Bayesian Multilevel Models for Count Data

Authors

  • Olumide Sunday Adesina
    Department of Mathematical Sciences, Redeemer’s University, Nigeria

Keywords:

Count Data, Health, Insurance, Dispersion, Multilevel Models.

Abstract

The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicate that all the observations are good. Also all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further analysis. Seven multi-level models were f itted and the Geometric model outperformed other model. 

Dimensions

M. S. Workie & A. M. Lakew, “Bayesian count regression analysis for determinants of antenatal care service visits among pregnant women in Amhara regional state, Ethiopia” Journal of Big Data 5 (2018) https://doi.org/10.1186/s40537-018-0117-8.

K.H.Lee,B.ACoull,A.B.Moscicki,B.J.Paster&J.R.Starr, “Bayesian Variable Selection for Multivariate Zero-Inflated Models: Application to Microbiome Count Data”, Biostatistics 21 (2020) 499. 1.

F. Famoye & K.P. Singh, “Zero-inflated generalized Poisson regression model with applications to domestic violence data”, Journal of Data Science 4 (2006) 117.

O. S. Adesina, T. O. Olatayo, O. O. Agboola, & P. E. Oguntunde, “Bayesian Dirichlet process mixture prior for count data”, International Journal of Mechanical Engineering and Technology 9 (2018) 630.

D. Lambert, “Zero-inflated Poisson regression, with an application to defects in manufacturing” Technometrics 34 (1992) .

F. Famoye&W.Wang,“CensoredgeneralizedPoisson regression model” Journal of Computational Statistics and Data Analysis 46 (2004) 547.

W. Su & X. Wang, “Hidden Markov model in multiple testing on dependent count data”, Journal of Statistical Computation and Simulation 5 (2020) 889.

F. Famoye & L. Carl “Exponentiated-exponential geometric regression model”, Journal of Applied Statistics 44 (2017) 2963.

A. H. Lee, K. Wang, J. A Scott, K. W Yau & G. J. McLachlan, “Multilevel zero-inflated Poisson regression modelling of correlated count data with excess zeros”, Statistical Methods in Medical Research 15 (2006) 47.

A. Moghimbeigi, M.R. Eshraghian, K. Mohammad & B. Mcardle “Multilevel zero-inflated negative binomial regression modeling for overdispersed count data with extra zeros”, Journal of Applied Statistics 35 (2008) 1193.

A. Almasi, M.R. Eshraghian, A. Moghimbeigic, A. Rahimib, K. Mohammad & S. Fallahigilan, “Multilevel zero-inflated generalized Poisson regression modelling for dispersed correlated count data”, Statistical Methodology 30 (2016) 1.

J. Fox & S. Weisberg, An R companion to applied regression, Second Edition, Sage (2010), ISBN-13: 978-1412975148

J. Mullahy “Specification and testing of some modified count data models”, Journal of Econometrics 33 (1986) 341.

D.Heilbron, “Generalized linear models for altered zero probabilities and overdispersion in count data” SIMS Technical Report 9, Department of Epidemiology and Biostatistics, University of California, San Francisco 9 (1989).

D.Heilbron“Zero-altered and other regression models for count data with added zeros”, Biometrical Journal 36 (1994) 531.

M. Ridout, C. G. B. Dem´etrio & J. Hinde “Models for count data with many zeros”, International Biometric Conference Cape Town (1998) 1.

P. C.Burkner. “brms: An RpackageforBayesian multilevel models using Sta”, Journal of Statistical Software (2017).

M. D. Hoffman & A. Gelman “The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo”, The Journal of Machine Learning Research 15 (2014) 1593.

R. Natarajan & R. E. Kass, “Reference Bayesian methods for generalized linear mixed models”, Journal of the American Statistical Association 95 (2000) 227.

R. E. Kass, R. Natarajan, “A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper)”, Bayesian Analysis 1 (2006) 535.

D. Lewandowski, D. Kurowicka & H. Joe, “Generating random correlation matrices based on vines and extended onion method”, Journal of Multivariate Analysis 100 (2009) 1989.

S. Duane, A. D. Kennedy, B. J. Pendleton & D. Roweth, “Hybrid Monte Carlo”, Physics Letters B, 195 (1987) 216.

R. M. Neal, Handbook of Markov Chain Monte Carlo, volume 2, chapter MCMCUsingHamiltonian Dynamics. CRC Press 2 (2011) 1.

S. Watanabe, “Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory”, The Journal of Machine Learning Research 11 (2011) 3571.

A.E.Gelfand, D.K.Dey, &C.H.Hang,“Modeldeterminationusingpredictive distributions with implementation via sampling-based methods.” Technical report, DTIC Document (1992)

A. Vehtari’, A. Gelman & J. Gabry Efficient Implementation of LeaveOne-Out Cross-Validation and WAIC for Evaluating Fitted Bayesian Models”, Unpublished manuscript, (2015).

A. Gelman, J. B. Carlin, H. S. Stern & D. B. Rubin, Bayesian Data Analysis, Taylor & Francis 2 (2014).

H. S. Klakattawi, V. Vinciotti & K. Yu, “A simple and adaptive dispersion regression model for count data”, Entropy 20 (2016) 1.

R Core Team. R: A language and environment for statistical computing. RFoundation for Statistical Computing, Vienna, Austria. https://www.Rproject.org (2020).

R. Vinciotti, crete “DWreg: Response”, Parametric Regression for DisR package version 2.0. https://CRAN.Rproject.org/package=DWreg (2016)

C. Kleiber & A. Zeileis, Applied Econometrics with R, New York: Springer-Verlag. ISBN 978-0-387-77316-2. URL https://CRAN.Rproject.org/package=AER (2008)

P. E. Oguntunde, A. O. Adejumo & E. A. Owoloko, “Exponential Inverse Exponential (EIE) distribution”, Asian Journal of Scientific Research, 10 (2017) 169.

P. E. Oguntunde, O. A. Odetunmibi & A. O. Adejumo, “ On the exponentiated generalized Weibull distribution: a generalization of the Weibull distribution”, Indian Journal of Science and Technology 8 (2015) 1.

Published

2021-08-29

How to Cite

Bayesian Multilevel Models for Count Data. (2021). Journal of the Nigerian Society of Physical Sciences, 3(3), 224-233. https://doi.org/10.46481/jnsps.2021.168

Issue

Volume 3, Issue 3, August 2021

Section

Original Research
Copyright & Licensing

Copyright (c) 2021 Journal of the Nigerian Society of Physical Sciences

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Bayesian Multilevel Models for Count Data. (2021). Journal of the Nigerian Society of Physical Sciences, 3(3), 224-233. https://doi.org/10.46481/jnsps.2021.168

Similar Articles

91-100 of 213

You may also start an advanced similarity search for this article.