Abstract
We consider multistate capture–recapture–recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason–Schwarz model has been fitted to such data where the state process is modeled as a firstorder Markov chain, though secondorder models have also been proposed and fitted to data. However, loworder Markov models may not accurately represent the underlying biology. For example, specifying a (timeindependent) firstorder Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying timedependent or higherorder processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason–Schwarz model by specifying a semiMarkov model for the state process, where the dwelltime distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semiMarkov Arnason–Schwarz model in terms of a simpler and computationally tractable hidden Markov model. SemiMarkov Arnason–Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semiMarkov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis.
Original language  English 

Pages (fromto)  619628 
Journal  Biometrics 
Volume  72 
Issue number  2 
Early online date  19 Nov 2015 
DOIs  
Publication status  Published  Jun 2016 
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Ruth King
 School of Mathematics  The Thomas Bayes Chair of Statistics
Person: Academic: Research Active (Teaching)