A Study of Count Regression Models for Mortality Rate

Anwar Fitrianto

Abstract


This paper discusses how overdispersed count data to be fit. Poisson regression model, Negative Binomial 1 regression model (NEGBIN 1) and Negative Binomial regression 2 (NEGBIN 2) model were proposed to fit mortality rate data. The method used is comparing the values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to find out which method suits the data the most. The results show that the data indeed display higher variability. Among the three models, the model preferred is NEGBIN 1 model.

Keywords


Mortality, Poisson, Regression, Binomial, Overdispersion

Full Text:

PDF

References


Tutz, G. Regression for categorical data, Cambridge University Press, New York, 2012.

Kumpusalo, E., Lakka, H.N., Laaksomen, D.E., Lakka, T.A., Niskanen, L.K., Salonen, J.T. and Tuomilehto, J., "The metabolic syndrome and total and cardiovascular disease mortality in middle-age men", Journal of American Medical Association, vol. 288, no. 3, pp. 2708-2716, 2002.

Gayle, H.D. and Hill, G.L. "Global impact of human immunodeficiency virus and AIDS". Clinical Microbiology Reviews, vol. 14, no. 2, pp. 327 – 335, 2001.

Breman, J.G., Jamison, D.T., and Measam, A.R., Disease control priorities in developing countries 2nd Edition: Worldbank, Washington (DC), 2006.

Claudio F. Lanata, Christa L. Fischer-Walker and Ana C. Olascoaga, Carla X. Torres, Martin J. Aryee, Robert E. Black, "Global causes of diarrheal disease mortality in children <5 years of age: a systematic review", PLoS ONE. vol. 8, no.9, pp. 1-11, 2013.

Bassett, L. and Levinson, F.J. Malnutrition is still a major contributor to child death. Population Reference Bureau, Boston, 2007.

Black, R.E., Hyder, A., Sacco, L. and Rice, A.L., Malnutrition as an underlying cause of childhood deaths associated with infectious diseases in developing countries. World Health Organization. Bulletin of the World Health Organization, 2000.

Gopalakrishnan, S. , "A public health perspective of road traffic accidents", Journal of Family Medicine and Primary Care, vol. 1, no. 2, pp. 144 – 150, 2012.

Wasserman, D., Cheng, Q., and Jiang, G.X., "Global suicide rates among young people age 15 – 19", World Psychiatry, vol. 4, no. 2, pp. 114 – 120, 2005.

Sheil, D, Alder, D., and Burshem, D., "The interpretation and misinterpretation of mortality rate measures", Journal of Ecology, vol.. 83, no. 2, pp. 331–333, 1995.

Koontz, D, Life Expectancy,, http://www.worldlifeexpectancy.com/life-expectancy-research (accessed 12 August 2021), 2021.

Özmen, I. and Fayome, F., "Count regressions model with an application to zoological data containing structural zero", Journal of Data Science, vol. 5, no. 4., pp. 491-502, 2007.

Ismail, N. and Zamani, H.,"Estimation of claim count data using Negative Binomal, Generalized Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Generalized Poisson model", Casualty Acturial Society E-Form. vol. 41, no. 20, pp. 1-28, 2013.

Greene, W. Functional form and heterogeneity in models for count data, Now Publisher Inc, 2008.

Gourieroux, C., Monfort, A., and Trognon, A. , "Pseudo maximum likelihood methods", Econometrica, vol. 52, no. 3,pp. 681-700, 1984.

Long, J. S. and Freese, J., Regression models for categorical dependent variables using Stata, Second Edition, College Station, TX: Stata Press, 2006.

Zwilling, M.L., "Negative Binomial regression", The Mathematical Journal, vol. 15, no. 1, pp. 1-18, 2013.

Cameron, C.A. and Trivedi, P.K., Regression aof count data, Cambridge University Press, Cambridge, 2013.

Berk, R and MacDonald, J., "Overdispersion and Poisson regression", Journal of Quantitative Criminology, vol. 24, no. 3., pp. 269-284.

Turner, H., Introduction to generalized linear model, ESRC National Centre for Research Method, 2008.

Yan, J., Guszcza, J., Flynn, M., and Wu, C.S., "Applications of the offset in property-casualty predictive modeling", Casualty Actuarial Society E-Forum, vol. 1, no. 1., pp. 366-385.




DOI: https://doi.org/10.18860/ca.v7i1.13642

Refbacks

  • There are currently no refbacks.


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

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.