multivariate poisson hidden markov models for analysis of spatial ...

model, as indicated by the loglikelihood values, increases significantly. Figure 6.12
indeed illustrates that the loglikelihood of the independence and the common covariance
models is higher than the loglikelihoods of the restricted covariance model over the
range of component solutions ( k =1 to 7). Figure 6.13 illustrates that the loglikelihood
of the independence model is higher than the loglikelihoods of the restricted and the
common covariance model over the range of component solutions ( k =1 to 7) for the
hidden Markov models.
-575
-675
Loglikelihood
-775
-875
-975
-1075
-1175
1 2 3 4 5 6 7
k ( the Number of States)
restricted covariance common covariance independence
Figure 6.13: Loglikelihood against the number of components ( k ) for the multivariate
Poisson hidden Markov models
From the viewpoint of model fit, Figure 6.13 this partly justifies the use of the model
with the independent covariance structure since the comparison of maximized
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