Generalized Multilevel Multisource Functional Regression With an Application to Alzheimer's Disease.

With population aging, Alzheimer's disease has gained increasing attention. Advances in medical technology and longitudinal studies such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) have generated diverse follow-up data, which can be viewed as multilevel multisource functional data for understanding disease progression. In this paper, we propose a new estimation method for the multilevel multisource functional principal components. This method first applies the multilevel functional principal component analysis on the univariate multilevel functional data, then obtains the estimation of the principal components of the multilevel multisource functional principal component model based on the relationship between the univariate and the multisource principal component models, thus realizing the multisource-component-based two-stage estimation of the generalized multilevel multisource functional regression model. We also further consider Bayesian estimation based on the two-stage estimation. Numerical simulations and empirical analyses show that both the proposed multisource-component-based two-stage estimation and Bayesian estimation methods work well. Compared to the multisource-component-based two-stage estimation methods, the classification performance of Bayesian estimation is significantly improved.