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

Table 6.6: Parameter estimates (bootstrap standard errors) of the five components
independence covariance model
Component θ
1
θ
2
θ
3
1 0.2232 0.0000 25.0084
(0.0976) (0.0000) (0.5254)
2 1.9591 0.1883 8.9511
(0.1523) (0.0334) (0.5148)
3 2.7836 0.3614 0.4916
(0.0471) (0.0159) (0.0175)
4 0.7413 0.4949 2.4109
(0.0412)
5 0.3781
(0.1096)
(0.0098)
0.0000
(0.0000)
(0.0699)
0.0085
(0.0138)
p
j
0.0252
0.1600
0.2342
0.2649
0.3156
Figure 6.5 illustrates the evolution of the loglikelihood for different components
( k =1,…,7) of the common covariance multivariate Poisson model. Furthermore, the
figure demonstrates that both the AIC and the BIC select five components solution.
Figure 6.6 illustrates the optimal value of the mixing proportions for the entire range of
models used (values of k from 2 to 7). Again, it can be seen that there is one large
component and the rest are small components in all models, except the sevencomponent
model. The mixing proportions tend to fluctuate over the different
component solutions.
Table 6.7 contains the parameter estimates for the model with five components. The
components with small mixing proportions got the larger estimated standard errors
compared to relatively large other components. The parameters with zero estimated
values were not differing significantly from zero.
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