Correlated evolution of categorical characters under a simple model

I describe a simple model for quantifying the strength of association between two categorical characters evolving on a phylogenetic tree. The model can be used to estimate a correlation statistic that asks whether or not the two characters tend to change at the same time (positive correlation) or at different times (no correlation). This is different than asking if changes in one character are associated with a particular state in another character, which has been the focus of most prior tests for phylogenetic correlation in categorical characters. Analyses of simulated data indicate that positive correlations can be accurately estimated over a range of different tree sizes and phylogenetic signals.