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

Abstract

We present a method to generate contingency tables that follow loglinear models with prescribed marginal probabilities and dependence structures. We make use of (loglinear) Poisson regression, where the dependence structures, described using odds ratios, are implemented using an offset term. We apply this methodology to carry out simulation studies in the context of population size estimation using dual system and triple system estimators, popular in official statistics. These estimators use contingency tables that summarise the counts of elements enumerated or captured within lists that are linked. The simulation is used to investigate these estimators in the situation that the model assumptions are fulfilled, and the situation that the model assumptions are violated.

A General Framework for Multiple-Recapture Estimation that Incorporates Linkage Error Correction

“…Table 2 differ with respect to the size of the population N , the number of sources k and log-linear model specifications (i.e. different values for p A, p B , p C , p D , θ AB , θ AC , θ AD , θ BC and θ CD , seeHammond et al, 2023, for further details). The odds-ratios LLM sim the log-linear model used to generate the contingency table.…”