Bayesian semiparametric Markov renewal mixed models for vocalization syntax

Speech and language play an important role in human vocal communication. Studies have shown that vocal disorders can result from genetic factors. In the absence of high-quality data on humans, mouse vocalization experiments in laboratory settings have been proven useful in providing valuable insights into mammalian vocal development, including especially the impact of certain genetic mutations. Such data sets usually consist of categorical syllable sequences along with continuous intersyllable interval (ISI) times for mice of different genotypes vocalizing under different contexts. ISIs are of particular importance as increased ISIs can be an indication of possible vocal impairment. Statistical methods for properly analyzing ISIs along with the transition probabilities have however been lacking. In this article, we propose a class of novel Markov renewal mixed models that capture the stochastic dynamics of both state transitions and ISI lengths. Specifically, we model the transition dynamics and the ISIs using Dirichlet and gamma mixtures, respectively, allowing the mixture probabilities in both cases to vary flexibly with fixed covariate effects as well as random individual-specific effects. We apply our model to analyze the impact of a mutation in the Foxp2 gene on mouse vocal behavior. We find that genotypes and social contexts significantly affect the length of ISIs but, compared to previous analyses, the influences of genotype and social context on the syllable transition dynamics are weaker.