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

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  • P. Z. Hadjipantelis
  • J. A. D. Aston
  • H. G. Müller
  • J. P. Evans

Abstract

Mandarin Chinese is characterized by being a tonal language; the pitch (or F 0 ) 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 F 0 contours (syllables), and reveals that phonetic information is jointly carried by both amplitude and phase variation. Supplementary materials for this article are available online.

Suggested Citation

  • P. Z. Hadjipantelis & J. A. D. Aston & H. G. Müller & J. P. Evans, 2015. "Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 545-559, June.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:510:p:545-559
    DOI: 10.1080/01621459.2015.1006729
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    Cited by:

    1. Juhyun Park & Jeongyoun Ahn, 2017. "Clustering multivariate functional data with phase variation," Biometrics, The International Biometric Society, vol. 73(1), pages 324-333, March.
    2. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    3. Wagner, Heiko & Kneip, Alois, 2019. "Nonparametric registration to low-dimensional function spaces," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 49-63.
    4. Niels Lundtorp Olsen & Bo Markussen & Lars Lau Raket, 2018. "Simultaneous inference for misaligned multivariate functional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1147-1176, November.
    5. Bingkai Wang & Xi Luo & Yi Zhao & Brian Caffo, 2021. "Semiparametric partial common principal component analysis for covariance matrices," Biometrics, The International Biometric Society, vol. 77(4), pages 1175-1186, December.

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