As suggested in Calculating log-likelihood for given MLE (Markov Chains) I want to perform a likelihood ratio test for two fitted models (i.e., first and second order markov chains). Simply comparing the resulting log-likelihood values is as suggested in the other thread not enough. I know how to calculate the likelihood ratio, but I am unsure about how to determine the statistical significane.
I need the degree of freedoms for both models. What exactly is this in the case of my Markov Chain MLEs. The number of non-zero probabilities in the MLE, or the number of states?