lllcrc: Local log-linear models (LLLMs) for capture-recapture (CRC)

Description

Fits local log-linear models. Each distinct covariate vector gets its own model. To reduce the number of models, some rounding of continuous covariates is done first.

Usage

lllcrc(dat, kfrac, models = NULL, ic = "BICpi", bw = NULL, averaging = FALSE, cell.adj = TRUE, round.vars = NULL, rounding.scale = 0.01, boot.control = NULL)

Arguments

dat

Capture-recapture data, as output of formatdata

kfrac

The approximate fraction of the data that is included in the support of the kernel for the local averages.

models

A list of models -- or an expression that returns a list of models -- to be considered in local model search. The default is NULL, and in this case make.hierarchical.term.sets(k = attributes(dat)$k) is called to generate all hierarchical models that include all main effects.

The information criterion for selection of local log-linear models. The default, BICpi, appears in Hook and Regal (1997).

A single-column matrix with rownames that match the covariate names in dat. The values in the column are scalars that are used in constructing distances between covariate vectors. Raw differences are divided by the corresponding scalars before being squared in the context of a Euclidean metric. Defaults to a column of 1's.

averaging

Logical: Should model averaging be done for each local model?

cell.adj

Logical: Whether to adjust the cells as in Evans and Bonett (1994). TRUE by default.

round.vars

See micro.post.stratify, which is called within lllcrc.

rounding.scale

See micro.post.stratify, which is called within lllcrc.

boot.control

A list of control parameters for bootstrapping the sampling distribution of the estimator(s). By default, there is no bootstrapping.

Value

est: A point estimate of the population size
llform: The set of log-linear terms
dat: The output of function micro.post.stratify, with estimated local rates of missingness appended as an extra column labeled pi0. In addition, mct (multinomial cell count) gives the number of observed units with that distinct covariate vector, and cpi0 (cumulative number missing) gives the the product of pi0 with mct, such that summing over this vectorized product is exactly the Horvitz-Thompson style sum in capture recapture.
ess: The local effective sample sizes that are based on the local averaging weights and used as eta_i in local model selection
hpi: The matrix of local averages
...: The output is of class lllcrc and has attributes cont.x and conteg.x, which relate the continuous and categorical variables in the model

Details

The key implementation of the thesis of Kurtz 2013, Carnegie Mellon University

References

Kurtz ZT (2013). "Smooth Post-Stratification for Multiple Capture-Recapture." arXiv preprint arXiv:1302.0890.

Anderson DR and Burnham KP (1999). "Understanding information criteria for selection among capture-recapture or ring recovery models." Bird Study, 46(S1), pp. S14-S21.

Fienberg SE (1972). "The Multiple Recapture Census for Closed Populations and Incomplete $2^k$ Contingency Tables." Biometrika, 59(3), pp. 591.

Evans MA and Bonett DG (1994). "Bias Reduction for Multiple-Recapture Estimators of Closed Population Size." Biometrics, 50(2), pp. 388-395.