Regression modeling of one-inflated positive count data (Q1685219)

The paper considers positive count data with excessive proportion of \textit{one} counts. One-inflated positive (OIP) regression models are proposed. The stochastic hierarchical representation of one-inflated positive Poisson and negative binomial models are achieved. It is illustrated that the standard OIP model may be inadequate in the presence of one-inflation and the lack of independence of responses. To overcome this difficulty, a class of two-level OIP regression models is introduced, with heterogeneity effects of subjects. A simulation study confirms theoretical findings and shows the following: when one-inflation or over-dispersion in the data generating process is ignored, parameter estimates are inefficient and statistical inference is unreliable. Note of the reviewer: In the proposed generalized linear regression models, a system of normal equations for the MLE is written down, but in the paper under review it is not proven that there exists a solution to the system. Instead, the authors refer to certain reliable procedures in standard statistical packages.