I have working with Hidden Markov Models for prediction purposes. I have used 8-HMMs each with 3,4,5 and 6 hidden states for a dataset. So, I have 4 sets:
8-HMMs with 3 hidden states 8-HMMs with 4 hidden states 8-HMMs with 5 hidden states 8-HMMs with 6 hidden states
I want to check which of set of HMMs is better suited for representing that dataset. Now, for each set of HMMs I have calculated the log-likelihood value of each HMM for that dataset and then I have calculated the average. So for example, the model with 3-hidden states:
HMM-1: -70232.798125587 HMM-2: -38679.58216672705 HMM-3: -70194.94484629184 HMM-4: -38668.501330454834 HMM-5: -38679.58216672705 HMM-6: -38663.0027094305 HMM-7: -38679.58216672705 HMM-8: -70194.8488774772 Average: -50499.10529867782
In the same manner:
4-state: -45515.76430788275 5-state: -43658.7436411216 6-state: -45807.01572201134
So, from this, can we say that the 5-state one is the best one as it has the largest value? Also, is this the correct way to perform this test? I would really appreciate it if someone sheds some light on it. Thanks.