estimatepopulation.0 {SparseMSE}

Estimate the total population including the dark figure. If the user wishes to find bootstrap confidence intervals then the routine estimatepopulation should be used instead.

Description

This routine estimates the total population size, which includes the dark figure, together with confidence intervals as specified. It also returns the details of the fitted model. The user can choose whether to fit main effects only, to fit a particular model containing specified two-list parameters, or to choose the model using the stepwise approach described by Chan, Silverman and Vincent (2019).

Usage

estimatepopulation.0(zdat, method = "stepwise", quantiles = c(0.025,
  0.975), mX = NULL, pthresh = 0.02)

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.

method

If method = "stepwise" the stepwise method implemented in stepwisefit is used. If method = "fixed" then a specified fixed model is used; the model is then given by mX. If method = "main" then main effects only are fitted.

quantiles

Quantiles of interest for confidence intervals.

mX

A 2 \times k matrix giving the k two-list parameters to be included in the model if method = "fixed". Each column of mX contains the numbers of the corresponding pair of lists. If mX = 0, then all two-list parameters are included. If mX = NULL, no two-list parameters are included and the main effects model is fitted. If only one two-list parameter is to be fitted, it is sufficient to specify it as a vector of length 2, e.g mX=c(1,3) for the parameter indexed by lists 1 and 3. If method is equal to "stepwise" or "main", then mX is ignored.

pthresh

Threshold p-value used if method = "stepwise".

Value

A list with components as below

estimate Point estimate and confidence interval estimates corresponding to specified quantiles.

MSEfit The model fitted to the data in the format described in modelfit.

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.

Examples

data(NewOrl)
data(NewOrl_5)
estimatepopulation.0(NewOrl, method="stepwise", quantiles=c(0.025,0.975))
estimatepopulation.0(NewOrl_5, method="main", quantiles=c(0.01, 0.05,0.95, 0.99))