I have a population, each unit of which exists in one of several states that change over time. I am using first-order Markov chains to model these state transitions.
My population can be segmented into various subpopulations of interest. I've obtained the transition matrices for each of these subpopulations, and would like to know if these subpopulations differ from the general population in some principled way.
I don't know of any principled way of comparing transition matrices in this way. Comparing the transition matrices row-wise to that of the general population seems like one approach, but I'm not sure how to go about interpreting this. Another approach might be a spectral/eigendecomposition approach, which is much more readily interpretable to me, but might be harder to squeeze insight/stylised facts from.
I've had a cursory search of the literature without much luck. Any suggestions?