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On the equivalence of one‐inflated zero‐truncated and zero‐truncated one‐inflated count data likelihoods
Author(s) -
Böhning Dankmar
Publication year - 2023
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.202100343
Subject(s) - zero (linguistics) , equivalence (formal languages) , mathematics , count data , maximum likelihood , population , statistics , discrete mathematics , philosophy , linguistics , demography , sociology , poisson distribution
One‐inflation in zero‐truncated count data has recently found considerable attention. There are currently two views in the literature. In the first approach, the untruncated model is considered as one‐inflated whereas in the second approach the truncated model is viewed as one‐inflated. Here, we show that both models have identical model spaces as well as identical maximum likelihoods. Consequences of population size estimation are illuminated, and the findings are illustrated at hand of two case studies.