LP_est {Petersen}

Estimate abundance after the LP conditional likelihood fit.

Description

This will take a previous fit and return estimates of abundance. 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_est(LP_fit, N_hat = ~1, conf_level = 0.95, trace = FALSE)

Arguments

LP_fit

A result of an LP_fit() call.

N_hat

A formula requesting which abundance estimates should be formed. The formula are expanded against the data frame to determine which records form part of the abundance estimate. The formula is evaluated against the data frame used in the fit using the model.matrix() function, and each column of the model matrix is used to form an estimate.

Some familiarity on how model.matrix() generates the model matrix of coefficients used in the expansion is needed. For example N_hat=~1 creates a model matrix with 1 column (representing the intercept) and so requests abundance over the entire population; Specifying N_hat=~-1+Sex creates a model matrix with 2 columns (one for each sex) consisting of 0/1 depending if that row of the data frame is M/F. Hence, two abundance estimates (one for each sex) is computed. On the other hand, N_hat=Sex generates a model matrix where the first column is all 1's, and a second column which is 0/1 depending if the row in the data frame is the "second" sex. Hence, this will request the overall abundance (over both sexes) and the estimate of abundance for the second sex.

In addition to the variables in the data frame, special variables include ..EF to allow access to the expansion factor so you can request a "truncated" Horvitz-Thompson estimator using N_hat=~-1+I(as.numeric(..EF<1000)) to only use those animals with expansion factors less than 1000 in forming the estimate.

conf_level

The expected coverage for confidence intervals on N.

trace

If trace flag is set in call when estimating functions

Value

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

• summary Data frame with abundance estimates, their SE, and CIs as requested

• detail List with many components, including the rawdata, model fitting information, observed and expected values, residual plot, etc

• datetime Date and time the estimation was done from the fit.

Author(s)

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

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