LP_fit {Petersen}

Fit a Lincoln-Petersen Model using conditional likelihood

Description

This will take a data frame of capture histories, frequencies, and additional covariates (e.g., strata and/or continuous covariates) and the model for the capture probabilities and will use conditional likelihood (Huggins, 1989) to fit the model. The population abundance is estimated using a Horvitz-Thompson type estimator and the user can request abundance estimates for sub-sets of the population.

Usage

LP_fit(data, p_model = ~..time, p_beta.start = NULL, trace = FALSE)

Arguments

data

Data frame containing the variables:

• cap_hist Capture history (see details below)

• freq Number of times this capture history was observed

plus any other covariates (e.g. discrete strata and/or continuous covariates) to be used in the model fitting.

p_model

Model for the captured probabilities. This can reference other variables in the data frame, plus a special reserved term ..time to indicate a time dependence in the capture probabilities. For example, p_model=~1 would indicate that the capture probabilities are equal across the sampling events; p_model=~..time would indicate that the capture probabilities vary by sampling events; p_model=~sex*..time would indicate that the capture probabilities vary across all combination of sampling events (..time) and a stratification variable (sex). The sex variable also needs to be in the data frame.

For some models (e.g., tag loss models), the ..time variable cannot be used because the conditional models (on being captured at the second event) end up having only have one capture probability (e.g., only for event 1) because of the conditioning process.

p_beta.start

Initial values for call to optimization routine for the beta parameters (on the logit scale). The values will be replicated to match the number of initial beta parameters needed. Some care is needed here!

trace

If trace flag is set in call when estimating functions

Details

The frequency variable (freq in the data argument) is the number of animals with the corresponding capture history.

Capture histories (cap_hist in the data argument) are character values of length 2.

• 10 Animals tagged but never seen again.

• 11 Animals tagged and recaptured and tag present at event 2.

• 01 Animals captured at event 2 that appear to be untagged.

Value

An list object of class LP_fit with abundance estimates and other information with the following elements

• summary A data frame with the model for the capture probabilities; the conditional log-likelihood; the number of parameters; the number of parameters, and method used to fit the model

• data A data frame with the raw data used in the fit

• fit Results of the fit from the optimizer

• datetime Date and time the fit was done

After the fit is done, use the LP_est() function to get estimates of abundance.

Author(s)

Schwarz, C. J. [e-mail].

References

Huggins, R. M. 1989. On the Statistical Analysis of Capture Experiments. Biometrika 76: 133–40.

Examples

# fit a simple Petersen model and get the estimated abundance
data(data_rodli)
fit <- Petersen::LP_fit(data=data_rodli, p_model=~..time)
fit$summary
# Now to get the estimated abundance
est <- Petersen::LP_est(fit, N_hat=~1)
est$summary

# repeat the fit with the Chapman correction
# we add an additional animal with history 11
rodli.chapman <- plyr::rbind.fill(data_rodli,
                                  data.frame(cap_hist="11",
                                             freq=1,
                                             comment="Added for Chapman"))

rodli.chapman
fit.chapman <- Petersen::LP_fit(data=rodli.chapman, p_model=~..time)
fit.chapman$summary
# Now to get the estimated abundance
est.chapman <- Petersen::LP_est(fit.chapman, N_hat=~1)
est.chapman$summary


# Example of simple stratification (by sex)
data(data_NorthernPike)
nop.red <- plyr::ddply(data_NorthernPike, c("cap_hist","Sex"), plyr::summarize,
                       freq=sum(freq))
nop.red # reduced capture history to speed execution time of example

# Fit the various models
nop.fit.sex.time   <- Petersen::LP_fit(nop.red, p_model=~-1+Sex:..time)
nop.fit.sex.time$summary

# estimate of overall abundance
nop.est.ALL   <- Petersen::LP_est(nop.fit.sex.time, N=~1)
nop.est.ALL$summary

# estimate of abundance for each sex
nop.est.by.sex <- Petersen::LP_est(nop.fit.sex.time, N=~-1+Sex)
nop.est.by.sex$summary


# Refer to vignettes for example using continuous variable (e.g. length) to model catchability