Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Abstract

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi-likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.

Modelling demographic processes in marked populations: proceedings of theEURING2013 analytical meeting

“…) or in combination with radio‐telemetry data (Schwarz, Cope & Fratton ); new model fitting technology in an MCMC framework for addressing individual covariates (Bonner & Schofield ); fitting temporally varying individual covariates in hierarchical nest survival models (Converse et al . ); using posterior predictive checking as an aid to model selection (Chambert, Rotella & Higgs ); using generalized estimating equations as an alternative to Bayesian approaches to model heterogeneity in catchability (Akanda & Alpizar‐Jara ); using hidden Markov models to expand the toolbox for mark–recapture modelling (Choquet, Béchet & Guédon ); approaches for integrating memory models with mark–recapture modelling (Cole et al . ); and methods to deal with incompletely read marks in mark‐resighting studies (McClintock et al .…”

Marginal or conditional regression models for correlated non‐normal data?

“…This discussion is still ongoing, also in ecology (Fieberg et al . , ; Koper & Manseau ; Akanda & Alpizar‐Jara ).…”

“…After it became viable to fit conditional models to complex and large data sets, a long discussion ensued in the statistical literature, whether to choose a conditional or a marginal model (Neuhaus, Kalbfleisch & Hauck 1991;Lindsey & Lambert 1998;Heagerty & Zeger 2000;Diggle et al 2002;Lee & Nelder 2004). This discussion is still ongoing, also in ecology (Fieberg et al 2009(Fieberg et al , 2010Koper & Manseau 2009;Akanda & Alpizar-Jara 2014).…”

“…Lindsey & Lambert (1998) and Lee & Nelder (2004) discuss shortcomings of marginal modelling approaches, while text books like Zuur et al (2009) or Hardin & Hilbe (2012) recommend them, and in particular GEEs, for correlated non-normal data. Marginal models fit by GEEs are hence popular in ecological applications (Keller et al 2002;Paradis & Claude 2002;Bowerman, Johnson & Bowerman 2010;Poncet et al 2010;Akanda & Alpizar-Jara 2014).…”

A Generalized Estimating Equations Approach to Model Heterogeneity and Time Dependence in Capture-Recapture Studies

“…Akanda & Alpizar-Jara (2014a) proposed a generalized estimating equations (GEE) approach which accounts for individual heterogeneity and dependency among capture occasions, but their approach mainly focused on the M bh model. They also showed that the performance of the GEE approach is better than the mixed effects approach considering the closed population capture-recapture model, M h (Akanda & Alpizar-Jara 2014b).…”