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We investigate use of two or more linked registers, or lists, for bothpopulation size estimation and to investigate the relationship betweenvariables appearing on all or only some registers. This relationship is usuallynot fully known because some individuals appear in only some registers, andsome are not in any register. These two problems have been solvedsimultaneously using the EM algorithm. We extend this approach to estimate thesize of the indigenous M\=aori population in New Zealand, leading to severalinnovations: (1) the approach is extended to four registers (including thepopulation census), where the reporting of M\=aori status differs betweenregisters; (2) some individuals in one or more registers have missingethnicity, and we adapt the approach to handle this additional missingness; (3)some registers cover subsets of the population by design. We discuss underwhich assumptions such structural undercoverage can be ignored and provide ageneral result; (4) we treat the M\=aori indicator in each register as avariable measured with error, and embed a latent class model in the multiplesystem estimation to estimate the population size of a latent variable,interpreted as the true M\=aori status. Finally, we discuss estimating theM\=aori population size from administrative data only. Supplementary materialsfor our article are available online.

Multiple system estimation using covariates having missing values and  measurement error: estimating the size of the M\=aori population in New  Zealand