Quantifying vowel category distinctness using Bayesian modelling

Phonetic and sociolinguistic studies of vowel merger require a measure of acoustic distinctness between vowel categories. Three desiderata for such a metric are that it be multivariate, in the sense that it account for correlations between dimensions (e.g., F1 and F2), control for other factors affecting vowel formants (e.g. surrounding consonants), and work for unbalanced data (common in naturalistic data). Previous work (Nycz and Hall-Lew, 2013; Kelley & Tucker, 2020) has considered a variety of measures, including variants of Euclidean distance, Pillai score, and Bhattacharyya affinity, but none meet all three criteria. We present a new method for quantifying vowel merger that meets all desiderata and can be applied to different metrics: we fit a Bayesian mixed-effects linear model to jointly predict F1 and F2, then compute any desired metric—here, Euclidean distance, Pillai score, and Bhattacharyya affinity—from the posterior. We evaluate each metric, and the overall method, to describe PIN-PEN across a range of English dialect corpora. We find that controlling for covariates and unbalanced data adds substantial signal, but that multivariate modelling does not perform substantially better than univariate modelling. Additionally, we argue that Bhattacharyya affinity has particularly desirable properties (e.g., allowing for heteroskedastic data: Johnson, 2015).