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

7.5.3 Weed species data
The observed covariance matrix and the observed correlation matrix for the weed
species data (Chapter 6) are given below:
⎡2.8099
⎢
0.0161
⎢
⎢⎣
0.1056
0.0161
0.3481
− 0.1029
0.1056 ⎤
− 0.1029
⎥
⎥
27.7325⎥⎦
⎡1
⎢
⎢
⎢⎣
0.0162
1
0.0119 ⎤
− 0.0331
⎥
.
⎥
1 ⎥⎦
As mentioned in Table 6.3 (section 6.2), all the pairs of the correlation coefficients were
not significantly different from zero. The covariance and the correlation matrices for the
different models presented in Chapter 6 are listed below.
(a) Finite mixture with the four components restricted model (AIC selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡1.9440
⎢
0.2232
⎢
⎢⎣
0.6911
0.2232
0.3620
0.3123
0.6911 ⎤
0.3123
⎥
⎥
21.6737⎥⎦
⎡1
⎢
⎢
⎢⎣
0.2661
1
0.1065⎤
0.1115
⎥
.
⎥
1 ⎥⎦
(b) Finite mixture with the five components restricted model (BIC selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡ 1.7512
⎢
− 0.0293
⎢
⎢⎣
0.5754
− 0.0293
0.7315
0.5485
0.5754 ⎤
0.5485
⎥
⎥
25.2162⎥⎦
⎡1
⎢
⎢
⎢⎣
− 0.0259
1
0.0866⎤
0.1277
⎥
.
⎥
1 ⎥⎦
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