Conditional functional clustering for longitudinal data with heterogeneous nonlinear patterns

Abstract

In studies of cognitive aging, it is crucial to distinguish subtypes of longitudinal cognition change while accounting for the effects of given covariates. The longitudinal cognition trajectories and the covariate effects can both be nonlinear with heterogeneous shapes that do not follow a simple parametric form, where flexible functional methods are preferred. However, most functional clustering methods for longitudinal data do not allow controlling for the possible functional effects of covariates. Although traditional mixture-of-experts methods can include covariates and be extended to the functional setting, using nonlinear basis functions, satisfactory parsimonious functional methods required for robust functional coefficient estimation and clustering are still lacking. In this paper we propose a novel latent class functional mixed-effects model in which we assume the covariates have fixed functional effects, and the random curves follow a mixture of Gaussian processes that facilitates a model-based conditional clustering. A transformed penalized B-spline approach is employed for parsimonious modeling and robust model estimation. We propose a new iterative-REML method to choose the penalty parameters in heterogeneous data. The new method is applied to the latest data from the Religious Orders Study and Rush Memory and Aging Project, and four novel subtypes of cognitive changes are identified.