We investigate the use of two or more linked lists, for both population size estimation and the relationship between variables appearing on all or only some lists. This relationship is usually not fully known because some individuals appear in only some lists, and some are not in any list. These two problems have been solved simultaneously using the EM algorithm. We extend this approach to estimate the size of the indigenous Māori population in New Zealand, leading to several innovations: (1) the approach is extended to four lists (including the population census), where the reporting of Māori status differs between registers; (2) some individuals in one or more lists have missing ethnicity, and we adapt the approach to handle this additional missingness; (3) some lists cover subsets of the population by design. We discuss under which assumptions such structural undercoverage can be ignored and provide a general result; (4) we treat the Māori indicator in each list as a variable measured with error, and embed a latent class model in the multiple system estimation to estimate the population size of a latent variable, interpreted as the true Māori status. Finally, we discuss estimating the Māori population size from administrative data only. Supplementary materials for our article are available online.

中文翻译：

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使用具有缺失值和测量误差的协变量进行多系统估计：估计新西兰毛利人口的规模

我们研究了两个或多个链表的使用，用于人口规模估计以及出现在所有或仅部分列表上的变量之间的关系。这种关系通常不完全清楚，因为有些人只出现在一些列表中，而有些则不在任何列表中。这两个问题已使用 EM 算法同时解决。我们扩展了这种方法来估计新西兰土著毛利人口的规模，带来了几项创新：（1）该方法扩展到四个列表（包括人口普查），其中毛利人身份的报告在登记册之间有所不同；(2) 一个或多个列表中的某些人缺少种族，我们采用这种方法来处理这种额外的缺失；(3) 一些列表按设计涵盖了人口的子集。我们讨论了在哪些假设下可以忽略这种结构性覆盖不足并提供一般结果；(4) 我们将每个列表中的毛利指标视为一个有误差测量的变量，并在多系统估计中嵌入一个潜在类别模型来估计一个潜在变量的人口规模，解释为真正的毛利人身份。最后，我们讨论仅从行政数据估计毛利人口规模。我们文章的补充材料可在线获取。我们仅讨论从行政数据估计毛利人口规模。我们文章的补充材料可在线获取。我们仅讨论从行政数据估计毛利人口规模。我们文章的补充材料可在线获取。