Working with population totals in the presence of missing data comparing imputation methods in terms of bias and precision

Missing observations in water bird censuses are commonly handled using the Underhill index or the birdSTATs tool which enables the use of TRIM under the hood. Multiple imputation is a standard technique for handling missing data that is rarely used in the field of ecology, but is a well known statistical technique in the fields of medical and social sciences. The purpose of this paper is to compare these three methods in terms of bias and variance. The bias in the Underhill method depends on the algorithm and starting values. birdSTATs and multiple imputation are unbiased in the case of missing values that are missing completely at random; more missing values implies less information, and so wider confidence intervals are expected as the missingness increases. The Underhill method and birdSTATs tool underestimate the variance; omitting data from a complete dataset and applying the Underhill index or birdSTATs tool results in smaller confidence intervals. Multiple imputation with an adequate imputation model provides wider confidence intervals. Biased parameter estimates with underestimated variance can potentially lead to incorrect management and policy conclusions. Hence, we dissuade the use of Underhill indices or the birdSTATs tool to handle missing data, rather we suggest that multiple imputation is a more robust alternative, even in suboptimal conditions.