Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity

Öznur İşçi Güneri; Burcu Durmuş

doi:10.53570/jnt.902066

Research Article

Year 2021, Issue: 35, 48 - 61, 30.06.2021

Öznur İşçi Güneri Burcu Durmuş

https://doi.org/10.53570/jnt.902066

Cited By: 2

Abstract

References

D. Kılıç, H. Bayrak, A Comparison on Count Data Models: Example of Problems That Occured in E-Commerce Over the Turkey, Selçuk University Journal of Science Faculty, 46(2) (2020) 85–102.
B. Pittman, E. Buta, S. Krishnan-Sarin, S. S. O’Malley, T. Liss, R. Gueorguieva, Models for Analyzing Zero-Inflated and Overdispersed Count Data: An Application to Cigarette and Marijuana Use, Nicotine and Tobacco Research 22(8) (2018) 1390–1398.
C. B. Dean, Testing for Overdispersion in Poisson and Binomial Regression Models, JASA 87(418) (1992) 451–457.
M. Harris, J. Marti, Y. Bhatti, H. Watt, J. Macinko, A. Darzi, Explicit Bias towards High-Income Country Research: A Randomized, Blinded, Crossover Experiment in English Clinicians, Health Affairs 36(11) (2017) 1–9.
A. Yeşilova, R. Atlıhan, Analysing the Effects of Different Temperatures on Egg Numbers of Scymnus subvillosus Using Mixture Poisson Regression, Yüzüncü Yıl University Journal of Agricultural Sciences 17(2) (2007) 73–79.
Z. Yang, J. W. Hardin, C. L. Addy, Q. H. Vuong, Testing Approaches for Overdispersion in Poisson Regression Versus the Generalized Poisson Model, Biometrical Journal 49 (2007) 565–584.
J. M. Hilbe, Modelling Count Data (First Edition). New York, 2014, Cambridge University Press.
T. Harris, J. M. Hilbe, J. W. Hardin, Modeling Count Data with Generalized Distributions, The Stata Journal 14(3) (2012) 562–579.
G. C. Jain, P. C. Consul, A Generalized Negative Binomial Distribution, SIAM Journal of Applied Mathematics 21(4) (1971) 501–513.
P. C. Consul, H. C. Gupta, The Generalized Negative Binomial Distribution and Its Characterization by Zero Regression, SIAM Journal on Applied Mathematics 39 (1980) 231–237.
F. Famoye, Generalized Binomial Regression Model, Biometrical Journal 37 (1995) 581–594.
P. C. Consul, F. Famoye, Generalized Poisson Regression Model, Communications in Statistics-Theory and Methods 21 (1992) 89–109.
J. O. Irwin, The Generalized Waring Distribution Applied to Accident Theory, Journal of the Royal Statistical Society Series A (General) 131(2) (1968) 205–225.
K. Wang, K. W. Y. Kelvin, H. L. Andy, A Zero-Inflated Poisson Mixed Model to Analyze Diagnosis Related Groups with Majority of Same-Day Hospital Stays, Computer Methods and Programs in Biomedicine 68 (2002) 195–203.
J. W. Hardin, J. M. Hilbe, Generalized Linear Models and Extensions, 3rd ed. College Station, TX: Stata Press, 2012.
J. Rodriguez-Avi, A. Conde-Sanchez, A. J. Saez-Castillo, M. J. Olmo-Jimenez, A. M. Martinez-Rodriguez, A Generalized Waring Regression Model for Count Data, Computational Statistics and Data Analysis 53 (2009) 3717–3725.
S. W. Martin, C. E. Rose, K. A. Wannemuehler, B. D. Plikaytis, On of the Zero-inflated and Hurdle Models for Modelling Vaccine Adverse event Count Data, Journal of Biopharmaceutical Statistics 16 (2006) 463–481.
Y. Cui, W. Yang, Zero-Inflated Generalized Poisson Regression Mixture Model for Mapping Quantitative Trait Loci Underlying Count Trait with Many Zeros, Journal of Theoretical Biology 256 (2009) 276–285.
M. Ridout, J. Hinde, C. G. B. Demetrio, A Score Test for a Zero-Inflated Poisson Regression Model Against Zero- Inflated Negative Binomial Alternatives, Biometrics 57 (2001) 219–233.
J. M. Miller, Comparing Poisson, Hurdle and Zip Model Fit Under Varying Degrees of Skew and Zero-Inflation, Doctoral Thesis, University of Florida, 2007.
F. Famoye, K. P. Singh, Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data, Journal of Data Science 4(1) (2006) 117–130.
C. Czado, V. Erhardt, A. Min, S. Wagner, Zero-Inflated Generalized Poisson Models with Regression Effects on The Mean, Dispersion and Zero-Inflation Level Applied To Patent Outsourcing Rates, Statistical Modelling 7 (2007) 125–153.
S. M. Mwalili, E. Lesare, D. Declerck, The Zero-Inflated Negative Binomial Regression Model with Correction for Misclassi_Cation: An Example in Caries Research, Statistical Methods in Medical Research 17(2) (2008) 123–139.
E. Altun, A New Zero-Inflated Regression Model with Application, Journal of Statisticians: Statistics and Actuarial Sciences 11(2) (2018) 73–80.
E. Pamukçu, C. Colak, N. Halisdemir, Modeling of The Number of Divorce in Turkey Using the Generalized Poisson, Quasi-Poisson and Negative Binomial Regression, Turkish Journal of Science & Technology 9(1) (2014) 89–96.
Z. Yang, J. W. Hardin, C. L. Addy, A Score Test for Overdispersion in Poisson Regression Based on The Generalized Poisson-2 Model, Journal of Statistical Planning and Inference 139 (2009) 1514–1521.
M. Logan, Biostatistical Design and Analysis Using R, Willey-Blackwell, 2010.
J. F. Lawless, Negative Binomial and Mixed Poisson Regression, The Canadian Journal of Statistics 15(3) (1987) 209–225.
Y. Kaya, A. Yeşilova, Investigation of E-Mail Traffic by Using Zero-Inflated Regression Models, Anadolu University of Sciences & Technology-A: Applied Sciences & Engineering 13(1) (2012) 51–63.
W. Wang, F. Famoye, Modeling Household Fertiliq' Decisions with Generalized Poisson Regression, Journal of Population Economics 10 (1997) 273–283.
H. Akaike, Information Theory and An Extension of The Maximum Likelihood Principle, Second International Symposium on Information Theory (1973) 267–281, Academia Kiado, Budapest.
C. M. Hurvich, C. L. Tsai, Regression and Time Series Model Selection in Small Samples, Biometrika 76 (1989) 297–307.
N. Sugiura, Further Analysts of the Data by Akaike's Information Criterion and the Finite Corrections, Communications in Statistics - Theory and Methods 7(1) (1978) 13–26.
A. D. R. Mcquarrie, C. Tsai, Regression and Time Series Model Selection, World Scientific Publishing Company, Singapore, 1998.
Q. H. Vuong, Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses, Econometrica 57 (1989) 307–333.
K. H. Pho, L. Sel, L. Sal, T. M. Lukusa, Comparison Among Akaike Information Criterion, Bayesian Information Criterion and Vuong's Test in Model Selection: A Case Study of Violated Speed Regulation in Taiwan, Journal of Advanced Engineering and Computation 3(1) (2019) 293–303.
N. Ismail, H. Zamani, Estimation of Claimcount Data Using Negative Binomial, Generalized Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Generalized Poisson Regression Models, Casualty Actuarial Society E-Forum 41(20) (2013) 1–28.
W. Hemmingsen, P. A. Jansen, K. Mackenzie, Crabs, Leeches and Trypanosomes: An Unholy Trinity?, Marine Pollution Bulletin 50(3) (2005) 336–339.

Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity

Year 2021, Issue: 35, 48 - 61, 30.06.2021

Öznur İşçi Güneri Burcu Durmuş

https://doi.org/10.53570/jnt.902066

Cited By: 2

Abstract

The Poisson regression model is widely used for count data. This model assumes equidispersion. In practice, equidispersion is seldom reflected in data. However, in real-life data, the variance usually exceeds the mean. This situation is known as overdispersion. Negative binomial distribution and other Poisson mix models are often used to model overdispersion count data. Another extension of the negative binomial distribution in another model for count data is the univariate generalized Waring. In addition, the model developed by Famoye can be used in the analysis of count data. When the count data contains a large number of zeros, it is necessary to use zero-inflated models. In this study, different generalized regression models are emphasized for the analysis of excessive zeros count data. For this purpose, a real data set was analysed with the generalized Poisson model, generalized negative binomial model, generalized negative binomial Famoye, generalized Waring model, and the foregoing zero-inflated models. Log-likelihood, Akaike information criterion, Bayes information criterion, Vuong statistics were used for model comparisons.

Keywords

Count data, overdispersion, generalized distribution models, zero-inflated

References

D. Kılıç, H. Bayrak, A Comparison on Count Data Models: Example of Problems That Occured in E-Commerce Over the Turkey, Selçuk University Journal of Science Faculty, 46(2) (2020) 85–102.
B. Pittman, E. Buta, S. Krishnan-Sarin, S. S. O’Malley, T. Liss, R. Gueorguieva, Models for Analyzing Zero-Inflated and Overdispersed Count Data: An Application to Cigarette and Marijuana Use, Nicotine and Tobacco Research 22(8) (2018) 1390–1398.
C. B. Dean, Testing for Overdispersion in Poisson and Binomial Regression Models, JASA 87(418) (1992) 451–457.
M. Harris, J. Marti, Y. Bhatti, H. Watt, J. Macinko, A. Darzi, Explicit Bias towards High-Income Country Research: A Randomized, Blinded, Crossover Experiment in English Clinicians, Health Affairs 36(11) (2017) 1–9.
A. Yeşilova, R. Atlıhan, Analysing the Effects of Different Temperatures on Egg Numbers of Scymnus subvillosus Using Mixture Poisson Regression, Yüzüncü Yıl University Journal of Agricultural Sciences 17(2) (2007) 73–79.
Z. Yang, J. W. Hardin, C. L. Addy, Q. H. Vuong, Testing Approaches for Overdispersion in Poisson Regression Versus the Generalized Poisson Model, Biometrical Journal 49 (2007) 565–584.
J. M. Hilbe, Modelling Count Data (First Edition). New York, 2014, Cambridge University Press.
T. Harris, J. M. Hilbe, J. W. Hardin, Modeling Count Data with Generalized Distributions, The Stata Journal 14(3) (2012) 562–579.
G. C. Jain, P. C. Consul, A Generalized Negative Binomial Distribution, SIAM Journal of Applied Mathematics 21(4) (1971) 501–513.
P. C. Consul, H. C. Gupta, The Generalized Negative Binomial Distribution and Its Characterization by Zero Regression, SIAM Journal on Applied Mathematics 39 (1980) 231–237.
F. Famoye, Generalized Binomial Regression Model, Biometrical Journal 37 (1995) 581–594.
P. C. Consul, F. Famoye, Generalized Poisson Regression Model, Communications in Statistics-Theory and Methods 21 (1992) 89–109.
J. O. Irwin, The Generalized Waring Distribution Applied to Accident Theory, Journal of the Royal Statistical Society Series A (General) 131(2) (1968) 205–225.
K. Wang, K. W. Y. Kelvin, H. L. Andy, A Zero-Inflated Poisson Mixed Model to Analyze Diagnosis Related Groups with Majority of Same-Day Hospital Stays, Computer Methods and Programs in Biomedicine 68 (2002) 195–203.
J. W. Hardin, J. M. Hilbe, Generalized Linear Models and Extensions, 3rd ed. College Station, TX: Stata Press, 2012.
J. Rodriguez-Avi, A. Conde-Sanchez, A. J. Saez-Castillo, M. J. Olmo-Jimenez, A. M. Martinez-Rodriguez, A Generalized Waring Regression Model for Count Data, Computational Statistics and Data Analysis 53 (2009) 3717–3725.
S. W. Martin, C. E. Rose, K. A. Wannemuehler, B. D. Plikaytis, On of the Zero-inflated and Hurdle Models for Modelling Vaccine Adverse event Count Data, Journal of Biopharmaceutical Statistics 16 (2006) 463–481.
Y. Cui, W. Yang, Zero-Inflated Generalized Poisson Regression Mixture Model for Mapping Quantitative Trait Loci Underlying Count Trait with Many Zeros, Journal of Theoretical Biology 256 (2009) 276–285.
M. Ridout, J. Hinde, C. G. B. Demetrio, A Score Test for a Zero-Inflated Poisson Regression Model Against Zero- Inflated Negative Binomial Alternatives, Biometrics 57 (2001) 219–233.
J. M. Miller, Comparing Poisson, Hurdle and Zip Model Fit Under Varying Degrees of Skew and Zero-Inflation, Doctoral Thesis, University of Florida, 2007.
F. Famoye, K. P. Singh, Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data, Journal of Data Science 4(1) (2006) 117–130.
C. Czado, V. Erhardt, A. Min, S. Wagner, Zero-Inflated Generalized Poisson Models with Regression Effects on The Mean, Dispersion and Zero-Inflation Level Applied To Patent Outsourcing Rates, Statistical Modelling 7 (2007) 125–153.
S. M. Mwalili, E. Lesare, D. Declerck, The Zero-Inflated Negative Binomial Regression Model with Correction for Misclassi_Cation: An Example in Caries Research, Statistical Methods in Medical Research 17(2) (2008) 123–139.
E. Altun, A New Zero-Inflated Regression Model with Application, Journal of Statisticians: Statistics and Actuarial Sciences 11(2) (2018) 73–80.
E. Pamukçu, C. Colak, N. Halisdemir, Modeling of The Number of Divorce in Turkey Using the Generalized Poisson, Quasi-Poisson and Negative Binomial Regression, Turkish Journal of Science & Technology 9(1) (2014) 89–96.
Z. Yang, J. W. Hardin, C. L. Addy, A Score Test for Overdispersion in Poisson Regression Based on The Generalized Poisson-2 Model, Journal of Statistical Planning and Inference 139 (2009) 1514–1521.
M. Logan, Biostatistical Design and Analysis Using R, Willey-Blackwell, 2010.
J. F. Lawless, Negative Binomial and Mixed Poisson Regression, The Canadian Journal of Statistics 15(3) (1987) 209–225.
Y. Kaya, A. Yeşilova, Investigation of E-Mail Traffic by Using Zero-Inflated Regression Models, Anadolu University of Sciences & Technology-A: Applied Sciences & Engineering 13(1) (2012) 51–63.
W. Wang, F. Famoye, Modeling Household Fertiliq' Decisions with Generalized Poisson Regression, Journal of Population Economics 10 (1997) 273–283.
H. Akaike, Information Theory and An Extension of The Maximum Likelihood Principle, Second International Symposium on Information Theory (1973) 267–281, Academia Kiado, Budapest.
C. M. Hurvich, C. L. Tsai, Regression and Time Series Model Selection in Small Samples, Biometrika 76 (1989) 297–307.
N. Sugiura, Further Analysts of the Data by Akaike's Information Criterion and the Finite Corrections, Communications in Statistics - Theory and Methods 7(1) (1978) 13–26.
A. D. R. Mcquarrie, C. Tsai, Regression and Time Series Model Selection, World Scientific Publishing Company, Singapore, 1998.
Q. H. Vuong, Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses, Econometrica 57 (1989) 307–333.
K. H. Pho, L. Sel, L. Sal, T. M. Lukusa, Comparison Among Akaike Information Criterion, Bayesian Information Criterion and Vuong's Test in Model Selection: A Case Study of Violated Speed Regulation in Taiwan, Journal of Advanced Engineering and Computation 3(1) (2019) 293–303.
N. Ismail, H. Zamani, Estimation of Claimcount Data Using Negative Binomial, Generalized Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Generalized Poisson Regression Models, Casualty Actuarial Society E-Forum 41(20) (2013) 1–28.
W. Hemmingsen, P. A. Jansen, K. Mackenzie, Crabs, Leeches and Trypanosomes: An Unholy Trinity?, Marine Pollution Bulletin 50(3) (2005) 336–339.

There are 38 citations in total.

Details

Primary Language	English
Subjects	Applied Mathematics
Journal Section	Research Article
Authors	Öznur İşçi Güneri 0000-0003-3677-7121 Burcu Durmuş 0000-0002-0298-0802
Publication Date	June 30, 2021
Submission Date	March 23, 2021
Published in Issue	Year 2021 Issue: 35

Cite

APA	İşçi Güneri, Ö., & Durmuş, B. (2021). Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity. Journal of New Theory(35), 48-61. https://doi.org/10.53570/jnt.902066
AMA	İşçi Güneri Ö, Durmuş B. Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity. JNT. June 2021;(35):48-61. doi:10.53570/jnt.902066
Chicago	İşçi Güneri, Öznur, and Burcu Durmuş. “Models for Overdispersion Count Data With Generalized Distribution: An Application to Parasites Intensity”. Journal of New Theory, no. 35 (June 2021): 48-61. https://doi.org/10.53570/jnt.902066.
EndNote	İşçi Güneri Ö, Durmuş B (June 1, 2021) Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity. Journal of New Theory 35 48–61.
IEEE	Ö. İşçi Güneri and B. Durmuş, “Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity”, JNT, no. 35, pp. 48–61, June 2021, doi: 10.53570/jnt.902066.
ISNAD	İşçi Güneri, Öznur - Durmuş, Burcu. “Models for Overdispersion Count Data With Generalized Distribution: An Application to Parasites Intensity”. Journal of New Theory 35 (June 2021), 48-61. https://doi.org/10.53570/jnt.902066.
JAMA	İşçi Güneri Ö, Durmuş B. Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity. JNT. 2021;:48–61.
MLA	İşçi Güneri, Öznur and Burcu Durmuş. “Models for Overdispersion Count Data With Generalized Distribution: An Application to Parasites Intensity”. Journal of New Theory, no. 35, 2021, pp. 48-61, doi:10.53570/jnt.902066.
Vancouver	İşçi Güneri Ö, Durmuş B. Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity. JNT. 2021(35):48-61.