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

Table 6.1: Mean, variance and variance/mean ratio for the three species
Species Mean Variance Variance/Mean
Wild Buckwheat 1.2867 2.8099 2.1838
(Species 1097)
Dandelion
0.2467 0.3481 1.4110
(Species 1213)
Wild Oats
(Species 1509)
2.8200 27.7325 9.8342
Table 6.2: Univariate Poisson mixture models
Number of clusters or
states
Wild buckwheat
(species 1097)
Dandelian
(species 1213)
Wild Oats
(species 1509)
Univariate Poisson finite
mixture models
Univariate Poisson Hidden
Markov models
AIC BIC AIC BIC
2 2 3 2
1 1 1 1
5 4 3 3
The univariate analysis was carried out for each species separately to determine how
many clusters or states are in each count distribution. The univariate Poisson finite
mixture models and univariate hidden Markov models (Leroux and Puterman, 1992)
were fitted for each species and AIC and BIC criterions were used to select the number
of components of the model. There were different numbers of clusters or states for three
species distributions (Table 6.2). The AIC selection was the same compared to the BIC
selection method for the most of the models except for two situations. This table gives
us an indication that there was more than one cluster or state in species distributions. It
is interested to see how many clusters or states were present at the multivariate case.
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