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Count data is prevalent and informative, with widespread application in many fields such as social psychology, personality, and public health. Classical statistical methods for the analysis of count outcomes are commonly variants of the log-linear model, including Poisson regression and Negative Binomial regression. However, a typical problem with count data modeling is inflation, in the sense that the counts are evidently accumulated on some integers. Such an inflation problem could distort the distribution of the observed counts, further bias estimation and increase error, making the classic methods infeasible. Traditional inflated value selection methods based on histogram inspection are easy to neglect true points and computationally expensive in addition. Therefore, we propose a multiple-inflated negative binomial model to handle count data modeling with multiple inflated values, achieving data-driven inflated value selection. The proposed approach provides simultaneous identification of important regression predictors on the target count response as well. More details about the proposed method are described in Li, Y., Wu, M., Wu, M., & Ma, S. (2023) doi:10.48550/arXiv.2309.15585.

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