LP_IS_fit {Petersen}

Fit a Lincoln-Petersen Model with incomplete stratification

Description

In some LP studies, stratification is only done on a random sample of unmarked fish, e.g., only a sample of fish is sexed. Is is known as incomplete stratification. This is a wrapper to the published code for the case of stratification by a discrete covariate. At the moment, no other covariates are allowed, but see the published code.

Usage

LP_IS_fit(
  data,
  p_model,
  theta_model = ~-1 + ..time,
  lambda_model = ~-1 + ..cat,
  logit_p_offset = 0,
  logit_theta_offset = 0,
  logit_lambda_offset = 0,
  cat.unknown = "U",
  p_beta.start = NULL,
  trace = FALSE,
  control.optim = list(trace = 0, maxit = 1000)
)

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. At the moment, you are not allowed to use these covariates to used in the modeling process, but see the published code for more details.

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.

theta_model

Model for theta (sampling fraction). Usually, this is set to be different for the two sampling occasions, but you can constrain this to have equal sampling fractions at both occasions.

lambda_model

Model for lambda category proportions. Usually this is set to different for the categories but you can constrain this with a null matrix and the logit_lamba_offset parameter

logit_p_offset

Used to fix capture probabilities at known values (seldom useful). Logit(p)=p_design %*% beta_p + logit_p_offset.

logit_theta_offset

Used to fix sampling fractions at known values (seldom useful). logit(theta) = theta_design %*% beta_theta + logit_theta_offset

logit_lambda_offset

Used to fix the sex ratio as a known value (e.g. .50) using logit(lambda) = lambda_design %*% beta_lambda + logit_lambda_offset. Set the design matrix to a matrix with all zeros. Notice that because the lambda proportions must sum to 1, only specify an offset matrix that is number of categories -1.

cat.unknown

Value of character used to indicate the unknown stratum in the capture histories. Currently, this is fixed to "U" regardless of what is specified.

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

control.optim

Control values passed to optim() optimizer.

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. The strata values are single character values with "U" typically representing a fish not measured for the stratification variable. For example, consider the case where only a sample of unmarked fish are examined for sex (M or F). Possible capture histories are:

• M0 Animals tagged and sexed as male but never seen again.

• MM Animals tagged and sexed as male and recaptured and tag present at event 2.

• 0M Animals captured at event 2 that appears to be untagged and was sexed as male.

• F0 Animals tagged and sexed as female but never seen again.

• FF Animals tagged and sexed as female and recaptured and tag present at event 2.

• 0F Animals captured at event 2 that appears to be untagged and was sexed as female.

• U0 Animals tagged and not sexed but never seen again.

• UU Animals tagged and not sexed and recaptured and tag present at event 2.

• 0U Animals captured at event 2 that appears to be untagged and was not sexed.

Capture histories such as UF or UM are not allowed since only UNTAGGED animals are examined and sexed. Similarly, capture histories such as FM or MF are not allowed.

Value

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

• summary A data frame with the model for the capture probabilities, the sampling fractions at each capture occasion, and the category proportions; 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 including the estimates, SE, vcov, etc.

• fit.call Arguments used in the fit

• datetime Date and time the fit was done

Author(s)

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

References

Premarathna, W.A.L., Schwarz, C.J., Jones, T.S. (2018) Partial stratification in two-sample capture–recapture experiments. Environmetrics, 29:e2498. doi:10.1002/env.2498

Examples

data(data_wae_is_short)
fit <- Petersen::LP_IS_fit(data=data_wae_is_short, p_model=~..time)
fit$summary
est <- LP_IS_est(fit, N_hat=~1)
est$summary