Abstract
This paper introduced a Quasi-Negative Binomial Regression as an extension of Quasi-Negative Binomial to handle response count datasets modulated with covariates. In some literature, Poisson regression is assumed to model the count data appropriately with exemption of excess-zero and over-dispersion more than other identical models. Nevertheless, in the presence of excess-zero and over-dispersion, the Negative Binomial regression and Generalized Poisson regression and their zero-inflation provided some respite. If the data were highly skewed, with long tail, they fit the data incorrectly. Therefore, Quasi-Negative Binomial is recommended even though it cannot accommodate data modulated with covariates, hence the proposed Quasi-Negative Binomial Regression model and its zero-inflated model. The estimates of the model parameters were derived using maximum likelihood method and the performance of the model was examined using simulation study. Also, the adequacy of the model was established by comparison with other competing models’ information criteria. The results showed that the proposed models outperformed the competing models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
The link to the data used in this study is provided here. http://qed.econ.queensu.ca/jae/1997-v12.3/deb-trivedi/dt-data.zip This link has been cited and does not need ethical clearance.
References
Berger, M., Tutz, G.: Transition models for count data: a flexible alternative to fixed distribution models. p. 25, 2020
Cameron, A., Trivedi, P.K., Milne, F., Piggott, J.: A microeconomics model of the demand for health care and health insurance in Australia. Rev. Econom. Studies 55(1), 85–106 (1988)
Consul, P.: Generalized poisson distributions: Properties and applications. Marcel Dekker, New York, 1989
Deb, P., Trivedi, P.K.: Demand for medical care by the elderly: a finite mixture approach. J. Appl. Econom. 12(3), 313–336 (1997)
Famoye,F.: Restricted generalized poisson regression model. Communication in Statistics—Theory and Methods, 22(5):1335–1354, 1 1993. 10.1080/03610929308831089
Famoye, F., Lee, C.: Exponentiated-exponential geometric regression model. Journal of Applied Statistics, 44(16): 2963–2977, 12 2017. ISSN 0266-4763, 1360-0532. 10.1080/02664763.2016.1267117
Greene, W. H.: Accounting for excess zeros and sample selection. Unpublished Technical Report, Department of Economics Stern School of Business New York University, p. 37, 1994
Gómez-Déniz, E., Gallardo, D. I. Gómez, H. W.: Quasi-binomial zero-inflated regression model suitable for variables with bounded support. Journal of Applied Statistics, 2019. ISSN 0266-4763. 10.1080/02664763.2019.1707517. URL https://www.tandfonline.com/loi/cjas20
Hassan, A., Bilal, S.: On some properties of quasi-negative-binomial distribution and its applications. Journal of Modern Applied Statistical Methods, 7(2):616–631, 11 2008. ISSN 1538-9472. 10.22237/jmasm/1225513500
Hur, K., Hedeker, D., Henderson, W., Khuri, S., Daley, J.: Modeling clustered count data with excess zeros in health care outcomes research. Health Services Outcomes Res. Methodol. 3, 5–20 (2002)
Husain, M., Bagmar, S. H.: Modeling under-dispersed count data using generalized poisson regression approach. Global Journal of Quantitative Science, 2(4):22–29, 12 2015
Janardhan, K.G.: Markov-polya urn model with pre-determined strategies. Gujarat Stat. Rev. 2(1), 17–32 (1975)
Lambert, D.: Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics, 34(1):1, 2 1992. ISSN 00401706. 10.2307/1269547
Lawal,B.: Zero-inflated count regression models with applications to some examples. Quality & Quantity: International Journal of Methodology, 46:19–38, 1 2012. 10.1007/s11135-010-9324-x
Lawless, J. F.: Statistical models and methods for lifetime data. Wiley series in probability and statistics. 2. ed edition. ISBN 978-0-471-37215-8
Li, S., Lee, C., Famoye, F.: On certain mixture distributions based on lagrangian probability models. 6: 10, 2008
Li, S., Yang, F., Famoye, F., Lee, C., Black, D.: Quasi-negative binomial distribution: Properties and applications. Computational Statistics & Data Analysis, 55(7):2363–2371, 7 2011. ISSN 01679473. 10.1016/j.csda.2011.02.003
Myung, I.J.: Tutorial on maximum likelihood estimation. J. Math. Psychol. 47(1), 90–100 (2003)
Olumoh, J. S., Sanni, O. O. M., Ajayi, O. O., Jolayemi, E. T.: A new mixture model from generalized poisson and generalized inverse gaussian distribution. Far East Journal of Theoretical Statistics, 53(3): 139–160, 6 2017. ISSN 09720863. 10.17654/TS053030139
Phang Y. N., Loh E. F. Zero inflated models for overdispersed count data. 7(8): 3, 2013
Sellers, K. F., Shmueli, G.: A flexible regression model for count data. The Annals of Applied Statistics, 4(2): 943–961, 6 2010. ISSN 1932-6157. 10.1214/09-AOAS306
Sen, K., Jain, R.: Generalized markov-polya urn models with predetermined strategies. J. Stat. Plan. Inference 54(1), 119–133 (1996). https://doi.org/10.1016/0378-3758(95)00161-1
Shankar, V., Milton, J., Mannering, F.: Modeling accident frequencies as zero-altered probability processes: An empirical inquiry. Accident Analysis & Prevention, 29(6):829–837, 11 1997. ISSN 00014575. 10.1016/S0001-4575(97)00052-3
Sáez-Castillo, A., Conde-Sánchez, A.: A hyper-poisson regression model for overdispersed and underdispersed count data. Computational Statistics & Data Analysis, 61: 148–157, 5 2013. ISSN 01679473. 10.1016/j.csda.2012.12.009
Yang, S., Harlow, L. L., Puggioni, G., Redding, C.A.: A comparison of different methods of zero-inflated data analysis and an application in health surveys. Journal of Modern Applied Statistical Methods, 16(1):518–543, 5 2017. ISSN 1538-9472. 10.22237/jmasm/1493598600
Yeilova, A., Salih, M., Kay, Y.: Zero-inflated regression methods for insecticides. In Insecticides—Basic and Other Applications. ISBN 978-953-51-0007-2
Acknowledgements
We are sincerely appreciative of comments and suggestions from the anonymous reviewers. The first author acknowledges the James Cook University, Australia for the special support, when developing this paper, in providing conducive research environment while the first author was visiting in 2019.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
No conflict of interest whatsoever.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Olumoh, J.S., Ajayi, O.O. & AbdulKadir, S.S. A quasi-negative binomial regression with an application to medical care data. Qual Quant 56, 3029–3052 (2022). https://doi.org/10.1007/s11135-021-01255-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-021-01255-y