# Calculates the variance of the log rate of change between 2 population estimates that rely on the same sightability model.

### Description

Calculates the variance of the log rate of change between 2 population estimates that rely on the same sightability model.

### Usage

1 | ```
varlog.lam(sight1, sight2)
``` |

### 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) |

NOTE: sight1 should correspond to the tau^[t], and sight2 to tau^[t+1]

### Details

This function uses the delta method to calculate an approximate variance for the log rate of change, log(tau^[t+1])-log(tau^[t]), while accounting for the positive covariance between the two estimates (as a result of using the same sightability model to correct for detection).

### Value

`loglambda` |
log rate of change = log(tau^[t+1]/tau^[t]) |

`varloglamda` |
approximate variance of loglambda |

### Author(s)

John Fieberg

### See Also

`vardiff`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# 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)
# Log rate of change
varlog.lam(tau.2006, tau.2007)
``` |