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

Table 7.6 Bacterial counts by 3 samplers in 50 sterile locations
X
1
X
2
X
3
X
1
X
2
X
3
X1
X
2
X
3
X1
X
2
X
3
X
1
X
2
X
3
1 2 11 3 6 6 3 8 2 7 10 5 22 9 6
8 6 0 3 9 14 1 1 30 2 2 8 5 2 4
2 13 5 4 2 25 4 5 15 3 15 3 2 0 6
2 8 1 9 7 3 7 6 3 1 8 2 2 1 1
5 6 5 5 4 8 8 10 4 4 6 0 4 6 4
14 1 7 4 4 7 3 2 10 8 7 3 4 9 2
3 9 2 7 3 2 6 8 5 6 6 6 8 4 6
7 6 8 1 14 6 2 3 10 4 14 7 3 10 6
3 4 12 2 13 0 1 7 3 3 3 14 4 7 10
1 9 7 14 9 5 2 9 12 6 8 3 2 4 6
The observed covariance matrix and the observed correlation matrix are given below:
⎡15.0714
⎢
0.2755
⎢
⎢⎣
− 3.6939
0.2755
13.6428
− 7.7347
− 3.6939⎤
− 7.7347
⎥
⎥
32.6122 ⎥⎦
⎡1
⎢
⎢
⎢⎣
0.0192
1
− 0.1666⎤
− 0.3667
⎥
⎥
.
1 ⎥⎦
Since the correlations were not very high, only the independence covariance structure is
considered and the loglikelihood and the AIC values are recorded. According to the
AIC criterion (Table 7.7), the model with the highest AIC value is selected
(loglikelihood of –382.2335). This model, the seven-component local independence
multivariate Poisson finite mixture model, gives a reasonable fit with respect to the
loglikelihood.
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