I'm working on a time-dependent dataset, where basically I have two different populations and we're building Markov chains to describe their behaviors. What I'm trying to do is compare the transition matrices associated to the two populations, and decide whether the transition matrices are really different, or whether they could be due to chance. So my question is, is there a good way to compare two transition matrices in order to determine whether they are statistically different? Part of the problem we're running into is that both matrices have a lot of zeroes in them, but not always in the same places. Any suggestions are welcome.

Thank you, Greg