Basic negative binomial models can only capture over-dispersed count responses, because the variance of the distribution is always greater than the mean value. So, they are not the best selection when the data are under-dispersed or have less dispersion than the negative binomial. Over the last years, a variety of new distributions that can account a wide range of dispersion in count data, have been introduced. One of these novel distributions is Conway–Maxwell type negative binomial distribution. In biomedical studies, it is common to demonstrate excess zeros and a pattern of dispersion in count data. Also, the observations may be correlated in clusters or longitudinally. Here, we propose a multilevel zero-inflated Conway–Maxwell type negative binomial model. Statistical inference is employed via an expectation-maximization algorithm for the parameter estimation. The model performance is illustrated by simulation studies and with a real data set.

基本的负二项式模型只能捕获过度分散的计数响应，因为分布的方差总是大于平均值。因此，当数据分散不足或分散程度小于负二项式时，它们不是最佳选择。在过去的几年里，已经引入了各种可以解释计数数据中广泛分散的新分布。这些新颖的分布之一是 Conway-Maxwell 型负二项式分布。在生物医学研究中，通常会出现过多的零和计数数据中的离散模式。此外，观察结果可以成簇或纵向相关。在这里，我们提出了一个多级零膨胀 Conway-Maxwell 型负二项式模型。通过用于参数估计的期望最大化算法采用统计推断。模型性能通过模拟研究和真实数据集来说明。