Evaluating generalised additive mixed modelling strategies for dynamic speech analysis

Abstract

Generalised additive mixed models (GAMMs) are increasingly popular in dynamic speech analysis, where the focus is on measurements with temporal or spatial structure such as formant, pitch or tongue contours. GAMMs provide a range of tools for dealing with the non-linear contour shapes and complex hierarchical organisation characteristic of such data sets. This, however, means that analysts are faced with non-trivial choices, many of which have a serious impact on the statistical validity of their analyses. This paper presents type I and type II error simulations to help researchers make informed decisions about modelling strategies when using GAMMs to analyse phonetic data. The simulations are based on two real data sets containing F2 and pitch contours, and a simulated data set modelled after the F2 data. They reflect typical scenarios in dynamic speech analysis. The main emphasis is on (i) dealing with dependencies within contours and higher-level units using random structures and other tools, and (ii) strategies for significance testing using GAMMs. The paper concludes with a small set of recommendations for fitting GAMMs, and provides advice on diagnosing issues and tailoring GAMMs to specific data sets. It is also accompanied by a GitHub repository including a tutorial on running type I error simulations for existing data sets: https://github.com/soskuthy/gamm_strategies.

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“…GAM(M)s are not yet used often in Human Life Sciences [46], but we find them an excellent match for the analysis at hand, and mixed-effect models gain support in biophysiological research such as visual perception [47] and nonvisual effects of light [48]. Guidelines on the theory behind GAMs and their practical use can be found in Wood (43), Simpson (49), Pedersen et al (50), and the guide by Sóskuthy (45).…”

“…Generalized Additive Models (GAMs) [43, 44] allow for a data-driven decomposition of the relationship between a dependent variable and user-defined predictor variables in both a parametric and nonparametric fashion. A variant of GAMs are Generalized Additive Mixed-Models (GAMMs or HGAMs), used in the context of hierarchical data as is the case in any repeated-measures setup such as ours [45]. GAMs are widely used in Biology , Ecology , and Linguistics [43].…”

“…If not stated otherwise, we used Akaike’s Information Criterion (AIC) for model selection, as suggested by several sources on GAM(M)s [43, 45, 49–51]. The AIC incorporates model fit (likelihood) and model size (number of parameters) [43].…”

“…T-tests obtain P-values for parametric terms. The p-values for nonparametric terms are approximate p-values , so called owing to the complexity of the degrees-of-freedom ( df ) concept used for statistical testing, and other underlying assumptions [43, 45]. For nonparametric terms, the hypothesis tested-against states that the relationship between predictor and dependent variable is a horizontal, flat line.…”

“…As random effects in Experiment I we had random intercepts b p and random smooths f p ( wavelength i ) for each participant p . In Experiment II and III , all participants took part in all protocols; we, therefore, had random effects for participants-by-protocol in those cases [45]. Random intercepts describe the deviation from the average PCA ( α ) depending on the participant (or participant-and-protocol), with independent and gaussian distributed values.…”