  Studying the neurological, genetic and evolutionary basis of human vocal
communication mechanisms is an important field of neuroscience. In the absence
of high quality data on humans, mouse vocalization experiments in laboratory
settings have been proven to be useful in providing valuable insights into
mammalian vocal development and evolution, including especially the impact of
certain genetic mutations. Data sets from mouse vocalization experiments
usually consist of categorical syllable sequences along with continuous
inter-syllable interval times for mice of different genotypes vocalizing under
various contexts. Few statistical models have considered the inference for both
transition probabilities and inter-state intervals. The latter is of particular
importance as increased inter-state intervals can be an indication of possible
vocal impairment. In this paper, we propose a class of novel Markov renewal
mixed models that capture the stochastic dynamics of both state transitions and
inter-state interval times. Specifically, we model the transition dynamics and
the inter-state intervals 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
inter-state interval times but, compared to previous analyses, the influences
of genotype and social context on the syllable transition dynamics are weaker.
