Pooling multiple imputations when the sample happens to be the population

TL;DR

This paper extends multiple imputation pooling rules to cases where the sample is the entire population, simplifying variance estimation and avoiding over-coverage when sampling variance is irrelevant.

Contribution

It introduces simplified pooling rules for multiply imputed data applicable when the sample equals the population, addressing a gap in existing methods.

Findings

Simplified pooling rules perform well when sampling variance is negligible.

Using standard pooling rules in such cases leads to overestimation of variance.

The new rules improve statistical power by preventing over-coverage.

Abstract

Current pooling rules for multiply imputed data assume infinite populations. In some situations this assumption is not feasible as every unit in the population has been observed, potentially leading to over-covered population estimates. We simplify the existing pooling rules for situations where the sampling variance is not of interest. We compare these rules to the conventional pooling rules and demonstrate their use in a situation where there is no sampling variance. Using the standard pooling rules in situations where sampling variance should not be considered, leads to overestimation of the variance of the estimates of interest, especially when the amount of missingness is not very large. As a result, populations estimates are over-covered, which may lead to a loss of statistical power. We conclude that the theory of multiple imputation can be extended to the situation where the sample happens to be the population. The simplified pooling rules can be easily implemented to obtain valid inference in cases where we have observed essentially all units and in simulation studies addressing the missingness mechanism only.