Zero-inflated Poisson (ZIP) regression is widely applied to model effects of covariates on an outcome count with excess zeros. In some applications, covariates in a ZIP regression model are partially observed. Based on the imputed data generated by applying the multiple imputation (MI) schemes developed by Wang and Chen (Ann Stat 37:490–517, 2009), two methods are proposed to estimate the parameters of a ZIP regression model with covariates missing at random. One, proposed by Rubin (in: Proceedings of the survey research methods section of the American Statistical Association, 1978), consists of obtaining a unified estimate as the average of estimates from all imputed datasets. The other, proposed by Fay (J Am Stat Assoc 91:490–498, 1996), consists of averaging the estimating scores from all imputed data sets to solve the imputed estimating equation. Moreover, it is shown that the two proposed estimation methods are asymptotically equivalent to the semiparametric inverse probability weighting method. A modified formula is proposed to estimate the variances of the MI estimators. An extensive simulation study is conducted to investigate the performance of the estimation methods. The practicality of the methodology is illustrated with a dataset of motorcycle survey of traffic regulations.

中文翻译：

---

通过非参数多重插补方法估计缺少协变量的零膨胀泊松回归模型

零膨胀泊松（ZIP）回归被广泛用于建模协变量对具有过多零的结果计数的影响。在某些应用中，部分观察到ZIP回归模型中的协变量。基于由Wang和Chen（Ann Stat 37：490–517，2009）开发的多重插补（MI）方案生成的插补数据，提出了两种方法来估计带有随机缺失协变量的ZIP回归模型的参数。鲁宾提出的一种方法（在《美国统计协会调查研究方法》，1978年）中，包括获得统一的估计值，作为所有估算数据集的估计值的平均值。另一个由Fay提出（J Am Stat Assoc 91：490-498，1996），包括对来自所有估算数据集的估算分数求平均值以求解估算估算方程。此外，证明了所提出的两种估计方法在渐近性上等同于半参数逆概率加权方法。提出了一种改进的公式来估计MI估计量的方差。进行了广泛的仿真研究，以研究估计方法的性能。该方法的实用性通过摩托车交通法规调查数据集得到说明。进行了广泛的仿真研究，以研究估计方法的性能。该方法的实用性通过摩托车交通法规调查数据集得到说明。进行了广泛的仿真研究，以研究估计方法的性能。该方法的实用性通过摩托车交通法规调查数据集得到说明。