A Note on Simplifying Likelihoods for Site Occupancy Models

Morgan, Byron J. T.; Revell, David J.; Freeman, Stephen N.

doi:10.1111/j.1541-0420.2006.00724.x

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…In this case (S d , d T ) is a sufficient statistic. The likelihood in (2.1) can be rewritten using a reparameterization of the type suggested by Morgan, Revell, and Freeman (2007) for likelihood functions of this form. Setting θ = ψ(1 − e −λL ), the probability of detecting the species at an occupied site leads to:…”

Section: Mles and Asymptotic Design Recommendationsmentioning

confidence: 99%

Species Occupancy Modeling for Detection Data Collected Along a Transect

Guillera‐Arroita

Morgan

Ridout

et al. 2011

JABES

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The proportion of sampling sites occupied by a species is a concept of interest in ecology and biodiversity conservation. Occupancy surveys based on collecting detection data along transects have become increasingly popular to monitor some species. To date, the analysis of such data has been carried out by discretizing the data, dividing the transects into discrete segments. Here we propose alternative occupancy models which describe the detection process as a continuous point process. These models provide a more natural description of the data and eliminate the need to divide transects into segments, which can be arbitrary and may lead to increased bias in the estimator of occupancy or increased chances of obtaining estimates on the boundary of the parameter space. We present a model that assumes independence between detections and an alternative model that describes the detection process as a Markov modulated Poisson process to account for potential clustering in the detections. The utility of these models is illustrated with the analysis of data from a recent survey of the Sumatran tiger Panthera tigris sumatrae. The models can also be applied to surveys that collect continuous data in time, such as those based on the use of camera-trap devices. Supplementary materials for this article are available online.

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Section: Mles and Asymptotic Design Recommendationsmentioning

confidence: 99%

Species Occupancy Modeling for Detection Data Collected Along a Transect

Guillera‐Arroita

Morgan

Ridout

et al. 2011

JABES

Self Cite

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“…The estimation procedure for conditional likelihood can also be applied to model (9). In doing so, the conditional likelihood method shares the same advantage as in Morgan et al (2007) who proposed a re-parametrization that simplifies the likelihood making computation/model fitting a lot easier. It turns out that the approach of Morgan et al (2007) can be viewed as a special case of conditional likelihood.…”

Section: Effects Of Ignoring Heterogeneity In the Presence Probabilitymentioning

confidence: 99%

“…In doing so, the conditional likelihood method shares the same advantage as in Morgan et al (2007) who proposed a re-parametrization that simplifies the likelihood making computation/model fitting a lot easier. It turns out that the approach of Morgan et al (2007) can be viewed as a special case of conditional likelihood. In addition to model ( 9), the inclusion of covariates in detection probabilities and/or presence probabilities is also straightforward, e.g., p i = H(θ x i ) and/or ψ i = H(γ z i ).…”

Section: Effects Of Ignoring Heterogeneity In the Presence Probabilitymentioning

confidence: 99%

On site occupancy models with heterogeneity

Hwang¹,

Stoklosa²,

Chen³

2022

Preprint

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“…In the removal design, there is by design at most one detection per site so 1 = and hence ( , ) are sufficient statistics. By doing a transformation = * (Morgan et al 2007), we can simplify the likelihood in (3) into two independent components as follows:…”

Section: Occupancy-detection Modelmentioning

confidence: 99%

Species occupancy estimation and imperfect detection: shall surveys continue after the first detection?

Guillera‐Arroita

Lahoz‐Monfort

2017

AStA Adv Stat Anal

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Species occupancy, the proportion of sites occupied by a species, is a state variable of interest in ecology. One challenge in its estimation is that detection is often imperfect in wildlife surveys. As a consequence, occupancy models that explicitly describe the observation process are becoming widely used in the discipline. These models require data that are informative about species detectability. Such information is often obtained by conducting repeat surveys to sampling sites. One strategy is to survey each site a predefined number of times, regardless of whether the species is detected. Alternatively, one can stop surveying a site once the species is detected and reallocate the effort saved to surveying new sites. In this paper we evaluate the merits of these two general design strategies under a range of realistic conditions. We conclude that continuing surveys after detection is beneficial unless the overall probability of detection at occupied sites is close to one, and that the benefits are greater when the sample size is small. Since detectability and sample size tend to be small in ecological applications, our recommendation is to follow a strategy where at least some of the sites continue to be sampled after first detection.

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A Note on Simplifying Likelihoods for Site Occupancy Models

Abstract: We show how a simple reparameterization can reduce the number of parameters that need to be estimated by numerical maximum likelihood in site occupancy models. Three examples are provided.

Cited by 4 publications

References 8 publications

Species Occupancy Modeling for Detection Data Collected Along a Transect

Species Occupancy Modeling for Detection Data Collected Along a Transect

On site occupancy models with heterogeneity

Species occupancy estimation and imperfect detection: shall surveys continue after the first detection?

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