Standard Poisson and negative binomial truncated regression models for count data include the regressors in the mean of the non-truncated distribution. In this paper, a new approach is proposed so that the explanatory variables determine directly the truncated mean. The main advantage is that the regression coefficients in the new models have a straightforward interpretation as the effect of a change in a covariate on the mean of the response variable. A simulation study has been carried out in order to analyze the performance of the proposed truncated regression models versus the standard ones showing that coefficient estimates are now more accurate in the sense that the standard errors are always lower. Also, the simulation study indicates that the estimates obtained with the standard models are biased. An application to real data illustrates the utility of the introduced truncated models in a hurdle model. Although in the example there are slight differences in the results between the two approaches, the proposed one provides a clear interpretation of the coefficient estimates.

中文翻译：

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计数数据截断回归的新方法

用于计数数据的标准Poisson和负二项式截断回归模型包括非截断分布均值中的回归值。本文提出了一种新的方法，使解释变量直接确定截短的均值。主要优势在于，新模型中的回归系数可以直接解释为协变量变化对响应变量平均值的影响。为了分析建议的截短回归模型与标准模型的性能，已进行了仿真研究，表明在标准误差始终较低的意义上，系数估计现在更加准确。此外，仿真研究表明，使用标准模型获得的估计值是有偏差的。实际数据的应用说明了引入的截断模型在障碍模型中的效用。尽管在该示例中，两种方法的结果略有不同，但所提出的方法对系数估计值提供了清晰的解释。