SightabilityModel (version 1.5.5)

vardiff: Function to estimate the variance of the difference between two population estimates

Description

Function to estimate the variance of the difference between two population estimates formed using the same sightability model (to correct for detection).

Usage

vardiff(sight1, sight2)

Value

vardiff

numeric = var(tau^[1])+var(tau^[2])-2*cov(tau^[1],tau^[2])

Arguments

sight1

Sightability model object for the first population estimate (formed by calling Sight.Est function)

sight2

Sightability model object for the second population estimate (formed by calling Sight.Est function)

Author

John Fieberg

Details

Population estimates constructed using the same sightability model will NOT be independent (they will typically exhibit positive covariance). This function estimates the covariance due to using the same sightability model and subtracts it from the summed variance.

Examples

# Example using moose survey data 
  data(obs.m) # observational moose survey data
  data(exp.m) # experimental moose survey data
  data(sampinfo.m) # information on sampling rates
 
# Estimate population size in 2006 and 2007 
 sampinfo <- sampinfo.m[sampinfo.m$year == 2007, ]
 tau.2007 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == 2007, ], 
                         sdat = exp.m, sampinfo.m[sampinfo.m$year == 2007, ], 
                         method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 
 tau.2006 <- Sight.Est(observed ~ voc, odat = obs.m[obs.m$year == 2006, ],
                         sdat = exp.m, sampinfo.m[sampinfo.m$year == 2006, ],
                         method = "Wong", logCI = TRUE, alpha = 0.05, Vm.boot = FALSE) 

# naive variance
  tau.2007$est[2]+tau.2006$est[2]

# variance after subtracting positvie covariance
  vardiff(tau.2007, tau.2006)