# Wong.est.Ratio: Sightability estimate of ratio with variance components... In SightabilityModel: Wildlife Sightability Modeling

 Wong.est.Ratio R Documentation

## Sightability estimate of ratio with variance components estimator from Wong (1996)

### Description

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

### Usage

``````Wong.est.Ratio(
numerator,
denominator,
srates,
nh,
Nh,
stratum,
subunit,
covars,
beta,
varbeta,
smat = NULL
)
``````

### Arguments

 `numerator, denominator` Number of animals in numerator and denominator of 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.Ratio, but may also be called directly by the user (e.g., in cases where the original sightability [test trial] data are not available, but the parameters and var/cov matrix from the logistic regression model is available in the literature).

### Value

 `ratio.hat` Sightability estimate of ratio, ratio^ `Vartot` Estimated variance of ratio^ ```VarSamp, VarSight, VarMod``` Estimated variance component due to sampling, sightability, model are set to NA

### Author(s)

Carl James Schwarz cschwarz.stat.sfu.ca@gmail.com

### 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.

`Sight.Est.Ratio`, `SS.est.Ratio`