A multilevel zero-inflated Conway-Maxwell type negative binomial model for analysing clustered count data

摘要

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.