Comparison of Fixed Effect, Random Effect, and Hierarchical Bayes Estimators for Mark Recapture Data Using AD Model Builder

  • Mark N. Maunder
  • Hans J. Skaug
  • David A. Fournier
  • Simon D. Hoyle
Part of the Environmental and Ecological Statistics book series (ENES, volume 3)


Mark-recapture studies are one of the most common methods used to obtain demographic parameters for wildlife populations. Time specific estimates of parameters representing population processes contain both temporal variability in the process (process error) and error in estimating the parameters (observation error). Therefore, to estimate the temporal variation in the population process, it is important to separate these two errors. Traditional random effect models can be used to separate the two errors. However, it is difficult to implement the required simultaneous maximization and integration for dynamic nonlinear non-Gaussian models. An alternative hierarchical Bayesian approach using MCMC integration is easier to apply, but requires priors for all model parameters.

AD Model Builder (ADMB) is a general software environment for fitting parameter rich nonlinear models to data. It uses automatic differentiation to provide a more efficient and stable parameter estimation framework. ADMB has both random effects using Laplace approximation and importance sampling, and MCMC to implement Bayesian analysis.

To demonstrate ADMB and investigate methods to analyze mark-recapture data, we implement fixed effect, random effect, and hierarchical Bayes estimators in ADMB and apply them to three mark-recapture data sets. Our results showed that unrestricted time-effects, random effects, and hierarchical Bayes methods often give similar results, but not in all cases or for all parameters.


Markov Chain Monte Carlo Nuisance Parameter Uncertainty Interval Profile Likelihood Laplace Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Mark N. Maunder
    • 1
  • Hans J. Skaug
  • David A. Fournier
  • Simon D. Hoyle
  1. 1.Inter-American Tropical Tuna CommissionUSA

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