abun.opt: Maximum empirical likelihood (EL) abundance estimation under...

In ecnuliuyang/CRAbun: Maximum likelihood abundance estimation from capture-recapture data under the Huggins-Alho model

Description

This function is used to calculate the maximum EL estimate and EL ratio confidence interval of the abundance under the H-A model, as well as the EL estimates of parameters in the H-A model. Thier standard errors are also provided for reference.

Usage

abun.opt(d, K = NULL, x = NULL, y = NULL,
  CI = TRUE, level = 0.95, SE = TRUE,
  beta.initial = NULL)

Arguments

d	a vector, the number of times of being captured.
K	a number, the number of capture occasions.
x	a vector, matrix or data.frame, stands for individual covariates without missingness.
y	a vector, matrix or data.frame, stands for individual covariates with missing values (NA).
CI	logistic, indiates whether the EL ratio confidence interval of the abundance is given (TRUE, default) or not (FALSE).
level	a number, the nominal confidence level (default: 0.95).
SE	logistic, indiates whether the Std. Error is given (TRUE, default) or not (FALSE).
beta.initial	a vector, with the same length as the parameters in H-A model. 0 means that the coefficient is fixed to zero, and non-zero values are seen as initial values when optimizing.

Details

Options d and K are necessary. In the absence of missing data, x stands for the observed covariates. Refer to Liu et al. (2017) for the EL method.

In the presence of missing data, x stands for the covariates without missingness, and y stands for the covariates with missing data (NA). Refer to Liu et al. (2020+) for the EL method.

Caution should be taken that beta.initial is NULL if all covariates are considered. When some coefficients of always observed covariates are zero, please specify the corresponding components of beta.initial as zero and others as none-zero values.

Value

A list containing the following main components:

n.big	the maximum EL estimate of the abundance.
n.big.se	Std. Error of n.big.
n.big.ci	the EL ratio confidence interval of the abundance.
beta	the maximum EL estimates of the parameters in the H-A model.
beta.se	Std. Error of beta.
like	the maximum EL value.
AIC	AIC value of the specified model.
prob	the estimate of covariates' probability mass function.

References

Liu, Y., P. Li, and J. Qin (2017). Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture data. Biometrika 104(3), 527–543.

Liu, Y., Y. Liu, P. Li, and L. Zhu (2020+). Maximum likelihood abundance estimation from capture-recapture data when covariates are missing at random. Submitted.

Examples

  ## Analysis results of the prinia data set.

  attach(prinia)

  ### EL in the absence of missingness (CC)
  r <- !is.na(tail.length)
  ## Model 1
  (cc1 <- abun.opt(d = number.of.capture, x = cbind(1,fat.index), K = 17) )
  ## Model 2
  (cc2 <- abun.opt(d = number.of.capture, x = cbind(1,wing.index), K = 17) )
  ## Model 3
  (cc3 <- abun.opt(d = number.of.capture, x = cbind(1,fat.index, wing.index), K = 17) )
  ## Model 4
  (cc4 <- abun.opt(d = number.of.capture[r], x = cbind(1, tail.length)[r,], K = 17) )
  ## Model 5
  (cc5 <- abun.opt(d = number.of.capture[r], x = cbind(1,fat.index, tail.length)[r,], K = 17) )
  ## Model 6
  (cc6 <- abun.opt(d = number.of.capture[r], x = cbind(1,wing.index, tail.length)[r,], K = 17) )
  ## Model 7
  (cc7 <- abun.opt(d = number.of.capture[r], x = cbind(1,fat.index, wing.index, tail.length)[r,], K = 17) )

  ### EL in the presence of missingness (EL)
  ## Model 7
  (el7 <- abun.opt(d = number.of.capture, x = cbind(1, fat.index, wing.index), y = tail.length, K=17,
                   beta.initial = c(-10,  1,  0.5, 0.1) ) )
  ## Model 4
  (el4 <- abun.opt(d = number.of.capture, x = cbind(1, fat.index, wing.index), y = tail.length, K = 17,
                   beta.initial = el7$beta*c(1, 0, 0, 1)) )
  ## Model 5
  (el5 <- abun.opt(d = number.of.capture, x = cbind(1, fat.index, wing.index), y = tail.length, K = 17,
                   beta.initial = el7$beta*c(1, 1, 0, 1)) )
  ## Model 6
  (el6 <- abun.opt(d = number.of.capture, x = cbind(1, fat.index, wing.index), y = tail.length, K = 17,
                   beta.initial = el7$beta*c(1, 0, 1, 1)) )

  detach(prinia)

ecnuliuyang/CRAbun documentation built on April 13, 2020, 7:45 p.m.