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

TL;DR

This paper develops an advanced statistical method using the EM algorithm to estimate the Maori population in New Zealand by integrating multiple registers, handling missing data, measurement error, and structural undercoverage.

Contribution

The paper extends multiple system estimation to four registers, incorporates missing ethnicity data, accounts for measurement error with a latent class model, and discusses estimation from administrative data.

Findings

Successfully estimated Maori population size considering missing data and measurement error.

Extended the approach to handle multiple registers with different coverage.

Provided theoretical insights on structural undercoverage assumptions.

Abstract

We investigate use of two or more linked registers, or lists, for both population size estimation and to investigate the relationship between variables appearing on all or only some registers. This relationship is usually not fully known because some individuals appear in only some registers, and some are not in any register. These two problems have been solved simultaneously using the EM algorithm. We extend this approach to estimate the size of the indigenous M\=aori population in New Zealand, leading to several innovations: (1) the approach is extended to four registers (including the population census), where the reporting of M\=aori status differs between registers; (2) some individuals in one or more registers have missing ethnicity, and we adapt the approach to handle this additional missingness; (3) some registers 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 M\=aori indicator in each register 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 M\=aori status. Finally, we discuss estimating the M\=aori population size from administrative data only. Supplementary materials for our article are available online.