  Understanding which phenotypic traits are consistently correlated throughout
evolution is a highly pertinent problem in modern evolutionary biology. Here,
we propose a multivariate phylogenetic latent liability model for assessing the
correlation between multiple types of data, while simultaneously controlling
for their unknown shared evolutionary history informed through molecular
sequences. The latent formulation enables us to consider in a single model
combinations of continuous traits, discrete binary traits and discrete traits
with multiple ordered and unordered states. Previous approaches have
entertained a single data type generally along a fixed history, precluding
estimation of correlation between traits and ignoring uncertainty in the
history. We implement our model in a Bayesian phylogenetic framework, and
discuss inference techniques for hypothesis testing. Finally, we showcase the
method through applications to columbine flower morphology, antibiotic
resistance in Salmonella and epitope evolution in influenza.
