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

Figure 6.3 illustrates the evolution of the loglikelihood, the AIC and the BIC for
different components ( k =1,…,7) of the local independence multivariate Poisson model.
This figure demonstrates that the AIC selects 6 components whereas the BIC selects 5
components. Therefore, in this case, the model with fewer components is selected for
interpretation.
-600
-650
-700
Loglikelihood
-750
-800
-850
-900
-950
-1000
1 2 3 4 5 6 7
k (the number of components)
Loglikelihood AIC BIC
Figure 6.3: Loglikelihood, AIC and BIC against the number of components for the
local independence multivariate Poisson finite mixture model
Figure 6.4 illustrates the optimal value of the mixing proportions for the range of
models used (values of k from 2 to 7). It can be seen that there is one large component
and the rest are small components in all models. In fact, the mixing proportions tend to
fluctuate over the different component solutions.
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