BICandbootstrapsim {SparseMSE}

Comparison of BIC approach and BCa approach

Description

This routine carries out the simulation study as detailed in Section 3.4 of Chan, Silverman and Vincent (2019). If the original data set has low counts, so that there is a possibility of a simulated data set containing empty lists, then it may be advisable to use the option noninformativelist=TRUE.

Usage

BICandbootstrapsim(zdat, nsims = 100, nboot = 100, pthresh = 0.02,
  iseed = 1234, alpha = c(0.025, 0.05, 0.1, 0.16, 0.5, 0.84, 0.9, 0.95,
  0.975), noninformativelist = F, verbose = F, ...)

Arguments

zdat

Data matrix with t+1 columns. The first t columns, each corresponding to a particular list, are 0s and 1s defining the capture histories observed. The last column is the count of cases with that particular capture history. List names A, B, ... are constructed if not supplied. Where a capture history is not explicitly listed, it is assumed that it has zero count.

nsims

Number of simulations to be carried out.

nboot

Number of bootstrap replications for each simulation

pthresh

p-value threshold used in estimatepopulation.0.

iseed

seed for initialization.

alpha

bootstrap quantiles of interests.

noninformativelist

if noninformativelist=TRUE then each generated data set in the simulation study (including all bootstrap replications) will be passed to removenoninformativelists.

verbose

If verbose=FALSE, then the progress of the simulation will not show. If verbose=TRUE, then the progress of the simulation will be shown.

...

other arguments.

Value

A list with components as below

popest Total population point estimate from the original data using estimatepopulation.0 with default threshold.

BICmodels The best model chosen by the BIC at each simulation.

BICvals Point estimates of the total population and standard error of the best model chosen by the BIC at each simulation.

simreps Counts associated to each capture history at each simulation.

modelmat A full capture history matrix excluding the row corresponding to the dark figure.

popestsim Total population estimate given by the BCa method in each simulation.

BCaquantiles bootstrap confidence intervals given by the BCa method.

BICconf confidence interval given by the BIC method.

References

Chan, L., Silverman, B. W., and Vincent, K. (2019). Multiple Systems Estimation for Sparse Capture Data: Inferential Challenges when there are Non-Overlapping Lists. Available from https://arxiv.org/abs/1902.05156.

DiCiccio, T. J. and Efron, B. (1996). Bootstrap Confidence Intervals. Statistical Science, 40(3), 189-228.

Rivest, L-P. and Baillargeon, S. (2014) Rcapture. CRAN package. Available from Available from https://CRAN.R-project.org/package=Rcapture.