Linguistic Pitch Analysis Using Functional Principal Component Mixed Effect Models

Abstract

Abstract. Fundamental frequency (F0, broadly "pitch") is an integral part of human language; however, a comprehensive quantitative model for F0 can be a challenge to formulate due to the large number of effects and interactions between effects that lie behind the human voice's production of F0, and the very nature of the data being a contour rather than a point. This paper presents a semi-parametric functional response model for F0 by incorporating linear mixed effects models through the functional principal component scores. This model is applied to the problem of modelling F0 in the tone language Qiang, a language in which relative pitch information is part of each word's dictionary entry.Date: October 13, 2008.

Linguistic and Human Effects on F₀ in a Tonal Dialect of Qiang

“…If one employed a time series LME model (which is substantially more complicated due to the correlation in the measurements across time), akin to those developed for econometrics, then the resulting model would be able to show changing effects, such as the degree to which a previous tone has a greater effect on the left edge of a syllable than on the right edge, etc. This particular method is explored in Aston et al [2010]; implementation of a continuous model is much more statistically and computationally complex than the LME model. The components responsible for 97% of the variance in the Aston et al [2010] model are essentially the same as those found significant in the single-value LME model presented here.…”

“…This particular method is explored in Aston et al [2010]; implementation of a continuous model is much more statistically and computationally complex than the LME model. The components responsible for 97% of the variance in the Aston et al [2010] model are essentially the same as those found significant in the single-value LME model presented here. Thus, the model that is simpler to implement yields much the same information as the more complicated model, and is easier to interpret.…”

Longitudinal high-dimensional principal components analysis with application to diffusion tensor imaging of multiple sclerosis

“…Successful modeling approaches involving wavelets and splines and adaptive kernels have been reported in the literature (Mohamed and Davatzikos, 2004; Morris and Carroll, 2006; Guo, 2002; Morris et al, 2011; Zhu et al, 2011; Rodriguez et al, 2009; Bigelow and Dunson, 2009; Reiss et al, 2005; Reiss and Ogden, 2008, 2010; Li et al, 2011; Hua et al, 2012; Yuan et al, 2014). A different direction of research has focused on principal component decompositions (Di et al, 2008; Crainiceanu et al, 2009; Aston et al, 2010; Staicu et al, 2010; Greven et al, 2010; Di et al, 2010; Zipunnikov et al, 2011b; Crainiceanu et al, 2011), which led to several applications to imaging data (Shinohara et al, 2011; Goldsmith et al, 2011; Zipunnikov et al, 2011a). However, the high dimensionality of new data sets, the inherent complexity of sampling designs and data collection, and the diversity of new technological measurements raise multiple challenges that are currently unaddressed.…”

Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density

“…Since then, functional linear regression model has been further extended or modified to take into account possible nonlinear relationship, some of the regression models include the functional polynomial regression model (Yao and Müller, 2010;Horváth and Reeder, 2012), functional additive regression model (Müller and Yao, 2008;Febrero-Bande and González-Manteiga, 2013;Fan and James, 2013), and nonparametric functional regression model (Ferraty and Vieu, 2006;Ferraty, Van Keilegom, and Vieu, 2010). Due to the fast development in functional regression models, it has gained an increasing popularity in various fields of application, such as atmospheric radiation (Hlubinka and Prchal, 2007), chemometrics (Frank and Friedman, 1993;Ferraty and Vieu, 2002;Burba et al, 2009;Yao and Müller, 2010), climate variation forecasting (Shang and Hyndman, 2011), demographic modeling and forecasting (Hyndman and Ullah, 2007;Hyndman and Booth, 2008;Hyndman and Shang, 2009;Chiou and Müller, 2009), earthquake modeling , gene expression (Yao et al, 2005a;Chiou and Müller, 2007), health science (Harezlak, Coull, Laird, Magari, and Christiani, 2007), linguistics (Hastie et al, 1995;Malfait and Ramsay, 2003;Aston et al, 2010), medical research (Ratcliffe et al, 2002;Yao et al, 2005b;Erbas et al, 2007), ozone level prediction (Quintela-del-Río and Francisco-Fernández, 2011), and sulfur dioxide level prediction (Fernandez de Castro et al, 2005).…”