investigateAIC: Plot of simulation study
In SparseMSE: 'Multiple Systems Estimation for Sparse Capture Data'

Description Usage Arguments Details Value References

This routine reproduces Figure 1 of Chan, Silverman and Vincent (2019).

1	investigateAIC(nsim = 10000, Nsamp = 1000, seed = 1001)

`nsim`	The number of simulation replications
`Nsamp`	The expected value of the total population size within each simulation
`seed`	The random number seed

Simulations are carried out for two different three-list models. In one model, the probabilities of capture are 0.01, 0.04 and 0.2 for the three lists respectively, while in the other the probability is 0.3 on all three lists. In both cases, captures on the lists occur independently of each other, so there are no two-list effects. The first model is chosen to be somewhat more typical of the sparse capture case, of the kind which often occurs in the human trafficking context, while the second, more reminiscent of a classical mark-recapture study.

The probability of an individual having each possible capture history is first evaluated. Then these probabilities are multiplied by Nsamp = 1000 and, for each simulation replicate, Poisson random values with expectations equal to these values are generated to give a full set of observed capture histories; together with the null capture history the expected number of counts (population size) is equal to Nsamp. Inference was carried out both for the model with main effects only, and for the model with the addition of a correlation effect between the first two lists. The reduction in deviance between the two models was determined. Ten thousand simulations were carried out.

Checking for compliance with the conditions for existence and identifiability of the estimates shows that a very small number of the simulations for the sparse model (two out of ten thousand) fail the checks for existence even within the extended maximum likelihood context. Detailed investigation shows that in neither of these cases is the dark figure itself not estimable; although the parameters themselves cannot all be estimated, there is a maximum likelihood estimate of the expected capture frequencies, and hence the deviance can still be calculated.

The routine produces QQ-plots of the resulting deviance reductions against quantiles of the χ^2_1 distribution, for nsim simulation replications.

An nsim \times 2 matrix giving the changes in deviance for each replication for each of the two models.

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.

SparseMSE documentation built on Dec. 26, 2019, 5:06 p.m.