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

Proportion
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2 3 4 5 6 7
Number of Components-k
Figure 6.4: The mixing proportions for model solutions with k =2 to 7 components for
the local independence multivariate Poisson finite mixture model
Table 6.6 contains the parameter estimates and the bootstrapped standard errors for the
model with 5 components. Here the bootstrap standard errors were considered because
of small sample size (McLachlan et al., 2000), and therefore, the asymptotic standard
errors were not valid. Special care was taken to avoid the label switching (Brijs et al.,
2004). This problem can be avoided by adding the relevant constraints,
p1 ≤ p2
≤ ... ≤ p j
to the optimization algorithm ( p
j
’s the mixing proportions). For
some of the small components with small mixing proportions, the estimated standard
errors were large. The parameters with zero estimated values and zero standard errors
can be interpreted as zero.
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