Statistical Approaches for Hidden Variables in Ecology. Nathalie Peyrard

of this figure, see www.iste.co.uk/peyrard/ecology.zip

      1.3.5.4. Choosing a number of states

The calculation of model selection criteria is valuable in helping to chose the number of states to use, as is the AIC. Table 1.1 shows AIC and ICL scores for different numbers of activities across our three trajectories.

Table 1.1. Evolution of model selection criteria (AIC and ICL) as a function of the number of hidden states J. In both cases, the best scores are attained for a model with six hidden states

J	2	3	4	5	6	7
AIC	29,044	24,213	18,773	16,624	14,220	19,480
ICL	29,195	24,210	18,887	16,720	14,821	21,003

      From a purely statistical perspective, a 6-state model appears preferable here.

Figure 1.13 shows states along a trajectory (using the bivariate velocity model) alongside the speed characteristics of these states. We see that a classification into six activities broadly corresponds to the creation of subdivisions in the intermediate state. States previously characterized as belonging to activity 2 or 3 (Figure 1.9, top left) are divided into four different groups in the new model. In our view, the choice of an optimum number of states in this case should be guided by our capacity to interpret the model, rather than by purely statistical considerations.

Figure 1.13. Study zone (red dot on the map) and three trajectories of three different red-footed boobies. Measured over a time step of 10 s. For a color version of this figure, see www.iste.co.uk/peyrard/ecology.zip

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