One‐Inflation and Zero‐Truncation Count Data Modelling Revisited With a View on Horvitz–Thompson Estimation of Population Size

Abstract

SummaryEstimating the size of a hard‐to‐count population is a challenging matter. We consider uni‐list approaches in which the count of identifications per unit is the basis of analysis. Unseen units have a zero count and do not occur in the sample leading to a zero‐truncated setting. Because of various mechanisms, one‐inflation is often an occurring phenomena that can lead to seriously biased estimates of population size. The current work reviews some recent advances on one‐inflation and zero‐truncation modelling, and furthermore focuses here on the impact it has on population size estimation. The zero‐truncated one‐inflated and the one‐inflated zero‐truncated model is compared (also with the model ignoring one‐inflation) in terms of Horvitz–Thompson estimation of population size. The simulation work shows clearly the biasing effect of ignoring one‐inflation. Both models, the zero‐truncated one‐inflated and the one‐inflated zero‐truncated one, are suitable to model ongoing one‐inflation. It is also important to choose an appropriate base‐line distributional model. Finally, all models derived in the paper are illustrated on a number of case studies.