Different methods to complete datasets used for capture-recapture estimation: Estimating the number of usual residents in the Netherlands

Abstract

Abstract. We are interested in an estimate of the usual residents in the Netherlands. Capture-recapture estimation with three registers enables us to estimate the size of the total population, of which the usual residents are a part. However, usual residence cannot be used as a covariate because it is not available in one of the registers. We approach this as a missing data problem. There are different methods available to handle missing data. In this manuscript we use Expectation Maximization (EM) algorithm and Predictive Mean Matching (PMM). The EM algorithm is often used in categorical data analysis, but PMM has the advantage of flexibility in the choice for a specific part of the observed data used for the imputation of the missing data. Four scenarios have been identified where the missing data are completed via either the EM algorithm or PMM imputation, resulting in different population size estimates for usual residence. It was found that the different scenarios lead to different population size estimates. Even small changes in the completed data lead to different population size estimates. In this study PMM imputation performs best according flexibility and it is theoretically better motivated.

Generating contingency tables with fixed marginal probabilities and dependence structures described by loglinear models

“…When the lists are dependent, and the independence model is fitted, the mean estimated population size is smaller than the true population size. This shows that positive odds ratios result in population size estimates being negatively biased (compare with Gerritse et al, 2015). In some cases, when the odds ratio = 1.1, the true population size falls within the confidence interval.…”

“…One of the key assumptions is that the probabilities of inclusion in the lists are independent, which is easily violated (Gerritse et al, 2015). However, with the data used for population size estimation, this assumption is impossible to verify and so the design of both lists is very important, to create the conditions where this assumption is likely to hold.…”

“…The methodology we propose is illustrated with an application to population size estimation, as has been used in population censuses. This follows on from the work of Brown, Abbott and Diamond (2006), Baffour, Brown and Smith (2013) and Gerritse, Bakker and van der Heijden (2015) who used a fixed odds ratio to investigate the impacts of dependence on population size estimation. In this application, lists where individuals within the target population are enumerated are used to estimate the population sizes.…”

An Overview of Population Size Estimation where Linking Registers Results in Incomplete Covariates, with an Application to Mode of Transport of Serious Road Casualties

“…The crime suspects register has no variable for duration. This is not problematic for persons who are also in the population register or the employment register, because then the residence variable of the latter can be used, but it is problematic for individuals who are only in the crime suspects Table 3, taken from Gerritse et al (2015a), where counts for people born in Poland and registered in one or more of the three registers are displayed. We find a 2 £ 2 £ 2 table for residence duration longer than a year and a 2 £ 2 £ 2 table for residence duration shorter than a year, where two cells are indicated with the label 'missing'.…”

“…The counts for the two cells labeled "missing" add up to 1,043. Data from Gerritse et al (2015a). covariates are completed with the EM-algorithm (denoted by EM).…”