A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments

Huggins, Richard; Hwang, Wen‐Han

doi:10.1111/j.1751-5823.2011.00157.x

Cited by 24 publications

(22 citation statements)

References 121 publications

(179 reference statements)

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“…The full likelihood of all model parameters is proportional to

\prod_{i = 1}^{n} \frac{p_{i} {(β)}^{T_{i}} {1 - p_{i} false(italicβ false)}^{m - T_{i}}}{{italicπ}_{i} false(italicβ false)} \prod_{i = 1}^{n} {italicπ}_{i} false(italicβ false) \prod_{i = n + 1}^{N} false{1 - π_{i} (β) false} .

As the number of total individuals, N , is unknown and the covariates are not known for individuals that are never captured, this likelihood cannot be directly evaluated. The conditional likelihood (Huggins ) is the first product component, and it can be formulated as a GLM (Huggins and Hwang ) for the positive Binomial distribution (Patil ). It may be rewritten as

\begin{matrix} \prod_{i = 1}^{n} p_{i} {(β)}^{T_{i} - 1} {1 - p_{i} false(italicβ false)}^{m - t_{i} - false(T_{i} - 1 false)} \\ \prod_{i = 1}^{n} 2.047em2.047emtrue[\frac{{1 - p_{i} false(italicβ false)}^{t_{i} - 1} p_{i} false(italicβ false)}{{italicπ}_{i} false(italicβ false)} 2.047em2.047emtrue] . \end{matrix}

…”

Section: Notation and Modelsmentioning

confidence: 99%

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

Akanda

Alpizar‐Jara

2014

Ecology and Evolution

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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.

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“…The full likelihood of all model parameters is proportional to

\prod_{i = 1}^{n} \frac{p_{i} {(β)}^{T_{i}} {1 - p_{i} false(italicβ false)}^{m - T_{i}}}{{italicπ}_{i} false(italicβ false)} \prod_{i = 1}^{n} {italicπ}_{i} false(italicβ false) \prod_{i = n + 1}^{N} false{1 - π_{i} (β) false} .

\begin{matrix} \prod_{i = 1}^{n} p_{i} {(β)}^{T_{i} - 1} {1 - p_{i} false(italicβ false)}^{m - t_{i} - false(T_{i} - 1 false)} \\ \prod_{i = 1}^{n} 2.047em2.047emtrue[\frac{{1 - p_{i} false(italicβ false)}^{t_{i} - 1} p_{i} false(italicβ false)}{{italicπ}_{i} false(italicβ false)} 2.047em2.047emtrue] . \end{matrix}

…”

Section: Notation and Modelsmentioning

confidence: 99%

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

Akanda

Alpizar‐Jara

2014

Ecology and Evolution

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“…The existing estimation methods for abundance are largely based on the conditional likelihood (CL) (Huggins and Hwang, ) and generally consist of two steps. In the first step, a desirable point estimator for the abundance is derived under some probability model on the capture process with or without covariates.…”

Section: Introductionmentioning

confidence: 99%

Full Likelihood Inference for Abundance from Continuous Time Capture–Recapture Data

Liu

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Capture–recapture experiments are widely used cost‐effective sampling techniques for estimating population sizes or abundances in biology, ecology, demography, epidemiology and reliability studies. For continuous time capture–recapture data, existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation. The corresponding Wald‐type confidence intervals for the abundance may have severe undercoverage, and their lower limits can be below the number of individuals captured. We propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood. Under both parametric and semiparametric intensity models, we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically χ2 with 1 degree of freedom. Simulations indicate that compared with conditional‐likelihood‐based methods, the maximum full likelihood estimator has a smaller mean‐square error, and the likelihood ratio confidence intervals often have remarkable gains in coverage probability. We illustrate the advantages of the proposed approach by analysing illegal immigrant data for the Netherlands and Prinia flaviventris data from Hong Kong.

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“…Capture-recapture (CR) surveys are widely used in ecology and epidemiology to estimate population sizes. In essence they are sampling schemes that allow the estimation of both n and p in a Binomial(n, p) experiment (Huggins and Hwang 2011). The simplest CR sampling design consists of units or individuals in some population that are captured or tagged across several sampling occasions, e.g., trapping a nocturnal mammal species on seven consecutive nights.…”

Section: Introductionmentioning

confidence: 99%

“…The capture probabilities are typically modeled as logistic regression functions of the covariates, and parameters are estimated using maximum likelihood. Importantly, these CR models are generalized linear models (GLMs;McCullagh and Nelder 1989;Huggins and Hwang 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Here, we maximize the conditional likelihood (or more formally the positive-Bernoulli distribution) models of Huggins (1989). This approach has become standard practice to carry out inferences when considering individual covariates, with several different software packages currently using this methodology, including: MARK (Cooch and White 2012), CARE-2 (Hwang and Chao 2003), and the R packages (R Core Team 2015): mra (McDonald 2012), RMark (Laake 2013) and Rcapture Rivest 2007, 2014), the latter package uses a log-linear approach, which can be shown to be equivalent to the conditional likelihood (Cormack 1989;Huggins and Hwang 2011). For a more detailed review of CR software see Bunge (2013).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

TheVGAMPackage for Capture-Recapture Data Using the Conditional Likelihood

Yee¹,

Stoklosa²,

Huggins³

2015

J. Stat. Soft.

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It is well known that using individual covariate information (such as body weight or gender) to model heterogeneity in capture-recapture (CR) experiments can greatly enhance inferences on the size of a closed population. Since individual covariates are only observable for captured individuals, complex conditional likelihood methods are usually required and these do not constitute a standard generalized linear model (GLM) family. Modern statistical techniques such as generalized additive models (GAMs), which allow a relaxing of the linearity assumptions on the covariates, are readily available for many standard GLM families. Fortunately, a natural statistical framework for maximizing conditional likelihoods is available in the Vector GLM and Vector GAM classes of models. We present several new R functions (implemented within the VGAM package) specifically developed to allow the incorporation of individual covariates in the analysis of closed population CR data using a GLM/GAM-like approach and the conditional likelihood. As a result, a wide variety of practical tools are now readily available in the VGAM object oriented framework. We discuss and demonstrate their advantages, features and flexibility using the new VGAM CR functions on several examples.

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A Review of the Use of Conditional Likelihood in Capture-Recapture Experiments

Cited by 24 publications

References 121 publications

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

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

Full Likelihood Inference for Abundance from Continuous Time Capture–Recapture Data

TheVGAMPackage for Capture-Recapture Data Using the Conditional Likelihood

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