estLCCR {LCCR}

Estimate latent class models for capture-recapture data with individual covariates

Description

For a latent class model for stratified capture-recapture data with individual covariates, it estimates the model on the basis of observed data by the unconditional likelihood method, exploiting weights associated to the different strata. Estimation of the model parameters, included the population size, is based on an EM algorithm.

Usage

estLCCR(Y, H, model = c("loglin", "logit"), W = NULL, X = NULL, N = NULL, biv = NULL,
        flag = c("no", "prev", "sum", "atleast"),
        main = c("LC", "same", "Rasch"),
        free_cov = c("no", "class", "resp", "both"),
        free_biv = c("no", "class", "int", "both"),
        free_flag = c("no", "class", "resp", "both"),
        N0 = NULL, be0 = NULL, la0 = NULL, maxit = 5000,
        verb = TRUE, init_rand = FALSE, se_out = FALSE)

Arguments

Y

matrix of frequencies for each stratum (by row)

H

number of latent classes

model

"loglin" for loglinear parametrization; "logit" for recursive logit parametrization

W

matrix of covariates on the class weights

X

array of covariates (n. strata x n. covariates x n. responses)

N

fixed population size

biv

matrix with two columns containing the list of bivariate interactions (for loglinear parametrization)

flag

"no" for no lag effect; "prev" for effect of the previous capture occasion only; "sum" for the effect of the sum of the previous capture occasions; "atleast" for the effect of at least one capture at the previous occasions (for recursive logit parametrization)

main

"LC" for the latent class model in which there is a separate main effect for each capture occasion and latent class; "same" for the constrained model in which the main effect is the same across capture occasions but different across latent classes; "Rasch" for the constrained model in which each main effect is expressed in an additive form with a parameter related to the latent class and another parameter related to the capture occasion

free_cov

"no" for constant effect of the covariates across capture occasions and latent classes; "class" for effect of covariates varying only with the latent class; "resp" for effect of covariates varying only with the capture occasion; "both" for effect of covariates varying with the capture occasion and the latent class

free_biv

"no" for constant bivariate interation effect with respect to the occasion and the latent class; "class" for free interaction with respect to the latent class; "int" for free effect only with respect to the interation; "both" for free effect with respect to interation and latent class (for loglinear parametrization)

free_flag

"no" for constant effect of the previous capture occasions with respect to the occasion and the latent class; "class" for free effect only with respect to the latent class; "int" for free effect only with respect to the occasion; "both" for free effect with respect to capture occasion and latent class (for recursive logit parametrization)

N0

initial value of the population size

be0

initial value of the parameters affecting the class weights

la0

initial value of the parameters affecting the conditional distribution of capture configurations given the latent class

maxit

maximum number of iterations of the EM algorithm

verb

to have partial output during the model fitting

init_rand

to use a random initialization of the parameters

se_out

to require computation of the standard errors

Value

be

estimate of the parameters affecting the class weights

la

estimate of the parameters affecting the conditional distribution of capture configurations given the latent class

lk

final log-likelihood value

N

estimate of the population size

np

number of free parameters

AIC

value of AIC for model selection

BIC

value of BIC for model selection

M

design matrices used for the recursive logit or loglinear parametrization of the conditional distribution of capture configurations given the latent class

tauv

estimate of the weights of each stratum

phiv

estimate of the probability of being never captured for each stratum

seN

standard error for the estimate of N

sebe

standard error for the estimate of beta

sela

standard error for the estimate of lambda

lk1

component of the log-likelihood based on the binomial factor in N

lk2

component of the log-likelihood involving N and the overall probability of being never captured

lk3

component of the log-likelihood involving the capture probabilities

lk4

component of the log-likelihood involving the stratum weights

Author(s)

Francesco Bartolucci, Antonio Forcina

References

Forcina, A. and Bartolucci, F. (2021). Estimating the size of a closed population by modeling latent and observed heterogeneity, arXiv:2106.03811.

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

See Also

design_matrix_logit, design_matrix_loglin, simLCCR

Examples

# estimate latent class model with 2 classes having the same weight on 5 lists
data(data_sim1)
est = estLCCR(Y=data_sim1,H=2)
est

# estimate latent class model with 2 classes, one covariate affecting the weights and bivariate 
# loglinear interactions between consecutive lists
data(data_sim2)
est = estLCCR(Y=data_sim2$Y,H=2,W=data_sim2$W,biv=matrix(c(1,2,3,4,2,3,4,5),4),main="same")
est

# estimate latent class model with 3 classes, one covariate affecting the logits of each response,
# and lag dependence
data(data_sim3)
est = estLCCR(Y=data_sim3$Y,H=3,model="logit",X=data_sim3$X,flag="atleast")
est

# estimate latent class model with 2 classes and covariates affecting both the class weights and
# conditional capture probabilities given the latent class
data(data_sim4)
est = estLCCR(Y=data_sim4$Y,H=2,X=data_sim4$X,W=data_sim4$W)
est