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

maximization (EM) algorithm is applicable (McLachlan and Peel, 2000 and Fraley and
Raftery, 1998).
For a multivariate finite mixture model, to avoid the computational difficulties, it is
often assumed that the observed variables are mutually independent within components
(Vermunt et al., 2002). If there are no restrictions on the dependency of variables, the
model with multivariate probability density functions is applicable. Sometimes the
model-based clustering problem involves estimating a separate set of means, variances,
and covariances for each mixture component, which quickly becomes computationally
burdensome (Brijs, 2002).
Several types of restrictions can be imposed on the variance-covariance matrix to create
the models in between the local independence model and the full covariance model. In
some situations, this may be necessary for practical reasons since the unrestricted model
may be inadequate. The reason for this inadequacy is that the number of free parameters
in the variance-covariance matrix for the full covariance model increases rapidly with
the number of mixture components and the number of indicator variables. Therefore,
more restricted models are defined by assuming certain pairs of y ’s to be mutually
independent within mixture components by fixing some but not all covariances to zero
(Karlis, 2003; Li et al., 1999).
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