Abstract
Advances in capture–recapture methodology have allowed the inclusion of continuous, time-dependent individual-covariates as predictors of survival and capture probabilities. The problem posed by these covariates is that they are only observed for an individual when that individual is captured. One solution is to assume a model of the covariate which defines the distribution of unobserved values, conditional on the observed values, and apply Bayesian methods to compute parameter estimates and to test the covariate’s effect.
Previous applications of this approach have modeled the survival probability as a linear function of the covariate on some scale (e.g. identity or logistic). In some applications a linear function may not adequately describe the true relationship. Here we incorporate semi-parametric regression to allow for more flexibility in the relationship between the covariate and the survival probabilities of the Cormack–Jolly–Seber model. A fully Bayesian, adaptive algorithm is used to model the relationship with splines, in which the complexity of the relationship is governed by the number and location of the knots in the spline. A reversible jump Markov chain Monte Carlo algorithm is implemented to explore splines with different knot configurations, and model averaging is used to compute the final estimates of the survival probabilities.
The method is applied to a simulated data set and to data collected through the Dutch Constant Effort Sites ringing project to study the survival of reed warblers (Acrocephalus scirpaceus) as a function of condition.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Biller C (2000) Adaptive Bayesian regression splines in semiparametric generalized linear models. Journal of Computational and Graphical Statistics 9(1):122–140.
Bonner SJ (2007) Time-Varying Covariates and Semi-Parametric Regression in Capture–Recapture: An Adaptive Spline Approach. Technical report, Simon Fraser University, Burnaby, BC.
Bonner SJ, Schwarz CJ (2006) An extension of the Cormack–Jolly–Seber model for continuous covariates with application to Microtus pennsylvanicus. Biometrics 62(1):142–149.
Chen M-H, Shao Q-M, Ibrahim JG (2000) Monte Carlo Methods in Bayesian Computation. Springer, New York.
Denison D, Mallick B, Smith A (1998) Automatic Bayesian curve fitting. Journal of the Royal Statistical Society, Series B 60:333–350.
Eubank RL (1999) Nonparametric Regression and Spline Smoothing. Marcell Dekker, Inc., New York, 2nd edition.
Fewster R (2008) Cubic splines for estimating the distribution of residence times using indvidual resighting data. In: Thomson DL, Cooch EG, Conroy MJ (eds.) Modeling Demographic Processes in Marked Populations. Environmental and Ecological Statistics, Springer, New York 3:393–416.
Gimenez O, Covas R, Brown CR, Anderson MD (2006a) Nonparametric estimation of natural selection on a quantitative trait using mark-recapture data. Evolution 60(3):460–466.
Gimenez O, Crainiceanu C, Barbraud C, Jenouvrier S, Morgan B (2006b) Semiparametric regression in capture–recapture modelling. Biometrics 62:691–698.
Green PJ (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82(4):711–7332.
Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial. Statistical Science 14:382–417.
Holmes C (2002) Discussion of: spline adaptation in extended linear models. Statistical Science 17(1):22–24.
Lebreton J-D, Burnham KP, Clobert J, Anderson DR (1992) Modelling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs 62(1):67–118.
Pradel R, Hines JE, Lebreton J-D, Nichols JD (1997) Capture–recapture survival models taking account of transients. Biometrics 53:60–72.
Ruppert D, Wand M, Carroll R (2003) Semiparametric Regression. Cambridge University Press, Cambridge, UK.
Schumaker LL (1993) Spline Functions: Basic Theory. John Wiley & Sons, Inc., New York, 2nd edition.
Seber GAF (1982) The Estimation of Animal Abundance: And Related Parameters. Macmillan, New York, 2nd edition.
Speek HG. Ces Handleiding. Technical report, Institute of Ecology Centre for Terrestrial Ecology, Heteren, Netherlands, December 2006. URL http://www.vogeltrekstation.nl/%20ces_handleiding.htm.
Waagepetersen R, Sorensen D (2001) A tutorial on reversible jump MCMC with a view toward applications in QTL-mapping. International Statistical Review 69:49–61.
Williams BK, Nichols JD, Conroy MJ (2002) Analysis and Management of Animal Populations. Academic Press, San Diego, CA.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Bonner, S.J., L. Thomson, D., Schwarz, C.J. (2009). Time-Varying Covariates and Semi-Parametric Regression in Capture–Recapture: An Adaptive Spline Approach. In: Thomson, D.L., Cooch, E.G., Conroy, M.J. (eds) Modeling Demographic Processes In Marked Populations. Environmental and Ecological Statistics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-78151-8_29
Download citation
DOI: https://doi.org/10.1007/978-0-387-78151-8_29
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-78150-1
Online ISBN: 978-0-387-78151-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)