One-inflated zero-truncated Poisson and negative binomial regression models

The workhorse model for zero-truncated count data (y = 1, 2, ...) is the zero-truncated negative binomial (ZTNB) model. We find it should seldom be used. Instead, we recommend the one-inflated zero-truncated negative binomial (OIZTNB) model developed here. Zero-truncated count data often contain an excess of 1s, leading to bias and inconsistency in the ZTNB model. The importance of the OIZTNB model is apparent given the obvious presence of one-inflation in four datasets that have traditionally championed the standard ZTNB. We provide estimation, marginal effects, and a suite of accompanying tools in the R package oneinfl, available on CRAN.