Using Quasi-Poisson Model to Analyze Thalassemia Patient Data
DOI:
https://doi.org/10.36322/jksc.v1i74(B).17726Keywords:
Poisson, Quasi-Poisson, Negative Binomial, Overdispersion, Variable Selection, AIC, Likelihood Ratio Test, P-valueAbstract
The last decade of the twentieth century witnessed a great interest in Poisson's models, which is one of the counting models that deal with the discrete variable as a dependent variable. Researchers have faced a number of challenges to apply this model in the real data world. Some data showed high heterogeneity, which caused the emergence of the problem of over-dispersion. The quasi-Poisson model and the negative binomial model have been proposed as alternative models to the Poisson model, with the presence of the problem of over-dispersion.
This search sought to study comparing the full Poisson model with the Poisson model after deleting a number of unimportant variables, with the quasi Poisson and negative binomial model after choosing the best Variables, this was implemented through the data of thalassemia patients.
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References
المراجع:
أولاً- المراجع العربية:
1. باستخدام أنموذج بواسون. Journal of Administration and Economics, (111), 241-255.
2. عبد المجيد حمزة الناصر , احلام احمد جمعة (2007) .. المقارنة بين طرائق تحديد رتبة انموذج الانحدار الذاتي الطبيعي باستخدام بيانات مولدّة وبيانات لبعض العناصر المناخية في العراق). Journal of Economics and Administrative Sciences, 13(48), 251-251. DOI: https://doi.org/10.33095/jeas.v13i48.1228
ثانياً- المراجع الإنكليزية
1. Acquah, H. D. G. (2010). Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship.
2. AKAIKE, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory Akademiai Kiado. (pp. 267-281).
3. Amaliana, L., Sa’adah, U., & Wardhani, N. W. S. (2017, December). Modeling Tetanus Neonatorum case using the regression of negative binomial and zero-inflated negative binomial. In Journal of Physics: Conference Series . IOP Publishing. (Vol. 943, No. 1, p. 012051).
4. Blocker, C., Conway, J., Demortier, L., Heinrich, J., Junk, T., Lyons, L., & Punzig, G. (2006). Simple facts about p-values. CDF8023.
5. Breslow, N. E. (1984). Extra‐Poisson variation in log‐linear models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 33(1), 38-44.
6. Brillinger, D. R. (1986). A biometrics invited paper with discussion: The natural variability of vital rates and associated statistics. Biometrics, 693-734.
7. Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304.
8. Dean, C. B. (1992). Testing for overdispersion in Poisson and binomial regression models. Journal of the American Statistical Association, 87(418), 451-457.
9. Dean, C. B., & Lundy, E. R. (2014). Overdispersion. Wiley StatsRef: Statistics Reference Online, 1-9.
10. Fisher, R. A. (1950). 236: The Significance of Deviations From Expectation in a Poisson Series.
11. Frome, E. L., & Checkoway, H. (1985). Use of Poisson regression models in estimating incidence rates and ratios. American journal of epidemiology , 121(2), 309-323.
12. Frome, E. L., Kutner, M. H., & Beauchamp, J. J. (1973). Regression analysis of Poisson-distributed data. Journal of the American Statistical Association , 68(344), 935-940.
13. Hardin, J. W., Hardin, J. W., Hilbe, J. M., & Hilbe, J. (2007). Generalized linear models and extensions. Stata press..
14. Hilbe, J. M. (2011). Negative binomial regression. Cambridge University Press..
15. Hilbe, J. M. (2014). Modeling count data. Cambridge University Press..
16. Ismail, N., & Jemain, A. A. (2007). Handling overdispersion with negative binomial and generalized Poisson regression models. In Casualty actuarial society forum (Vol. 2007, pp. 103-58). Citeseer.
17. Konishi, S., & Kitagawa, G. (2008). Information criteria and statistical modeling.
18. Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. Sociological methods & research, 33(2), 188-229.
19. Larsen, R. J., & Marx, M. L. (2005). An introduction to mathematical statistics. Prentice Hall..
20. Lindén, A., & Mäntyniemi, S. (2011). Using the negative binomial distribution to model overdispersion in ecological count data. Ecology, 92(7), 1414-1421.
21. Manton, K. G., & Stallard, E. (1981). Methods for the analysis of mortality risks across heterogeneous small populations: examination of space-time gradients in cancer mortality in North Carolina counties 1970–75. Demography, 18(2), 217-230.
22. Mutua, F. M. (1994). The use of the Akaike Information Criterion in the identification of an optimum flood frequency model. Hy drological Sciences Journa 39(3), 235-244.
23. Neath, A. A., & Cavanaugh, J. E. (2012). The Bayesian information criterion: background, derivation, and applications. Wiley Interdisciplinary Reviews: Computational Statistics, 4(2), 199-203.
24. Nussbaum, E. M., Elsadat, S., & Khago, A. H. (2008). Best practices in analyzing count data: Poisson regression. Best practices in quantitative methods, 306-323.
25. Padilla, D. P. (2003). A graphical approach for goodness-of-fit of Poisson model. University of Nevada, Las Vegas..
26. Snipes, M., & Taylor, D. C. (2014). Model selection and Akaike Information Criteria: An example from wine ratings and prices. Wine Economics and Policy, 3(1), 3-9.
27. Student. (1919). An explanation of deviations from Poisson's law in practice. Biometrika, 211-215.
28. Thiese, M. S., Ronna, B., & Ott, U. (2016). P value interpretations and considerations. Journal of thoracic disease, 8(9), E928.
29. Ver Hoef, J. M., & Boveng, P. L. (2007). Quasi‐Poisson vs. negative binomial regression: how should we model overdispersed count data?. Ecology, 88(11), 2766-2772.
30. Vogt, A., & Bared, J. (1998). Accident models for two-lane rural segments and intersections. Transportation Research Record, 1635(1), 18-29.
31. Wedderburn, R. W. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method. Biometrika, 61(3), 439-447.
References:
First: Arabic References:
1. باستخدام أنموذج بواسون. Journal of Administration and Economics, (111), 241-255.
2. Abdul Majeed Hamza Al-Nasser, Ahlam Ahmed Jumaa (2007) Comparison of methods for determining the rank of the natural autoregressive model using generating data and data for some climatic elements in Iraq). Journal of Economics and Administrative Sciences, 13(48), 251-251.
English references
1. Acquah, H. D. G. (2010). Comparison of Akaike information criterion (AIC) and Bayesian information criterion (BIC) in selection of an asymmetric price relationship.
2. AKAIKE, H. (1973). Information theory and an extension of the maximum likelihood principle. In 2nd International Symposium on Information Theory Akademiai Kiado. (pp. 267-281).
3. Amaliana, L., Sa’adah, U., & Wardhani, N. W. S. (2017, December). Modeling Tetanus Neonatorum case using the regression of negative binomial and zero-inflated negative binomial. In Journal of Physics: Conference Series . IOP Publishing. (Vol. 943, No. 1, p. 012051). DOI: https://doi.org/10.1088/1742-6596/943/1/012051
4. Blocker, C., Conway, J., Demortier, L., Heinrich, J., Junk, T., Lyons, L., & Punzig, G. (2006). Simple facts about p-values. CDF8023.
5. Breslow, N. E. (1984). Extra‐Poisson variation in log‐linear models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 33(1), 38-44. DOI: https://doi.org/10.2307/2347661
6. Brillinger, D. R. (1986). A biometrics invited paper with discussion: The natural variability of vital rates and associated statistics. Biometrics, 693-734. DOI: https://doi.org/10.2307/2530689
7. Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304. DOI: https://doi.org/10.1177/0049124104268644
8. Dean, C. B. (1992). Testing for overdispersion in Poisson and binomial regression models. Journal of the American Statistical Association, 87(418), 451-457. DOI: https://doi.org/10.1080/01621459.1992.10475225
9. Dean, C. B., & Lundy, E. R. (2014). Overdispersion. Wiley StatsRef: Statistics Reference Online, 1-9. DOI: https://doi.org/10.1002/9781118445112.stat06788.pub2
10. Fisher, R. A. (1950). 236: The Significance of Deviations From Expectation in a Poisson Series. DOI: https://doi.org/10.2307/3001420
11. Frome, E. L., & Checkoway, H. (1985). Use of Poisson regression models in estimating incidence rates and ratios. American journal of epidemiology , 121(2), 309-323. DOI: https://doi.org/10.1093/oxfordjournals.aje.a114001
12. Frome, E. L., Kutner, M. H., & Beauchamp, J. J. (1973). Regression analysis of Poisson-distributed data. Journal of the American Statistical Association , 68(344), 935-940. DOI: https://doi.org/10.1080/01621459.1973.10481449
13. Hardin, J. W., Hardin, J. W., Hilbe, J. M., & Hilbe, J. (2007). Generalized linear models and extensions. Stata press..
14. Hilbe, J. M. (2011). Negative binomial regression. Cambridge University Press.. DOI: https://doi.org/10.1017/CBO9780511973420
15. Hilbe, J. M. (2014). Modeling count data. Cambridge University Press.. DOI: https://doi.org/10.1017/CBO9781139236065
16. Ismail, N., & Jemain, A. A. (2007). Handling overdispersion with negative binomial and generalized Poisson regression models. In Casualty actuarial society forum (Vol. 2007, pp. 103-58). Citeseer.
17. Konishi, S., & Kitagawa, G. (2008). Information criteria and statistical modeling. DOI: https://doi.org/10.1007/978-0-387-71887-3
18. Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. Sociological methods & research, 33(2), 188-229. DOI: https://doi.org/10.1177/0049124103262065
19. Larsen, R. J., & Marx, M. L. (2005). An introduction to mathematical statistics. Prentice Hall..
20. Lindén, A., & Mäntyniemi, S. (2011). Using the negative binomial distribution to model overdispersion in ecological count data. Ecology, 92(7), 1414-1421. DOI: https://doi.org/10.1890/10-1831.1
21. Manton, K. G., & Stallard, E. (1981). Methods for the analysis of mortality risks across heterogeneous small populations: examination of space-time gradients in cancer mortality in North Carolina counties 1970–75. Demography, 18(2), 217-230. DOI: https://doi.org/10.2307/2061094
22. Mutua, F. M. (1994). The use of the Akaike Information Criterion in the identification of an optimum flood frequency model. Hy drological Sciences Journa 39(3), 235-244. DOI: https://doi.org/10.1080/02626669409492740
23. Neath, A. A., & Cavanaugh, J. E. (2012). The Bayesian information criterion: background, derivation, and applications. Wiley Interdisciplinary Reviews: Computational Statistics, 4(2), 199-203. DOI: https://doi.org/10.1002/wics.199
24. Nussbaum, E. M., Elsadat, S., & Khago, A. H. (2008). Best practices in analyzing count data: Poisson regression. Best practices in quantitative methods, 306-323. DOI: https://doi.org/10.4135/9781412995627.d26
25. Padilla, D. P. (2003). A graphical approach for goodness-of-fit of Poisson model. University of Nevada, Las Vegas..
26. Snipes, M., & Taylor, D. C. (2014). Model selection and Akaike Information Criteria: An example from wine ratings and prices. Wine Economics and Policy, 3(1), 3-9. DOI: https://doi.org/10.1016/j.wep.2014.03.001
27. Student. (1919). An explanation of deviations from Poisson's law in practice. Biometrika, 211-215. DOI: https://doi.org/10.1093/biomet/12.3-4.211
28. Thiese, M. S., Ronna, B., & Ott, U. (2016). P value interpretations and considerations. Journal of thoracic disease, 8(9), E928. DOI: https://doi.org/10.21037/jtd.2016.08.16
29. Ver Hoef, J. M., & Boveng, P. L. (2007). Quasi‐Poisson vs. negative binomial regression: how should we model overdispersed count data?. Ecology, 88(11), 2766-2772. DOI: https://doi.org/10.1890/07-0043.1
30. Vogt, A., & Bared, J. (1998). Accident models for two-lane rural segments and intersections. Transportation Research Record, 1635(1), 18-29. DOI: https://doi.org/10.3141/1635-03
31. Wedderburn, R. W. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method. Biometrika, 61(3), 439-447. DOI: https://doi.org/10.1093/biomet/61.3.439
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