Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models.
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 gray 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.
Département Génie Mathématique, INSA de Rouen, Saint-Étienne-du-Rouvray, France.
Théo
T
Michelot
School of Mathematics and Statistics and Centre for Research into Ecological and Environmental Modelling, University of St Andrews, St Andrews, UK.
Roland
R
Langrock
Department of Economics, Georg August University Göttingen, Göttingen, Germany.
Thomas
T
Kneib
School of Mathematics and Statistics and Centre for Research into Ecological and Environmental Modelling, University of St Andrews, St Andrews, UK.
Ruth
R
King
D000328:Adult; D000818:Animals; D002675:Child, Preschool; D006801:Humans; D007223:Infant; D016013:Likelihood Functions; D015233:Models, Statistical; D015999:Multivariate Analysis; D011157:Population Dynamics; D034561:Sheep, Domestic; D018709:Statistics, Nonparametric; D016019:Survival Analysis; D035501:Uncertainty
Cormack-Jolly-Seber model; Hidden Markov model; Nonparametric regression; P-splines; m-Array