Sensitivity of Population Size Estimation for Violating Parametric Assumptions in Log-linear Models

An important quality aspect of censuses is the degree of coverage of the population. When administrative registers are available undercoverage can be estimated via capture-recapture methodology. The standard approach uses the log-linear model that relies on the assumption that being in the first register is independent of being in the second register. In models using covariates, this assumption of independence is relaxed into independence conditional on covariates. In this article we describe, in a general setting, how sensitivity analyses can be carried out to assess the robustness of the population size estimate. We make use of log-linear Poisson regression using an offset, to simulate departure from the model. This approach can be extended to the case where we have covariates observed in both registers, and to a model with covariates observed in only one register. The robustness of the population size estimate is a function of implied coverage: as implied coverage is low the robustness is low. We conclude that it is important for researchers to investigate and report the estimated robustness of their population size estimate for quality reasons. Extensions are made to log-linear modeling in case of more than two registers and the multiplier method