Model in Application to Multivariate Growth Curves of Infant Data

Abstract

Motivated by a medical study that attempts to analyze the relationship between growth curves and other variables and to measure the association among multiple growth curves, the authors develop a functional multiple-outcome model to decompose the total variation of multiple functional outcomes into variation explained by independent variables with time-varying coefficient functions, by latent factors and by noise. The latent factors are the hidden common factors that influence the multiple outcomes and are found through the combined functional principal component analysis approach. Through the coefficients of the latent factors one may further explore the association of the multiple outcomes. This method is applied to the multivariate growth data of infants in a real medical study in Shanghai and produces interpretable results. Convergence rates for the proposed estimates of the varying coefficient and covariance functions of the model are derived under mild conditions.