  We consider mark-recapture-recovery (MRR) data of animals where the model
parameters are a function of individual time-varying continuous covariates. For
such covariates, the covariate value is unobserved if the corresponding
individual is unobserved, in which case the survival probability cannot be
evaluated. For continuous-valued covariates, the corresponding likelihood can
only be expressed in the form of an integral that is analytically intractable
and, to date, no maximum likelihood approach that uses all the information in
the data has been developed. Assuming a first-order Markov process for the
covariate values, we accomplish this task by formulating the MRR setting in a
state-space framework and considering an approximate likelihood approach which
essentially discretizes the range of covariate values, reducing the integral to
a summation. The likelihood can then be efficiently calculated and maximized
using standard techniques for hidden Markov models. We initially assess the
approach using simulated data before applying to real data relating to Soay
sheep, specifying the survival probability as a function of body mass. Models
that have previously been suggested for the corresponding covariate process are
typically of the form of diffusive random walks. We consider an alternative
nondiffusive AR(1)-type model which appears to provide a significantly better
fit to the Soay sheep data.
