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.


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