Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development.

For longitudinal studies with multivariate observations, we propose statistical methods to identify clusters of archetypal subjects by using techniques from functional data analysis and to relate longitudinal patterns to outcomes. We demonstrate how this approach can be applied to examine associations between multiple time-varying exposures and subsequent health outcomes, where the former are recorded sparsely and irregularly in time, with emphasis on the utility of multiple longitudinal observations in the framework of dimension reduction techniques. In applications to children's growth data, we investigate archetypes of infant growth patterns and identify subgroups that are related to cognitive development in childhood. Specifically, "Stunting" and "Faltering" time-dynamic patterns of head circumference, body length and weight in the first 12 months are associated with lower levels of long-term cognitive development in comparison to "Generally Large" and "Catch-up" growth. Our findings provide evidence for the statistical association between multivariate growth patterns in infancy and long-term cognitive development.

Function-valued traits in evolution.

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical, statistical approach to infer ancestral function-valued traits, and estimate the generative evolutionary process. We do this by combining dimension reduction and phylogenetic Gaussian process regression, a non-parametric procedure that explicitly accounts for known phylogenetic relationships. We test the performance of methods on simulated, function-valued data generated from a stochastic evolutionary model. The methods are applied assuming that only the phylogeny, and the function-valued traits of taxa at its tips are known. Our method is robust and applicable to a wide range of function-valued data, and also offers a phylogenetically aware method for estimating the autocorrelation of function-valued traits.

Characterizing fundamental frequency in Mandarin: a functional principal component approach utilizing mixed effect models.

A model for fundamental frequency (F0, or commonly pitch) employing a functional principal component (FPC) analysis framework is presented. The model is applied to Mandarin Chinese; this Sino-Tibetan language is rich in pitch-related information as the relative pitch curve is specified for most syllables in the lexicon. The approach yields a quantification of the influence carried by each identified component in relation to original tonal content, without formulating any assumptions on the shape of the tonal components. The original five speaker corpus is preprocessed using a locally weighted least squares smoother to produce F0 curves. These smoothed curves are then utilized as input for the computation of FPC scores and their corresponding eigenfunctions. These scores are analyzed in a series of penalized mixed effect models, through which meaningful categorical prototypes are built. The prototypes appear to confirm known tonal characteristics of the language, as well as suggest the presence of a sinusoid tonal component that is previously undocumented.