Sight.Est.Ratio: Sightability Model Estimator - Ratio of variables

In SightabilityModel: Wildlife Sightability Modeling

Sightability Model Estimator - Ratio of variables

Description

Estimates population ratios by 1) fitting a sightability (logistic regression) model to "test trial" data; 2) applying the fitted model to independent (operational) survey data to correct for detection rates < 1.

Usage

Sight.Est.Ratio(
  form,
  sdat = NULL,
  odat,
  sampinfo,
  method = "Wong",
  logCI = TRUE,
  alpha = 0.05,
  Vm.boot = FALSE,
  nboot = 1000,
  bet = NULL,
  varbet = NULL
)

Arguments

form	a symbolic description of the sightability model to be fit (e.g., "y ~ x1 + x2 + ..."), where y is a binary response variable (= 1 if the animal is seen and 0 otherwise) and x1, x2, ... are a set of predictor variables thought to influence detection
sdat	'sightability' data frame. Each row represents an independent sightability trial, and columns contain the response (a binary random variable = 1 if the animal was observed and 0 otherwise) and the covariates used to model detection probabilities.
odat	'observational survey' data frame containing the following variable names (stratum, subunit, numerator, denominator) along with the same covariates used to model detection probabilities (each record corresponds to an independently sighted group of animals). stratum = stratum identifier (will take on a single value for non-stratified surveys); subunit = numeric plot unit identifier; numerator = total number of observed animals (for each independently sighted group of animals for numerator of ratio); denominator = total number of observed animals (for each independently sighted group of animals for denominator of ratio).
sampinfo	data frame containing sampling information pertaining to the observational survey. Must include the following variables (stratum, nh, Nh). stratum = stratum identifier (must take on the same values as stratum variable in observational data set), nh = number of sampled units in stratum h, Nh = number of population units in stratum h; note (this dataset will contain a single record for non-stratified designs).
method	method for estimating variance of the abundance estimator. Should be one of ("Wong", "SS"). See details for more information.
logCI	Boolean variable, default (= TRUE), indicates the confidence interval should be constructed under the assumption that (tau^ - T) has a lognormal distribution, where T is the total number of animals observed (see details)
alpha	type I error rate for confidence interval construction
Vm.boot	Boolean variable, when = TRUE indicates a bootstrap should be used to estimate cov(theta[i,j],theta[i',j']), var/cov matrix of the expansion factors (1/detection prob)
nboot	number of bootstrap replicates to use if Vm.boot = TRUE
bet	regression parameters (if the sightability model is not to be fit by Sight.Est). Make sure the order is consistent with the specification in the "form" argument.
varbet	variance-covariance matrix for beta^ (if the sightability model is not to be fit by Sight.Est). Make sure the order is consistent with the specification in the "form" argument.

Details

Variance estimation methods: method = Wong implements the variance estimator from Wong (1996) and is the recommended approach. Method = SS implements the variance estimator of Steinhorst and Samuel (1989), with a modification detailed in the Appendix of Samuel et al. (1992).

Estimates of the variance may be biased low when the number of test trials used to estimate model parameters is small (see Wong 1996, Fieberg and Giudice 2008). A bootstrap can be used to aid the estimation process by specifying Vm.boot = TRUE [note: this method is experimental, and can be time intensive].

Confidence interval construction: often the sampling distribution of tau^ is skewed right. If logCI = TRUE, the confidence interval for tau^ will be constructed under an assumption that (tau^ - T) has a lognormal distribution, where T is the total number of animals seen. In this case, the upper and lower limits are constructed as follows [see Wong(1996, p. 64-67)]:

LCL = T + [(tau^-T)/C]*sqrt(1+cv^2), UCL = T+[(tau^-T)*C]*sqrt(1+cv^2), where cv^2 = var(tau^)/(tau^-T)^2 and C = exp[z[alpha/2]*sqrt(ln(1+cv^2))].

Value

An object of class sightest_ratio, a list that includes the following elements:

sight.model	the fitted sightability model
est	ratio estimate, ratio.hat,abundance estimate [tau.hat] and its estimate of uncertainty [Varratio] as well as variance components due to sampling [Varsamp], detection [VarSight], and model uncertainty [VarMod]

The list also includes the estimates for the numerator and denominator total, the original test trial and operational survey data, sampling information, and information needed to construct a confidence interval for the population estimate.

Author(s)

Carl James Schwarz, StatMathComp Consulting by Schwarz, [e-mail]

References

Fieberg, J. 2012. Estimating Population Abundance Using Sightability Models: R SightabilityModel Package. Journal of Statistical Software, 51(9), 1-20. URL https://doi.org/10.18637/jss.v051.i09.

Fieberg, John and Giudice, John. 2008 Variance of Stratified Survey Estimators With Probability of Detection Adjustments. Journal of Wildlife Management 72:837-844.

Samuel, Michael D. and Steinhorst, R. Kirk and Garton, Edward O. and Unsworth, James W. 1992. Estimation of Wildlife Population Ratios Incorporating Survey Design and Visibility Bias. Journal of Wildlife Management 56:718-725.

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.

Examples

# Load data frames
  data(obs.m) # observational survey data frame
  data(exp.m) # experimental survey data frame
  data(sampinfo.m) # information on sampling rates (contained in a data frame)
 
# Estimate ratio of bulls to cows in 2007 only
  sampinfo <- sampinfo.m[sampinfo.m$year == 2007,]

  obs.m$numerator   <- obs.m$bulls
  obs.m$denominator <- obs.m$cows
  
  Sight.Est.Ratio(observed ~ voc, odat = obs.m[obs.m$year == 2007,],
    sdat = exp.m, sampinfo, method = "Wong", 
    logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 

SightabilityModel documentation built on Aug. 20, 2023, 1:08 a.m.