Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese

Mandarin Chinese is characterized by being a tonal language; the pitch (or F₀) of its utterances carries considerable linguistic information. However, speech samples from different individuals are subject to changes in amplitude and phase, which must be accounted for in any analysis that attempts to provide a linguistically meaningful description of the language. A joint model for amplitude, phase, and duration is presented, which combines elements from functional data analysis, compositional data analysis, and linear mixed effects models. By decomposing functions via a functional principal component analysis, and connecting registration functions to compositional data analysis, a joint multivariate mixed effect model can be formulated, which gives insights into the relationship between the different modes of variation as well as their dependence on linguistic and nonlinguistic covariates. The model is applied to the COSPRO-1 dataset, a comprehensive database of spoken Taiwanese Mandarin, containing approximately 50,000 phonetically diverse sample F₀ contours (syllables), and reveals that phonetic information is jointly carried by both amplitude and phase variation. Supplementary materials for this article are available online.