ABSTRACT
This chapter presents the (in)variance of population size estimates derived from loglinear models that include covariates. Including covariates in log-linear models of population registers improves population size estimates for two reasons. Firstly, it is possible to take heterogeneity of inclusion probabilities over the levels of a covariate into account; and secondly, it allows subdivision of the estimated population by the levels of the covariates, giving insight into characteristics of individuals that are not included in any of the registers. The issue of whether/not marginalizing the full table of registers by covariates over one or more covariates leaves the estimated population size estimate invariant, is intimately related to collapsibility of contingency tables. With information from two registers it is shown that population size invariance is equivalent to the simultaneous collapsibility of each margin consisting of one register and the covariates. Covariates that are collapsible are called passive, to distinguish them from covariates that are not collapsible and are termed active.
