Bayesian Models for Zero Truncated Count Data
Asian Journal of Probability and Statistics,
It is important to fit count data with suitable model(s), models such as Poisson Regression, Quassi Poisson, Negative Binomial, to mention but a few have been adopted by researchers to fit zero truncated count data in the past. In recent times, dedicated models for fitting zero truncated count data have been developed, and they are considered sufficient. This study proposed Bayesian multi-level Poisson and Bayesian multi-level Geometric model, Bayesian Monte Carlo Markov Chain Generalized linear Mixed Models (MCMCglmms) of zero truncated Poisson and MCMCglmms Poisson regression model to fit health count data that is truncated at zero. Suitable model selection criteria were used to determine preferred models for fitting zero truncated data. Results obtained showed that Bayesian multi-level Poisson outperformed Bayesian multi-level Poisson Geometric model; also MCMCglmms of zero truncated Poisson outperformed MCMCglmms Poisson.
- Count data
- Bayesian inference
- health insurance
- multi-level models.
How to Cite
Paleti R. Generalized extreme value models for count data: Application to worker telecommuting frequency choices. Transportation Research Part B: Methodological. 2016;83:104-120.
Adesina OS, Agunbiade DA, Osundina SA. Bayesian regression model for counts in scholarship. Journal of Mathematical Theory and Modelling. 2017;7(9):46-57.
Adesina OS, Olatayo TO, Agboola OO, Oguntunde PE. Bayesian dirichlet process mixture prior for count data. International Journal of Mechanical Engineering and Technology. 2018;9(12):630-646.
Cameron AC, Johansson P. Count data regression using series expansion: With applications. J. Appl. Econom. 1997;12:203–223.
Cameron AC, Trivedi PK. Count panel data. Oxford Handbook of Panel Data Econometrics, Oxford University Press; 2013.
Kokonendji CC. Over-and under-dispersion models, in methods and applications of statistics in clinical trials, Planning, Analysis, and Inferential Methods, N. Balakrishnan, ed., Wiley, Hoboken, NJ. 2014;2:506–526.
Haselimashhadi H, Vinciotti V, Yu K. A new Bayesian regression model for counts in medicine. arXiv: 1601.02820 [Stat. ME]. 2016;1-21.
Workie MS, Lakew AM. Bayesian count regression analysis for determinants of antenatal care service visits among pregnant women in Amhara regional state, Ethiopia. Journal of Big Data. 2018; 5:7.
Cameron AC, Trivedi PK. Regression analysis for count data, econometric society monograph. 2nd ed., Cambridge, UK, Cambridge University Press; 1998.
Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics. 1992;34:1–14.
Famoye F, Wang W. Censored generalized Poisson regression model. J. Comput. Stat. Data. Anal. 2004;46:547–560.
Famoye F, Singh KP. Zero-inflated generalized Poisson regression model with applications to domestic violence data. J. Data Sci. 2006;4:117–130.
Nelder JA, Wedderburn RWA. Generalized linear models. Journal of the Royal Statistical Society. Series A (General). 1972;135(3):370–384.
Fox J, Weisberg S. An R companion to applied regression Second Edition. Sage; 2011.
Hadfield JD. MCMC methods for multi-response generalized linear mixed models: The MCMCglmm R Package. Journal of Statistical Software. 2010;33(2):1-22.
Kleiber C, Zeileis A. Applied econometrics with R. New York: Springer-Verlag, ISBN 978-0-387-77316-2; 2008.
Burkner PC. Brms: An R Package for Bayesian Multilevel Models using Stan. Journal of Statistical Software; 2017.
Watanabe S. Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. The Journal of Machine Learning Research. 2010;11:3571-3594.
Gelfand AE, Dey DK, Chang H. Model determination using predictive distributions with implementation via sampling-based methods. Technical report, DTIC Document; 1992.
Vehtari A, Gelman A, Gabry J. Efficient implementation of leave-one-out cross-validation and WAIC for evaluating fitted Bayesian models. Unpublished Manuscript. 2015;1-22.
R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria; 2018.
Brooks ME, Kristensen K, Benthem KJ, Magnusson A, Berg CW, Nielsen A, Skaug HJ, Maechle M, Bolker M. Modelling zero-inflated count data with glmm TMB. bioRxiv Preprint Biorxiv: 132753; 2017.
Hoffman MD, Gelman A. The No-U-Turn Sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. The Journal of Machine Learning Research. 2014;15(1):1593-1623.
Lewandowski D, Kurowicka D, Joe H. Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis. 2009;100(9):1989-2001.
Abstract View: 2099 times
PDF Download: 730 times