  We find that in zero-truncated count data (y=1,2,...), individuals often gain
information at first observation (y=1), leading to a common but unaddressed
phenomenon of "one-inflation". The current standard, the zero-truncated
negative binomial (ZTNB) model, is misspecified under one-inflation, causing
bias and inconsistency. To address this, we introduce the one-inflated
zero-truncated negative binomial (OIZTNB) regression model. The importance of
our model is highlighted through simulation studies, and through the discovery
of one-inflation in four datasets that have traditionally championed ZTNB. We
recommended OIZTNB over ZTNB for most data, and provide estimation, marginal
effects, and testing in the accompanying R package oneinfl.
