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

Abstract

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.

KEYWORDS:

• Count data
• Conway–Maxwell type negative binomial distribution
• multilevel data
• zero-inflation
• random effects

Acknowledgements

This work is a part of Ph.D. thesis in Biostatistics of the first author and it was supported by Hamadan University of Medical Sciences under grant number 9609286040. The authors would like to thank the editor and the reviewers for the very helpful comments which lead to considerable improvement of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

Note: RMSE, root mean square error.

Note: RMSE, root mean square error.

 ^* p-value < 0.1.

Note: ZICMNB, zero-inflated Conway-Maxwell type negative binomial.

* p-value < 0.1.

Note: ZIP, zero-inflated Poisson; ZINB, zero-inflated negative binomial; ZICMNB, zero-inflated Conway-Maxwell type negative binomial; AIC, Akaike Information Criterion.

Additional information

Funding

This work was supported by Hamadan University of Medical Sciences: [Grant Number 9609286040].