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Journal articles on the topic 'Negative binomial regression model'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Cepeda-Cuervo, Edilberto, and María Victoria Cifuentes-Amado. "Double Generalized Beta-Binomial and Negative Binomial Regression Models." Revista Colombiana de Estadística 40, no. 1 (2017): 141–63. http://dx.doi.org/10.15446/rce.v40n1.61779.

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Overdispersion is a common phenomenon in count datasets, that can greatly affect inferences about the model. In this paper develop three joint mean and dispersion regression models in order to fit overdispersed data. These models are based on reparameterizations of the beta-binomial and negative binomial distributions. Finally, we propose a Bayesian approach to estimate the parameters of the overdispersion regression models and use it to fit a school absenteeism dataset.

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2

Famoye, Felix. "On the bivariate negative binomial regression model." Journal of Applied Statistics 37, no. 6 (2010): 969–81. http://dx.doi.org/10.1080/02664760902984618.

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3

Xue, Dixi, and James A. Deddens. "Overdispersed negative binomial regression models." Communications in Statistics - Theory and Methods 21, no. 8 (1992): 2215–26. http://dx.doi.org/10.1080/03610929208830908.

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4

Li, Chin-Shang. "Semiparametric Negative Binomial Regression Models." Communications in Statistics - Simulation and Computation 39, no. 3 (2010): 475–86. http://dx.doi.org/10.1080/03610910903480834.

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5

Hung, Lai-Fa. "A Negative Binomial Regression Model for Accuracy Tests." Applied Psychological Measurement 36, no. 2 (2012): 88–103. http://dx.doi.org/10.1177/0146621611429548.

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Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an overdispersion framework and proposes new estimation methods. The parameters in the proposed model can be estimated using the Markov chain Monte Carlo method implemented in WinBUGS and the marginal maximum likelihood method implemented in SAS. An empirical example based on models generated by the results of empirical data, which are fitted and discussed, is examined.

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D’Andrea, Amanda, Ricardo Rocha, Vera Tomazella, and Francisco Louzada. "Negative Binomial Kumaraswamy-G Cure Rate Regression Model." Journal of Risk and Financial Management 11, no. 1 (2018): 6. http://dx.doi.org/10.3390/jrfm11010006.

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Rashad, Nadwa Khazaal, Nawal Mahmood Hammood, and Zakariya Yahya Algamal. "Generalized ridge estimator in negative binomial regression model." Journal of Physics: Conference Series 1897, no. 1 (2021): 012019. http://dx.doi.org/10.1088/1742-6596/1897/1/012019.

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Allison, Paul D., and Richard P. Waterman. "7. Fixed-Effects Negative Binomial Regression Models." Sociological Methodology 32, no. 1 (2002): 247–65. http://dx.doi.org/10.1111/1467-9531.00117.

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This paper demonstrates that the conditional negative binomial model for panel data, proposed by Hausman, Hall, and Griliches (1984), is not a true fixed-effects method. This method—which has been implemented in both Stata and LIMDEP—does not in fact control for all stable covariates. Three alternative methods are explored. A negative multinomial model yields the same estimator as the conditional Poisson estimator and hence does not provide any additional leverage for dealing with over-dispersion. On the other hand, a simulation study yields good results from applying an unconditional negative binomial regression estimator with dummy variables to represent the fixed effects. There is no evidence for any incidental parameters bias in the coefficients, and downward bias in the standard error estimates can be easily and effectively corrected using the deviance statistic. Finally, an approximate conditional method is found to perform at about the same level as the unconditional estimator.

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Faroughi, Pouya, and Noriszura Ismail. "Bivariate zero-inflated negative binomial regression model with applications." Journal of Statistical Computation and Simulation 87, no. 3 (2016): 457–77. http://dx.doi.org/10.1080/00949655.2016.1213843.

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Türkan, Semra, and Gamze Özel. "A Jackknifed estimators for the negative binomial regression model." Communications in Statistics - Simulation and Computation 47, no. 6 (2017): 1845–65. http://dx.doi.org/10.1080/03610918.2017.1327069.

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Månsson, Kristofer. "On ridge estimators for the negative binomial regression model." Economic Modelling 29, no. 2 (2012): 178–84. http://dx.doi.org/10.1016/j.econmod.2011.09.009.

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12

Naghawi, Hana. "Negative Binomial Regression Model for Road Crash Severity Prediction." Modern Applied Science 12, no. 4 (2018): 38. http://dx.doi.org/10.5539/mas.v12n4p38.

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In this paper, the Negative Binominal Regression (NBR) technique was used to develop crash severity prediction model in Jordan. The primary crash data needed were obtained from Jordan Traffic Institute for the year 2014. The collected data included number and severity of crashes. The data were organized into eight crash contributing factors including: age, age and gender, drivers’ faults, environmental factors, crash time, roadway defects and vehicle defects. First of all, descriptive analysis of the crash contributing factors was done to identify and quantify factors affecting crash severity, then the NBR technique using R-statistic software was used for the development of the crash prediction model that linked crash severities to the identified factors. The NBR model results indicated that severe crashes decreased significantly as the age of both male and female drivers increased. They significantly decreased as the environmental conditions improved. In addition, sever crashes were significantly higher during weekdays than weekends and in the morning than in the evening. The results also indicated that sever crashes significantly increased as drivers have faults while driving. In addition, mirror and brake deficits were found to be the only factors among all possible vehicle deficits factors that contributed significantly to severe crashes. Finally, it was found that the results of the NBR model are in agreement with the descriptive analysis of the crash contributing factors.

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Su, Zhangwen, Haiqing Hu, Mulualem Tigabu, Guangyu Wang, Aicong Zeng, and Futao Guo. "Geographically Weighted Negative Binomial Regression Model Predicts Wildfire Occurrence in the Great Xing’an Mountains Better Than Negative Binomial Model." Forests 10, no. 5 (2019): 377. http://dx.doi.org/10.3390/f10050377.

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Wildfire is a major disturbance that affects large area globally every year. Thus, a better prediction of the likelihood of wildfire occurrence is essential to develop appropriate fire prevention measures. We applied a global negative Binomial (NB) and a geographically weighted negative Binomial regression (GWNBR) models to determine the relationship between wildfire occurrence and its drivers factors in the boreal forests of the Great Xing’an Mountains, northeast China. Using geo-weighted techniques to consider the geospatial information of meteorological, topographic, vegetation type and human factors, we aimed to verify whether the performance of the NB model can be improved. Our results confirmed that the model fitting and predictions of GWNBR model were better than the global NB model, produced more precise and stable model parameter estimation, yielded a more realistic spatial distribution of model predictions, and provided the detection of the impact hotpots of these predictor variables. We found slope, vegetation cover, average precipitation, average temperature, and average relative humidity as important predictors of wildfire occurrence in the Great Xing’an Mountains. Thus, spatially differing relations improves the explanatory power of the global NB model, which does not explain sufficiently the relationship between wildfire occurrence and its drivers. Thus, the GWNBR model can complement the global NB model in overcoming the issue of nonstationary variables, thereby enabling a better prediction of the occurrence of wildfires in large geographical areas and improving management practices of wildfire.

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Purnama, Drajat Indra. "Comparison of Zero Inflated Poisson (ZIP) Regression, Zero Inflated Negative Binomial Regression (ZINB) and Binomial Negative Hurdle Regression (HNB) to Model Daily Cigarette Consumption Data for Adult Population in Indonesia." Jurnal Matematika, Statistika dan Komputasi 17, no. 3 (2021): 357–69. http://dx.doi.org/10.20956/j.v17i3.12278.

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Smoking is a habit that is not good for health. Smoking habits are generally practiced by adults but it is possible for teenagers to do so.The Report of Southeast Asia Tobacco Control Alliance (SEATCA) entitled The Tobacco Control Atlas, ASEAN Region shows that Indonesia is the country with the highest number of smokers in ASEAN, namely 65.19 million people. This figure is equivalent to 34 percent of the total population of Indonesia in 2016. Based on these data, the authors are interested in modeling the daily cigarette consumption data for adults in Indonesia obtained from the 2015 Indonesia Family Life Survey. The variables used include the variable amount of cigarette consumption, education, level of welfare and income per month. The author wants to compare the best model that can be used to model the daily cigarette consumption of adults in Indonesia. The models being compared are Zero Inflated Poisson Regression (ZIP), Zero Inflated Negative Binomial Regression (ZINB) and Binomial Negative Hurdle Regression (HNB). The comparison results of the three models obtained that the best model is the Zero Inflated Negative Binomial (ZINB) Regression model because it has the smallest Akaike's Information Criterion (AIC) value.

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Tran, Phoebe, and Lam Tran. "Validating negative binomial lyme disease regression model with bootstrap resampling." Environmental Modelling & Software 82 (August 2016): 121–27. http://dx.doi.org/10.1016/j.envsoft.2016.04.019.

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Kim, Dong-Seok, Seul-Gi Jeong, and Dong-Hee Lee. "Bivariate Zero-Inflated Negative Binomial Regression Model with Heterogeneous Dispersions." Communications for Statistical Applications and Methods 18, no. 5 (2011): 571–79. http://dx.doi.org/10.5351/ckss.2011.18.5.571.

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Quintanilha, J. A., and L. L. Ho. "Analyzing wildfire threat counts using a negative binomial regression model." Environmetrics 17, no. 6 (2006): 529–38. http://dx.doi.org/10.1002/env.762.

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18

Huang, Jiewu, and Hu Yang. "A two-parameter estimator in the negative binomial regression model." Journal of Statistical Computation and Simulation 84, no. 1 (2012): 124–34. http://dx.doi.org/10.1080/00949655.2012.696648.

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19

Astuti, Cindy Cahyaning, and Angga Dwi Mulyanto. "Estimation Parameters And Modelling Zero Inflated Negative Binomial." CAUCHY 4, no. 3 (2016): 115. http://dx.doi.org/10.18860/ca.v4i3.3656.

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Regression analysis is used to determine relationship between one or several response variable (Y) with one or several predictor variables (X). Regression model between predictor variables and the Poisson distributed response variable is called Poisson Regression Model. Since, Poisson Regression requires an equality between mean and variance, it is not appropriate to apply this model on overdispersion (variance is higher than mean). Poisson regression model is commonly used to analyze the count data. On the count data type, it is often to encounteredd some observations that have zero value with large proportion of zero value on the response variable (zero Inflation). Poisson regression can be used to analyze count data but it has not been able to solve problem of excess zero value on the response variable. An alternative model which is more suitable for overdispersion data and can solve the problem of excess zero value on the response variable is Zero Inflated Negative Binomial (ZINB). In this research, ZINB is applied on the case of Tetanus Neonatorum in East Java. The aim of this research is to examine the likelihood function and to form an algorithm to estimate the parameter of ZINB and also applying ZINB model in the case of Tetanus Neonatorum in East Java. Maximum Likelihood Estimation (MLE) method is used to estimate the parameter on ZINB and the likelihood function is maximized using Expectation Maximization (EM) algorithm. Test results of ZINB regression model showed that the predictor variable have a partial significant effect at negative binomial model is the percentage of pregnant women visits and the percentage of maternal health personnel assisted, while the predictor variables that have a partial significant effect at zero inflation model is the percentage of neonatus visits.

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20

Li, Chin-Shang. "Testing the linearity of negative binomial regression models." Journal of Statistical Computation and Simulation 85, no. 5 (2013): 1013–25. http://dx.doi.org/10.1080/00949655.2013.860138.

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21

Sawalha, Z., and T. Sayed. "Traffic accident modeling: some statistical issues." Canadian Journal of Civil Engineering 33, no. 9 (2006): 1115–24. http://dx.doi.org/10.1139/l06-056.

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Accident prediction models are invaluable tools that have many applications in road safety analysis. However, there are certain statistical issues related to accident modeling that either deserve further attention or have not been dealt with adequately in the road safety literature. This paper discusses and illustrates how to deal with two statistical issues related to modeling accidents using Poisson and negative binomial regression. The first issue is that of model building or deciding which explanatory variables to include in an accident prediction model. The study differentiates between applications for which it is advisable to avoid model over-fitting and other applications for which it is desirable to fit the model to the data as closely as possible. It then suggests procedures for developing parsimonious models, i.e., models that are not over-fitted, and best-fit models. The second issue discussed in the paper is that of outlier analysis. The study suggests a procedure for the identification and exclusion of extremely influential outliers from the development of Poisson and negative binomial regression models. The procedures suggested for model building and conducting outlier analysis are more straightforward to apply in the case of Poisson regression models because of an added complexity presented by the shape parameter of the negative binomial distribution. The paper, therefore, presents flowcharts detailing the application of the procedures when modeling is carried out using negative binomial regression. The described procedures are then applied in the development of negative binomial accident prediction models for the urban arterials of the cities of Vancouver and Richmond located in the province of British Columbia, Canada. Key words: accident prediction models, overfitting, parsimony, outlier analysis, Poisson regression, negative binomial regression.

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22

Liu, Feng, and David Pitt. "Application of bivariate negative binomial regression model in analysing insurance count data." Annals of Actuarial Science 11, no. 2 (2017): 390–411. http://dx.doi.org/10.1017/s1748499517000070.

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AbstractIn this paper we analyse insurance claim frequency data using the bivariate negative binomial regression (BNBR) model. We use general insurance data on claims from simple third-party liability insurance and comprehensive insurance. We find that bivariate regression, with its capacity for modelling correlation between the two observed claim counts, provides both a superior fit and out-of-sample prediction compared with the more common practice of fitting univariate negative binomial regression models separately to each claim type. Noting the complexity of BNBR models and their potential for a large number of parameters, we explore the use of model shrinkage methodology, namely the least absolute shrinkage and selection operator (Lasso) and ridge regression. We find that models estimated using shrinkage methods outperform the ordinary likelihood-based models when being used to make predictions out-of-sample. We find that the Lasso performs better than ridge regression as a method of shrinkage.

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23

Wu, Rongning. "On variance estimation in a negative binomial time series regression model." Journal of Multivariate Analysis 112 (November 2012): 145–55. http://dx.doi.org/10.1016/j.jmva.2012.06.006.

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Shim, Jung-Suk, Dong-Hee Lee, and Byoung-Cheol Jun. "Bayesian Inference for the Zero In ated Negative Binomial Regression Model." Korean Journal of Applied Statistics 24, no. 5 (2011): 951–61. http://dx.doi.org/10.5351/kjas.2011.24.5.951.

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25

Wang, Peiming, and Joseph D. Alba. "A zero-inflated negative binomial regression model with hidden Markov chain." Economics Letters 92, no. 2 (2006): 209–13. http://dx.doi.org/10.1016/j.econlet.2006.02.009.

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Gawdat Yehia, Enas. "Power of Overdispersion Tests in Zero-Truncated Negative Binomial Regression Model." American Journal of Theoretical and Applied Statistics 10, no. 3 (2021): 152. http://dx.doi.org/10.11648/j.ajtas.20211003.13.

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Marliana, Reny Rian. "PENAKSIRAN PENJUALAN PRODUK BERDASARKAN PENDEKATAN MODEL REGRESI NEGATIF BINOMIAL." Prima: Jurnal Pendidikan Matematika 3, no. 1 (2019): 25. http://dx.doi.org/10.31000/prima.v3i1.648.

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AbstrakPenelitian bertujuan untuk membandingkan hasil penaksiran parameter model regresi binomial negative dengan model Poisson untuk underreported counts pada penelitian sebelumnya. Model regresi dibentuk pada data penjualan produk yang mengalami underreporting counts, akibat keterlambatan input data ke aplikasi penjualan produk (sales cycle). Pada penelitian sebelumnya, model yang digunakan merupakan gabungan antara distribusi Binomial dan distribusi Poisson. Parameter model regresi ditaksir menggunakan pendekatan Bayes dan simulasi Markov Chain Monte Carlo melalui Algoritma Gibbs Sampling. Hasil penaksiran menunjukkan adanya perbedaan antara banyaknya penjualan yang dilaporkan dengan banyaknya penjualan produk yang sebenarnya. Besar perbedaan tersebut merupakan banyaknya penjualan produk yang tidak terlaporkan. Pada penelitian lanjutan ini, model yang digunakan adalah Model Regresi Negatif Binomial. Parameter regresi ditaksir menggunakan metode Iterasi Newton Rapson. Hasil penaksiran menunjukkan selisih yang cukup besar dimana model Poisson untuk underreported counts lebih robust sesuai dengan komponen musiman yang ada.Kata Kunci: underreported, generalized poisson, negative binomial AbstractThe goal of study is to compare the parameters of the negative Binomial regression model and the Poisson Model for underreported counts in the previous study. A model is a regression model for the number of product sales that run ito underreporting counts, caused by a delay on input process to the product sales applications (called sales cycle). The model used in the previous study is a mixture of the poisson and the binomial distributions developed by Winkelmann (1996). The regression parameters are estimated by a Bayesian approach and Markov Chain Monte Carlo simulation using Gibbs sampling algorithm. The results show the difference between the actual number and the reported number. This difference is the number of unreported product sales. In this study, the model used is the negative binomial regression model. The regression parameters are estimated using Newton Rapson iteration method. The results show a big gap from the previous study. It means that the Poisson Model for underreported counts is more robust in accordance with the seasonal components.Keywords: underreported, generalized poisson, negative binomial

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Hasebe, Takuya. "Endogenous switching regression model and treatment effects of count-data outcome." Stata Journal: Promoting communications on statistics and Stata 20, no. 3 (2020): 627–46. http://dx.doi.org/10.1177/1536867x20953573.

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In this article, I describe the escount command, which implements the estimation of an endogenous switching model with count-data outcomes, where a potential outcome differs across two alternate treatment statuses. escount allows for either a Poisson or a negative binomial regression model with lognormal latent heterogeneity. After estimating the parameters of the switching regression model, one can estimate various treatment effects with the command teescount. I also describe the command lncount, which fits the Poisson or negative binomial regression model with lognormal latent heterogeneity.

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Ramadhan, Riza F., and Robert Kurniawan. "PEMODELAN DATA KEMATIAN BAYI DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION." MEDIA STATISTIKA 9, no. 2 (2017): 95. http://dx.doi.org/10.14710/medstat.9.2.95-106.

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Overdispersion phenomenon and the influence of location or spatial aspect on data are handled using Binomial Geographically Weighted Regression (GWNBR). GWNBR is the best solution to form a regression analysis that is specific to each observation’s location. The analysis resulted in parameter value which different from one observation to another between location. The Weighting Matrix Selection is done before doing The GWNBR modeling. Different weighting will resulted in different model. Thus this study aims to investigate the best fit model using infant mortality data that is produced by some kind of weighting such as fixed kernel Gaussian, fixed kernel Bisquare, adaptive kernel Gaussian and adaptive kernal Bisquare in GWNBR modeling. This region study covers all the districts/municipalities in Java because the number of observations are more numerous and have more diverse characteristics. The study shows that out of four kernel functions, infant mortality data in Java2012, the best fit model is produced by fixed kernel Gaussian function. Besides that GWNBR with fixed kernel Gaussian also shows better result than the poisson regression and negative binomial regression for data modeling on infant mortality based on the value of AIC and Deviance. Keywords: GWNBR, infant mortality, fixed gaussian, fixed bisquare, adaptive gaussian, adaptive bisquare.

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Gómez, Fidel, and Juan Pablo Bocarejo. "Accident Prediction Models for Bus Rapid Transit Systems." Transportation Research Record: Journal of the Transportation Research Board 2512, no. 1 (2015): 38–45. http://dx.doi.org/10.3141/2512-05.

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This research sought to model traffic accidents in the bus rapid transit (BRT) system in Bogotá, Colombia. For each BRT station, 35 variables related to system flows, infrastructure, service, surroundings, and socio-economic context were tested. After a selection process, a set of 11 explanatory variables was obtained and used in the development of generalized linear models (Poisson and negative binomial models) and a neural network model. The results showed that the neural network model had better predictability indicators than did those obtained by the Poisson and negative binomial models. Additionally, the negative binomial regression model did not produce better predictions than did the Poisson regression model. Finally, a scenario analysis was developed from the most relevant variables: bus flow, number of accesses, and proximity to at-grade vehicular intersections.

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Nam, Yeongeun, Jihyun Seo, Gayeong Choi, and Kyeongjun Lee. "A Study on Shipments of Swimming Crab Using Negative Binomial Regression Model." Korean Data Analysis Society 20, no. 6 (2018): 2941–51. http://dx.doi.org/10.37727/jkdas.2018.20.6.2941.

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Hu, Shou-Ren, Chin-Shang Li, and Chi-Kang Lee. "Model crash frequency at highway–railroad grade crossings using negative binomial regression." Journal of the Chinese Institute of Engineers 35, no. 7 (2012): 841–52. http://dx.doi.org/10.1080/02533839.2012.708527.

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Bond, Simon J., and Vernon T. Farewell. "Likelihood estimation for a longitudinal negative binomial regression model with missing outcomes." Journal of the Royal Statistical Society: Series C (Applied Statistics) 58, no. 3 (2009): 369–82. http://dx.doi.org/10.1111/j.1467-9876.2008.00651.x.

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So, Sunha, Dong-Hee Lee, and Byoung Cheol Jung. "An alternative bivariate zero-inflated negative binomial regression model using a copula." Economics Letters 113, no. 2 (2011): 183–85. http://dx.doi.org/10.1016/j.econlet.2011.07.017.

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Minami, M., C. E. Lennert-Cody, W. Gao, and M. Román-Verdesoto. "Modeling shark bycatch: The zero-inflated negative binomial regression model with smoothing." Fisheries Research 84, no. 2 (2007): 210–21. http://dx.doi.org/10.1016/j.fishres.2006.10.019.

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Lee, Hyeryeong, Wongu Lee, and Hunyoung Jung. "Analysis of Factors Affecting Carsharing Usage through a Negative Binomial Regression Model." Journal of Korea Planning Association 56, no. 3 (2021): 104–12. http://dx.doi.org/10.17208/jkpa.2021.06.56.3.104.

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Wibisono, Fitri Anugerahani, and Eva R. Kurniawati. "MODELING THE NUMBER OF MULTIBACILLARY LEPROSY USING NEGATIVE BINOMIAL REGRESSION TO OVERCOME OVERDISPERSION IN POISSON REGRESSION." Jurnal Biometrika dan Kependudukan 9, no. 2 (2020): 153. http://dx.doi.org/10.20473/jbk.v9i2.2020.153-160.

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Poisson regression is used on discrete data (count) for the formation of the model. There is often a violation in Poisson regression analysis assumptions i.e., overdispersion, which means the average value of the data is smaller than the value of the variance. The number of multibacillary leprosy (MB) in 31 Surabaya districts orderly from 2015 to 2017 has increased as many as 127 cases, 140 cases, and 158 cases. This study aimed to model the number of MB leprosy in Surabaya in 2017 with a Negative Binomial regression in overdispersion. This was quantitative research with a descriptive method that uses secondary data. The data sourced from Surabaya City Health Profile in 2017. The independent variables studied include BCG immunization coverage, the percentage of healthy houses, the percentage of Households with Clean and Healthy Behavior (HCHB), the percentage of the male population, and the population density level. MB leprosy incidence modeling with Poisson regression proved to be overdispersed so that the Negative Binomial regression was used to overcome it. The variable that influenced the MB leprosy incidence with a Negative Binomial regression analysis was the percentage of healthy houses (p = 0.019). MB leprosy occurence will decrease if the percentage of healthy houses increases. The percentage of healthy houses in Surabaya was 86.99%, which increased compared to the previous year with an increase of 1.78%. Public awareness about healthy houses is required to reduce the number of MB leprosy in Surabaya.

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Purnama, D. I. "Model Regresi Hurdle Negative Binomial (HNB) untuk Pemodelan Konsumsi Rokok di Provinsi Sulawesi Tengah." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 18, no. 1 (2021): 21–31. http://dx.doi.org/10.22487/2540766x.2021.v18.i1.15506.

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The average expenditure on cigarettes per capita in Sulawesi Tengah Province has increased in 2020. There are several factors that can affect a person's cigarette consumption including gender, age, education and health. To model cigarette consumption with several influencing factors can be use the poison regression model or the Zero Inflated Poisson (ZIP) model. However, the two regression models cannot solve the excess zero and overdispersion problems so use the Hurdle Negative Binomial (HNB) regression model. The results of the analysis of cigarette consumption data in Central Sulawesi Province using the HNB model provide the best modeling results compared to the poisson regression model and the ZIP model because it has the smallest Akaike's Information Criterion (AIC) value. The results of testing the factors that significantly influence cigarette consumption in Central Sulawesi Province in the HNB regression model, namely the count model are gender, age and health. Whereas in the zerohurdle model, it is gender, age and education.

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Kim, Jeonghwan, and Woojoo Lee. "On testing the hidden heterogeneity in negative binomial regression models." Metrika 82, no. 4 (2018): 457–70. http://dx.doi.org/10.1007/s00184-018-0684-x.

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Lee, Simon CK. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing." Risks 8, no. 1 (2020): 19. http://dx.doi.org/10.3390/risks8010019.

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This study proposes an efficacious approach to analyze the over-dispersed insurance frequency data as it is imperative for the insurers to have decisive informative insights for precisely underwriting and pricing insurance products, retaining existing customer base and gaining an edge in the highly competitive retail insurance market. The delta boosting implementation of the negative binomial regression, both by one-parameter estimation and a novel two-parameter estimation, was tested on the empirical data. Accurate parameter estimation of the negative binomial regression is complicated with considerations of incomplete insurance exposures, negative convexity, and co-linearity. The issues mainly originate from the unique nature of insurance operations and the adoption of distribution outside the exponential family. We studied how the issues could significantly impact the quality of estimation. In addition to a novel approach to simultaneously estimate two parameters in regression through boosting, we further enrich the study by proposing an alteration of the base algorithm to address the problems. The algorithm was able to withstand the competition against popular regression methodologies in a real-life dataset. Common diagnostics were applied to compare the performance of the relevant candidates, leading to our conclusion to move from light-tail Poisson to negative binomial for over-dispersed data, from generalized linear model (GLM) to boosting for non-linear and interaction patterns, from one-parameter to two-parameter estimation to reflect more closely the reality.

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Ver Hoef, Jay M., and Peter L. Boveng. "QUASI-POISSON VS. NEGATIVE BINOMIAL REGRESSION: HOW SHOULD WE MODEL OVERDISPERSED COUNT DATA?" Ecology 88, no. 11 (2007): 2766–72. http://dx.doi.org/10.1890/07-0043.1.

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Kim, Dongseok. "A simple zero inflated bivariate negative binomial regression model with different dispersion parameters." Journal of the Korean Data and Information Science Society 24, no. 4 (2013): 895–900. http://dx.doi.org/10.7465/jkdi.2013.24.4.895.

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Love, Peter E. D., and Pauline Teo. "Statistical Analysis of Injury and Nonconformance Frequencies in Construction: Negative Binomial Regression Model." Journal of Construction Engineering and Management 143, no. 8 (2017): 05017011. http://dx.doi.org/10.1061/(asce)co.1943-7862.0001326.

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Rehder, Kristoffer, and Sarah Bowen. "PTSD Symptom Severity, Cannabis, and Gender: A Zero-Inflated Negative Binomial Regression Model." Substance Use & Misuse 54, no. 8 (2019): 1309–18. http://dx.doi.org/10.1080/10826084.2019.1575421.

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Chai, Tian, De-qi Xiong, and Jinxian Weng. "A Zero-Inflated Negative Binomial Regression Model to Evaluate Ship Sinking Accident Mortalities." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 11 (2018): 65–72. http://dx.doi.org/10.1177/0361198118787388.

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Abstract:

Sinking accidents are a seafarer’s nightmare. Using 10 years’ of worldwide sinking accident data, this study aims to develop a mortality count model to evaluate the human life loss resulting from sinking accidents using zero-inflated negative binomial regression approaches. The model results show that the increase of the expected human life loss is the largest when a ship suffers a precedent accident of capsizing, followed by fire/explosion or collisions. Lower human life loss is associated with contact and machinery/hull damage accidents. Consistent with our expectation, cruise ships involved in sinking accidents usually suffer more human life loss than non-cruise ships and there is be a bigger mortality count for sinking accidents that occur far away from the coastal area/harbor/port. Fatalities can be less when the ship is moored or docked. The results of this study are beneficial for policy-makers in proposing efficient strategies to reduce sinking accident mortalities.

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Månsson, Kristofer. "Developing a Liu estimator for the negative binomial regression model: method and application." Journal of Statistical Computation and Simulation 83, no. 9 (2013): 1773–80. http://dx.doi.org/10.1080/00949655.2012.673127.

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Tzougas, G., W. L. Hoon, and J. M. Lim. "The negative binomial-inverse Gaussian regression model with an application to insurance ratemaking." European Actuarial Journal 9, no. 1 (2018): 323–44. http://dx.doi.org/10.1007/s13385-018-0186-2.

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Yasin, H., I. Suryani, and P. Kartikasari. "Graphical interface of geographically weighted negative binomial regression (GWNBR) model using R-Shiny." Journal of Physics: Conference Series 1943, no. 1 (2021): 012155. http://dx.doi.org/10.1088/1742-6596/1943/1/012155.

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Chen, Jianguo, Lin Liu, Luzi Xiao, Chong Xu, and Dongping Long. "Integrative Analysis of Spatial Heterogeneity and Overdispersion of Crime with a Geographically Weighted Negative Binomial Model." ISPRS International Journal of Geo-Information 9, no. 1 (2020): 60. http://dx.doi.org/10.3390/ijgi9010060.

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Negative binomial (NB) regression model has been used to analyze crime in previous studies. The disadvantage of the NB model is that it cannot deal with spatial effects. Therefore, spatial regression models, such as the geographically weighted Poisson regression (GWPR) model, were introduced to address spatial heterogeneity in crime analysis. However, GWPR could not account for overdispersion, which is commonly observed in crime data. The geographically weighted negative binomial model (GWNBR) was adopted to address spatial heterogeneity and overdispersion simultaneously in crime analysis, based on a 3-year data set collected from ZG city, China, in this study. The count of residential burglaries was used as the dependent variable to calibrate the above models, and the results revealed that the GWPR and GWNBR models performed better than NB for reducing spatial dependency in the model residuals. GWNBR outperformed GWPR for incorporating overdispersion. Therefore, GWNBR was proven to be a promising tool for crime modeling.

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Habeeb Hashim, Luay, and Ahmad Naeem Flaih. "Selecting the best model to fit the Rainfall Count data Using Some Zero Type models with application." Journal of Al-Qadisiyah for computer science and mathematics 11, no. 2 (2019): 28–41. http://dx.doi.org/10.29304/jqcm.2019.11.2.555.

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        28         Counts data models cope with the response variable counts, where the number of times that a certain event occurs in a fixed point is called count data, its observations consists of non-negative integers values {0,1,2,…}. Because of the nature of count data, the response variables are usually considered doing not follow normal distribution. Therefore, linear regression is not an appropriate method to analysis count data due to the skewed distribution. Hence, using linear regression model to analysis count data is likely to bias the results, under these limitations, Poisson regression model and “Negative binomial regression” are likely the appropriate models to analysis count data. Sometimes researchers may Counts more zeros than the expected. Count data with many Zeros leads to a concept called “Zero-inflation”. Data with abundant zeros are especially popular in health, marketing, finance, econometric, ecology, statistics quality control, geographical, and environmental fields when counting the occurrence of certain behavioral and natural events, such as frequency of alcohol use, take drugs, number of cigarettes smoked, the occurrence of earthquakes, rainfall, and etc. Some models have been used to analyzing count data such as the “zero- altered Poisson” (ZAP) model and the “negative binomial” model. In this paper, the models, Poisson, Negative Binomial, ZAP, and ZANB were been used to analyze rainfall data.

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