Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models

Theo Michelot, Roland Langrock, Thomas Kneib, Ruth King

Research output: Contribution to journalArticlepeer-review


We discuss the semiparametric modeling of mark-recapture-recovery data where the temporal and/or individual variation of model parameters is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the
covariates of interest. In this paper, we discuss the modeling of the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validation to choose the smoothing parameters in a data-driven way. Our contribution builds on and extends the existing literature, providing a unified inferential framework for semiparametric mark-recapture-recovery models for open populations,
where the interest typically lies in the estimation of survival probabilities. The approach is applied to two real datasets, corresponding to grey herons (Ardea Cinerea), where we model the survival probability as a function of environmental condition (a time-varying global covariate), and Soay sheep (Ovis Aries), where
we model the survival probability as a function of individual weight (a time-varying individual-specific covariate). The proposed semiparametric approach is compared to a standard parametric (logistic) regression and new interesting underlying dynamics are observed in both cases.
Original languageEnglish
Pages (from-to)222-239
JournalBiometrical Journal
Issue number1
Early online date20 Aug 2015
Publication statusPublished - Jan 2016


  • Cormack-Jolly-Seber model
  • Hidden Markov model
  • M-array
  • Nonparametric regression
  • P-splines
  • QA Mathematics
  • QH Natural history


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