Sightability estimate with variance components estimator from Wong (1996)

Description

Estimates population size, with variance estimated using Wong's (1996) estimator. This function will usualled be called by Sight.Est function (but see details).

Usage

1
Wong.est(total, srates, nh, Nh, stratum, subunit, covars, beta, varbeta, smat = NULL)

Arguments

total

Number of animals in each independently sighted group

srates

Vector of plot-level sampling probabilities (same dimension as total).

nh

Number of sample plots in each stratum

Nh

Number of population plots in each stratum

stratum

Stratum identifiers (associated with the independently observed animal groups)

subunit

Plot ID (associated with the independently observed animal groups)

covars

Matrix of sightability covariates (associated with the independently observed animal groups)

beta

Logistic regression parameter estimates (from fitted sightability model)

varbeta

Estimated variance-covariance matrix for the logistic regression parameter estimates (from fitted sightability model)

smat

Estimated variance-covariance matrix for the inflation factors (1/probability of detection). This is an n.animal x n.animal matrix, and is usually calculated within the Wong.est function. Non-null values can be passed to the function (e.g., if a bootstrap is used to estimate uncertainty due to the estimated detection parameters).

Details

This function is called by Sight.Est, but may also be called directly by the user (e.g., in cases where the original sighability [test trial] data are not available, but the parameters and var/cov matrix from the logistic regression model is available in the literature).

Value

tau.hat

Sightability estimate of population size, tau^

Vartot

Estimated variance of tau^

VarSamp

Estimated variance component due to sampling aerial units

VarSight

Estimated variance component due to sighting process (i.e., series of binomial rv for each animal group)

Varmod

Estimated variance component due to estimating detection probabilities using test trial data

Author(s)

John Fieberg

References

Rice CG, Jenkins KJ, Chang WY (2009). Sightability Model for Mountain Goats." The Journal of Wildlife Management, 73(3), 468- 478.

Steinhorst, R. K., and M.D. Samuel. (1989). Sightability adjustment methods for aerial surveys of wildlife populations. Biometrics 45:415-425.

Wong, C. (1996). Population size estimation using the modified Horvitz-Thompson estimator with estimated sighting probabilities. Dissertation, Colorado State University, Fort Collins, USA.

See Also

Sight.Est, SS.est