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Journal articles on the topic 'Zero-inflated Poisson model'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Lim, Hwa Kyung, Wai Keung Li, and Philip L. H. Yu. "Zero-inflated Poisson regression mixture model." Computational Statistics & Data Analysis 71 (March 2014): 151–58. http://dx.doi.org/10.1016/j.csda.2013.06.021.

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2

Tang, Yi, and Wan Tang. "Testing modified zeros for Poisson regression models." Statistical Methods in Medical Research 28, no. 10-11 (2018): 3123–41. http://dx.doi.org/10.1177/0962280218796253.

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Excessive zeros are common in practice and may cause overdispersion and invalidate inferences when fitting Poisson regression models. Zero-inflated Poisson regression models may be applied if there are inflated zeros; however, it is desirable to test if there are inflated zeros before such zero-inflated Poisson models are applied. Assuming a constant probability of being a structural zero in a zero-inflated Poisson regression model, the existence of the inflated zeros may be tested by testing whether the constant probability is zero. In such situations, the Wald, score, and likelihood ratio tests can be applied. Without specifying a zero-inflated Poisson model, He et al. recently developed a test by comparing the amount of observed zeros with that expected under the Poisson model. In this paper, we develop a closed form for the test and compare it with the Wald, score, and likelihood ratio tests through simulation studies. The simulation studies show that the test of He et al. is the best in controlling type I errors, while the score test generally has the least power among the tests. The tests are illustrated with two real data examples.

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3

Cheung, Yin Bun, and K. F. Lam. "Bivariate Poisson–Poisson model of zero-inflated absenteeism data." Statistics in Medicine 25, no. 21 (2006): 3707–17. http://dx.doi.org/10.1002/sim.2485.

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4

Lee, Ji-Ho, Tae-Ryon Choi, and Yoon-Sung Wo. "Bayesian Approaches to Zero Inflated Poisson Model." Korean Journal of Applied Statistics 24, no. 4 (2011): 677–93. http://dx.doi.org/10.5351/kjas.2011.24.4.677.

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5

Kassahun, Wondwosen, Thomas Neyens, Christel Faes, Geert Molenberghs, and Geert Verbeke. "A zero-inflated overdispersed hierarchical Poisson model." Statistical Modelling: An International Journal 14, no. 5 (2014): 439–56. http://dx.doi.org/10.1177/1471082x14524676.

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6

Yang, Jun, and Xin Zhang. "Zero-Inflated Poisson Model with Group Data." Advanced Materials Research 569 (September 2012): 627–31. http://dx.doi.org/10.4028/www.scientific.net/amr.569.627.

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The Zero-inflated Poisson model has been widely used in many fields for count data with excessive zeroes. In fact, group data are often collected for many count data, such as cigarette consumption. In order to solve the problem, Zero-inflated Poisson model with group data is investigated in this paper. Parameter estimation is given by the maximum likelihood estimate, model selection is discussed by the Chi-square test, and one real example is given for application in the end.

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7

Akbarzadeh Baghban, Alireza, Asma Pourhoseingholi, Farid Zayeri, Ali Akbar Jafari, and Seyed Moayed Alavian. "Application of Zero-Inflated Poisson Mixed Models in Prognostic Factors of Hepatitis C." BioMed Research International 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/403151.

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Background and Objectives. In recent years, hepatitis C virus (HCV) infection represents a major public health problem. Evaluation of risk factors is one of the solutions which help protect people from the infection. This study aims to employ zero-inflated Poisson mixed models to evaluate prognostic factors of hepatitis C.Methods. The data was collected from a longitudinal study during 2005–2010. First, mixed Poisson regression (PR) model was fitted to the data. Then, a mixed zero-inflated Poisson model was fitted with compound Poisson random effects. For evaluating the performance of the proposed mixed model, standard errors of estimators were compared.Results. The results obtained from mixed PR showed that genotype 3 and treatment protocol were statistically significant. Results of zero-inflated Poisson mixed model showed that age, sex, genotypes 2 and 3, the treatment protocol, and having risk factors had significant effects on viral load of HCV patients. Of these two models, the estimators of zero-inflated Poisson mixed model had the minimum standard errors.Conclusions. The results showed that a mixed zero-inflated Poisson model was the almost best fit. The proposed model can capture serial dependence, additional overdispersion, and excess zeros in the longitudinal count data.

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8

Tawiah, Kassim, Wahab Abdul Iddrisu, and Killian Asampana Asosega. "Zero-Inflated Time Series Modelling of COVID-19 Deaths in Ghana." Journal of Environmental and Public Health 2021 (April 30, 2021): 1–9. http://dx.doi.org/10.1155/2021/5543977.

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Discrete count time series data with an excessive number of zeros have warranted the development of zero-inflated time series models to incorporate the inflation of zeros and the overdispersion that comes with it. In this paper, we investigated the characteristics of the trend of daily count of COVID-19 deaths in Ghana using zero-inflated models. We envisaged that the trend of COVID-19 deaths per day in Ghana portrays a general increase from the onset of the pandemic in the country to about day 160 after which there is a general decrease onward. We fitted a zero-inflated Poisson autoregressive model and zero-inflated negative binomial autoregressive model to the data in the partial-likelihood framework. The zero-inflated negative binomial autoregressive model outperformed the zero-inflated Poisson autoregressive model. On the other hand, the dynamic zero-inflated Poisson autoregressive model performed better than the dynamic negative binomial autoregressive model. The predicted new death based on the zero-inflated negative binomial autoregressive model indicated that Ghana’s COVID-19 death per day will rise sharply few days after 30th November 2020 and drastically fall just as in the observed data.

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9

He, Hua, Hui Zhang, Peng Ye, and Wan Tang. "A test of inflated zeros for Poisson regression models." Statistical Methods in Medical Research 28, no. 4 (2017): 1157–69. http://dx.doi.org/10.1177/0962280217749991.

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Excessive zeros are common in practice and may cause overdispersion and invalidate inference when fitting Poisson regression models. There is a large body of literature on zero-inflated Poisson models. However, methods for testing whether there are excessive zeros are less well developed. The Vuong test comparing a Poisson and a zero-inflated Poisson model is commonly applied in practice. However, the type I error of the test often deviates seriously from the nominal level, rendering serious doubts on the validity of the test in such applications. In this paper, we develop a new approach for testing inflated zeros under the Poisson model. Unlike the Vuong test for inflated zeros, our method does not require a zero-inflated Poisson model to perform the test. Simulation studies show that when compared with the Vuong test our approach not only better at controlling type I error rate, but also yield more power.

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10

Purhadi, Yuliani Setia Dewi, and Luthfatul Amaliana. "Zero Inflated Poisson and Geographically Weighted Zero- Inflated Poisson Regression Model: Application to Elephantiasis (Filariasis) Counts Data." Journal of Mathematics and Statistics 11, no. 2 (2015): 52–60. http://dx.doi.org/10.3844/jmssp.2015.52.60.

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11

Han, Bo, and Jian Xu. "Analysis of Crash Counts Using a Multilevel Zero-Inflated Negative Binomial Model." Advanced Materials Research 912-914 (April 2014): 1164–68. http://dx.doi.org/10.4028/www.scientific.net/amr.912-914.1164.

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Due to that roadway crashes are generally discrete and rare, researchers frequently have several observational units (e.g., census tract, segment) with excess zeros reported crashes during the period. In this study, a multilevel zero-inflated negative binomial (MZINB) model was developed for analysis, allowing for overdispersion and excess zeros, as well as the factors of roadway design and traffic characteristic. Several goodness-of-fit measures are used for examining and comparing, using Markov chain Monte Carlo (MCMC) methods. The estimation results show that MZINB model is better than multilevel zero-inflated Poisson (MZIP) model and zero-inflated negative binomial (ZINB) and zero-inflated Poisson (ZIP) models.

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12

vel, K. M. Sakthi, and C. S. Raji tha. "Estimation of Zero-Inflation Parameter in Zero-Inflated Poisson Model." International Journal of Mathematics Trends and Technology 56, no. 2 (2018): 135–40. http://dx.doi.org/10.14445/22315373/ijmtt-v56p519.

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13

Yang, Zhao, James W. Hardin, and Cheryl L. Addy. "Testing overdispersion in the zero-inflated Poisson model." Journal of Statistical Planning and Inference 139, no. 9 (2009): 3340–53. http://dx.doi.org/10.1016/j.jspi.2009.03.016.

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14

Xie, M., B. He, and T. N. Goh. "Zero-inflated Poisson model in statistical process control." Computational Statistics & Data Analysis 38, no. 2 (2001): 191–201. http://dx.doi.org/10.1016/s0167-9473(01)00033-0.

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15

Bohara, Alok K., and Randall G. Krieg. "A Zero-inflated Poisson Model of Migration Frequency." International Regional Science Review 19, no. 3 (1996): 211–22. http://dx.doi.org/10.1177/016001769601900302.

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16

Muniswamy, B., Dejen Tesfaw Molla, and N. Konda Reddy. "Comparison of Test Statistic for Zero-Inflated Negative Binomial against Zero-Inflated Poisson Model." Indian Journal of Science and Technology 8, no. 4 (2015): 349. http://dx.doi.org/10.17485/ijst/2015/v8i1/59610.

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17

Muniswamy, B. "Comparison of Test Statistic for Zero-Inflated Negative Binomial against Zero-Inflated Poisson Model." Indian Journal of Science and Technology 8, no. 1 (2015): 349–57. http://dx.doi.org/10.17485/ijst/2015/v8i4/59610.

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18

Dzupire, Nelson Christopher, Philip Ngare, and Leo Odongo. "A Poisson-Gamma Model for Zero Inflated Rainfall Data." Journal of Probability and Statistics 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/1012647.

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Rainfall modeling is significant for prediction and forecasting purposes in agriculture, weather derivatives, hydrology, and risk and disaster preparedness. Normally two models are used to model the rainfall process as a chain dependent process representing the occurrence and intensity of rainfall. Such two models help in understanding the physical features and dynamics of rainfall process. However rainfall data is zero inflated and exhibits overdispersion which is always underestimated by such models. In this study we have modeled the two processes simultaneously as a compound Poisson process. The rainfall events are modeled as a Poisson process while the intensity of each rainfall event is Gamma distributed. We minimize overdispersion by introducing the dispersion parameter in the model implemented through Tweedie distributions. Simulated rainfall data from the model shows a resemblance of the actual rainfall data in terms of seasonal variation, means, variance, and magnitude. The model also provides mechanisms for small but important properties of the rainfall process. The model developed can be used in forecasting and predicting rainfall amounts and occurrences which is important in weather derivatives, agriculture, hydrology, and prediction of drought and flood occurrences.

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19

Mohammadi, Tayeb, Soleiman Kheiri, and Morteza Sedehi. "Analysis of Blood Transfusion Data Using Bivariate Zero-Inflated Poisson Model: A Bayesian Approach." Computational and Mathematical Methods in Medicine 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7878325.

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Recognizing the factors affecting the number of blood donation and blood deferral has a major impact on blood transfusion. There is a positive correlation between the variables “number of blood donation” and “number of blood deferral”: as the number of return for donation increases, so does the number of blood deferral. On the other hand, due to the fact that many donors never return to donate, there is an extra zero frequency for both of the above-mentioned variables. In this study, in order to apply the correlation and to explain the frequency of the excessive zero, the bivariate zero-inflated Poisson regression model was used for joint modeling of the number of blood donation and number of blood deferral. The data was analyzed using the Bayesian approach applying noninformative priors at the presence and absence of covariates. Estimating the parameters of the model, that is, correlation, zero-inflation parameter, and regression coefficients, was done through MCMC simulation. Eventually double-Poisson model, bivariate Poisson model, and bivariate zero-inflated Poisson model were fitted on the data and were compared using the deviance information criteria (DIC). The results showed that the bivariate zero-inflated Poisson regression model fitted the data better than the other models.

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20

Thavaneswaran, Aerambamoorthy, Saumen Mandal, and Dharini Pathmanathan. "Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions." International Journal of Statistics and Probability 5, no. 3 (2016): 1. http://dx.doi.org/10.5539/ijsp.v5n3p1.

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There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

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21

Lee, JungBok, Byoung Cheol Jung, and Seo Hoon Jin. "Tests for zero inflation in a bivariate zero-inflated Poisson model." Statistica Neerlandica 63, no. 4 (2009): 400–417. http://dx.doi.org/10.1111/j.1467-9574.2009.00430.x.

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22

Angers, Jean-François, and Atanu Biswas. "A Bayesian analysis of zero-inflated generalized Poisson model." Computational Statistics & Data Analysis 42, no. 1-2 (2003): 37–46. http://dx.doi.org/10.1016/s0167-9473(02)00154-8.

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23

Gupta, Pushpa Lata, Ramesh C. Gupta, and Ram C. Tripathi. "Score Test for Zero Inflated Generalized Poisson Regression Model." Communications in Statistics - Theory and Methods 33, no. 1 (2005): 47–64. http://dx.doi.org/10.1081/sta-120026576.

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24

Zhao, Weihua, Riquan Zhang, Jicai Liu, and Yazhao Lv. "Semi Varying Coefficient Zero-Inflated Generalized Poisson Regression Model." Communications in Statistics - Theory and Methods 44, no. 1 (2014): 171–85. http://dx.doi.org/10.1080/03610926.2012.735325.

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25

Zhang, Chi, Guo-Liang Tian, Kam Chuen Yuen, Qin Wu, and Tao Li. "Multivariate zero-and-one inflated Poisson model with applications." Journal of Computational and Applied Mathematics 365 (February 2020): 112356. http://dx.doi.org/10.1016/j.cam.2019.112356.

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26

Ye, Peng, Wan Tang, Jiang He, and Hua He. "A GEE-type approach to untangle structural and random zeros in predictors." Statistical Methods in Medical Research 28, no. 12 (2018): 3683–96. http://dx.doi.org/10.1177/0962280218812228.

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Count outcomes with excessive zeros are common in behavioral and social studies, and zero-inflated count models such as zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) can be applied when such zero-inflated count data are used as response variable. However, when the zero-inflated count data are used as predictors, ignoring the difference of structural and random zeros can result in biased estimates. In this paper, a generalized estimating equation (GEE)-type mixture model is proposed to jointly model the response of interest and the zero-inflated count predictors. Simulation studies show that the proposed method performs well for practical settings and is more robust for model misspecification than the likelihood-based approach. A case study is also provided for illustration.

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27

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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28

Yusuf, Oyindamola B., Rotimi Felix Afolabi, and Ayoola S. Ayoola. "Modelling Excess Zeros in Count Data with Application to Antenatal Care Utilisation." International Journal of Statistics and Probability 7, no. 3 (2018): 22. http://dx.doi.org/10.5539/ijsp.v7n3p22.

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Poisson and negative binomial regression models have been used as a standard for modelling count outcomes; but these methods do not take into account the problems associated with excess zeros. However, zero-inflated and hurdle models have been proposed to model count data with excess zeros. The study therefore compared the performance of Zero-inflated (Zero-inflated Poisson (ZIP) and Zero-inflated negative binomial (ZINB)), and hurdle (Hurdle Poisson (HP) and Hurdle negative binomial (HNB)) models in determining the factors associated with the number of Antenatal Care (ANC) visits in Nigeria. Using the 2013 Nigeria Demographic and Health Survey dataset, a sample of 19 652 women of reproductive age who gave birth five years prior to the survey and provided information about ANC visits was utilised. Data were analysed using descriptive statistics, ZIP, ZINB, HP and HNB models, and information criteria (AIC/BIC) was used to assess model fit. Participants’ mean age was 29.5 ± 7.3 years and median number of ANC visits was 4 (range: 0 - 30). About half (54.9%) of the participants had at least 4 ANC visits while 33.9% had none. The ZINB (AIC = 83 039.4; BIC = 83 470.3) fitted the data better than the ZIP or HP; however, HNB (AIC = 83 041.4; BIC = 83 472.3) competed favorably well with it. The Zero-inflated negative binomial model provided the better fit for the data. We suggest the Zero-inflated negative binomial model for count data with excess zeros of unknown sources such as the number of ANC visits in Nigeria.

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29

Li, Qiuya, Geoffrey KF Tso, Yichen Qin, Travis I. Lovejoy, Timothy G. Heckman, and Yang Li. "Penalized multiple inflated values selection method with application to SAFER data." Statistical Methods in Medical Research 28, no. 10-11 (2018): 3205–25. http://dx.doi.org/10.1177/0962280218797148.

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Expanding on the zero-inflated Poisson model, the multiple-inflated Poisson model is applied to analyze count data with multiple inflated values. The existing studies on the multiple-inflated Poisson model determined the inflated values by inspecting the histogram of count response and fitting the model with different combinations of inflated values, which leads to relatively complicated computations and may overlook some real inflated points. We address a two-stage inflated values selection method, which takes all values of count response as potential inflated values and adopts the adaptive lasso regularization on the mixing proportion of those values. Numerical studies demonstrate the excellent performance both on inflated values selection and parameters estimation. Moreover, a specially designed simulation, based on the structure of data from a randomized clinical trial of an HIV sexual risk education intervention, performs well and ensures our method could be generalized to the real situation. An empirical analysis of a clinical trial dataset is used to elucidate the multiple-inflated Poisson model.

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30

Brobbey, Anita, Aerambamoorthy Thavaneswaran, and Saumen Mandal. "Wrapped Zero-inflated Poisson Distribution and Its Properties." International Journal of Statistics and Probability 5, no. 1 (2015): 111. http://dx.doi.org/10.5539/ijsp.v5n1p111.

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Recently, there has been a growing interest in discrete valued wrapped distributions and the trigonometric moments.<br />Characteristic functions of stable processes have been used to study the estimation of the model parameters using<br />estimating function approach (Thavaneswaran et al., 2013). In this paper, we introduce a new discrete circular distribution,<br />the wrapped zero-inflated Poisson distribution and derive its population characteristics.<br /><br />

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31

Zuo, Guoxin, Kang Fu, Xianhua Dai, and Liwei Zhang. "Generalized Poisson Hurdle Model for Count Data and Its Application in Ear Disease." Entropy 23, no. 9 (2021): 1206. http://dx.doi.org/10.3390/e23091206.

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For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

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32

Nanjundan, G., and Sadiq Pasha. "A Note on the Characterization of Zero-Inflated Poisson Model." Open Journal of Statistics 05, no. 02 (2015): 140–42. http://dx.doi.org/10.4236/ojs.2015.52017.

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33

Liu, Wenchen, Yincai Tang, and Ancha Xu. "A zero-and-one inflated Poisson model and its application." Statistics and Its Interface 11, no. 2 (2018): 339–51. http://dx.doi.org/10.4310/sii.2018.v11.n2.a11.

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34

Tennekoon, Vidhura. "Counting unreported abortions: A binomial-thinned zero-inflated Poisson model." Demographic Research 36 (January 4, 2017): 41–72. http://dx.doi.org/10.4054/demres.2017.36.2.

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35

Dagne, Getachew A. "Bayesian semiparametric zero-inflated Poisson model for longitudinal count data." Mathematical Biosciences 224, no. 2 (2010): 126–30. http://dx.doi.org/10.1016/j.mbs.2010.01.004.

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36

Leann Long, D., John S. Preisser, Amy H. Herring, and Carol E. Golin. "A marginalized zero-inflated Poisson regression model with random effects." Journal of the Royal Statistical Society: Series C (Applied Statistics) 64, no. 5 (2015): 815–30. http://dx.doi.org/10.1111/rssc.12104.

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37

Jiang, Mengmeng, and Hang Zhang. "Sparse estimation in high-dimensional zero-inflated Poisson regression model." Journal of Physics: Conference Series 1053 (July 2018): 012128. http://dx.doi.org/10.1088/1742-6596/1053/1/012128.

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38

Rathbun, Stephen L., and Songlin Fei. "A spatial zero-inflated poisson regression model for oak regeneration." Environmental and Ecological Statistics 13, no. 4 (2006): 409–26. http://dx.doi.org/10.1007/s10651-006-0020-x.

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39

Faroughi, Pouya, and Noriszura Ismail. "Bivariate zero-inflated generalized Poisson regression model with flexible covariance." Communications in Statistics - Theory and Methods 46, no. 15 (2017): 7769–85. http://dx.doi.org/10.1080/03610926.2016.1165846.

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40

Kibria, B. M. Golam, Kristofer Månsson, and Ghazi Shukur. "Some ridge regression estimators for the zero-inflated Poisson model." Journal of Applied Statistics 40, no. 4 (2013): 721–35. http://dx.doi.org/10.1080/02664763.2012.752448.

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41

Zamani, Hossein, and Noriszura Ismail. "Functional Form for the Zero-Inflated Generalized Poisson Regression Model." Communications in Statistics - Theory and Methods 43, no. 3 (2014): 515–29. http://dx.doi.org/10.1080/03610926.2012.665553.

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42

Ridout, Martin, John Hinde, and Clarice G. B. Demétrio. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives." Biometrics 57, no. 1 (2001): 219–23. http://dx.doi.org/10.1111/j.0006-341x.2001.00219.x.

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43

Alam, Morshed, Naim Al Mahi, and Munni Begum. "Zero-Inflated Models for RNA-Seq Count Data." Journal of Biomedical Analytics 1, no. 2 (2018): 55–70. http://dx.doi.org/10.30577/jba.2018.v1n2.23.

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One of the main objectives of many biological studies is to explore differential gene expression profiles between samples. Genes are referred to as differentially expressed (DE) if the read counts change across treatments or conditions systematically. Poisson and negative binomial (NB) regressions are widely used methods for non-over-dispersed (NOD) and over-dispersed (OD) count data respectively. However, in the presence of excessive number of zeros, these methods need adjustments. In this paper, we consider a zero-inflated Poisson mixed effects model (ZIPMM) and zero-inflated negative binomial mixed effects model (ZINBMM) to address excessive zero counts in the NOD and OD RNA-seq data respectively in the presence of random effects. We apply these methods to both simulated and real RNA-seq datasets. The ZIPMM and ZINBMM perform better on both simulated and real datasets.

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Oritogun, Kolawole S., and Elijah A. Bamgboye. "Robustness of Poisson Mixture models in identifying risk factors for Under-Five mortality in Nigeria." Annals of Health Research 4, no. 2 (2018): 141–54. http://dx.doi.org/10.30442/ahr.0402-6-17.

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Background: Estimates of Under-Five mortality (U5M) have taken advantage of indirect methods but U5M risk factors have been identified using fixed statistical models with little considerations for the potentials of mixture models. Mixture models such as Poisson-Mixture models exhibit flexibility tendency, which is an attribute of robustness lacking in fixed models. Objective: To examine the robustness of Poisson-Mixture models in identifying reliable determinants of U5M. Methods: The data on 18,855 women used in this study were obtained from the 2008 Nigeria Demographic and Health Survey (NDHS). Six different Poisson-Mixture models namely: Poisson (PO), Zero-Inflated Poisson (ZIP), Poisson Hurdle (PH), Negative Binomial (NBI), Zero-Inflated Negative Binomial (ZINBI) and Negative Binomial Hurdle (NBIH) were fitted separately to the data. The Akaike Information Criteria (AIC) and diagnostic check for normality were used to select robust models. All tests were conducted at p = 0.05. Results: The models and AIC values for U5M were: 38763.47 (PO), 38654.55 (ZIP), 44270.77 (PH), 38526.26 (NBI), 38513.71 (ZINBI) and 44269.30 (NBIH). The PO, ZIP, PH and NBIH met normality test criteria, and the ZIP model was of best fit. The model identified breastfeeding, paternal education, toilet type, maternal education, place of delivery, birth-order and antenatal-visits as significant determinants of U5M at the national level. Conclusion: The Zero-Inflated Poisson model provided the best robust estimates of Under-five Mortality in Nigeria, while maternal education and birth-order were identified as the most important determinants. The Poisson-mixture models are recommended for modelling Under-five Mortality in Nigeria.

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Eminita, Viarti, Anang Kurnia, and Kusman Sadik. "PENANGANAN OVERDISPERSI PADA PEMODELAN DATA CACAH DENGAN RESPON NOL BERLEBIH (ZERO-INFLATED)." FIBONACCI: Jurnal Pendidikan Matematika dan Matematika 5, no. 1 (2019): 71. http://dx.doi.org/10.24853/fbc.5.1.71-80.

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Overdispersi pada data cacah yang disebabkan karena kasus nol berlebih tidak dapat ditangani dengan metode model linier umum biasa seperti Poisson dan Binomial Negatif. Penanganan overdispersi karena nol berlebih dapat dilakukan dengan menggunakan model Zero-Inflated. Zero-Inflated Poisson (ZIP) dan Zero-Inflated Binomial Negatif (ZIBN) telah diyakini performanya dalam menangani masalah ini. Selain menangani masalah tersebut kedua model ini juga dapat memberikan informasi mengenai penyebab nol berlebih pada data respon. Performa ke Empat model tersebut dibandingkan dalam menduga model dari jumlah anak yang tidak sekolah dalam keluarga di Provinsi Jawa Barat pada tahun 2017. Berdasarkan nilai dari ukuran Pearson Chi-Squares, Likelihood Ratio Chi-Square, dan Akaike Information Crieteria (AIC). Pearson Chi-Squares, model ZIP lebih baik dibandingkan ZIBN dan model lainnya, walaupun berbeda sedikit dengan ZIBN.

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LEE, J. H., G. HAN, W. J. FULP, and A. R. GIULIANO. "Analysis of overdispersed count data: application to the Human Papillomavirus Infection in Men (HIM) Study." Epidemiology and Infection 140, no. 6 (2011): 1087–94. http://dx.doi.org/10.1017/s095026881100166x.

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SUMMARYThe Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.

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Philp, Fraser, Ahmad Al-shallawi, Theocharis Kyriacou, Dimitra Blana, and Anand Pandyan. "Improving predictor selection for injury modelling methods in male footballers." BMJ Open Sport & Exercise Medicine 6, no. 1 (2020): e000634. http://dx.doi.org/10.1136/bmjsem-2019-000634.

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ObjectivesThis objective of this study was to evaluate whether combining existing methods of elastic net for zero-inflated Poisson and zero-inflated Poisson regression methods could improve real-life applicability of injury prediction models in football.MethodsPredictor selection and model development was conducted on a pre-existing dataset of 24 male participants from a single English football team’s 2015/2016 season.ResultsThe elastic net for zero-inflated Poisson penalty method was successful in shrinking the total number of predictors in the presence of high levels of multicollinearity. It was additionally identified that easily measurable data, that is, mass and body fat content, training type, duration and surface, fitness levels, normalised period of ‘no-play’ and time in competition could contribute to the probability of acquiring a time-loss injury. Furthermore, prolonged series of match-play and increased in-season injury reduced the probability of not sustaining an injury.ConclusionFor predictor selection, the elastic net for zero-inflated Poisson penalised method in combination with the use of ZIP regression modelling for predicting time-loss injuries have been identified appropriate methods for improving real-life applicability of injury prediction models. These methods are more appropriate for datasets subject to multicollinearity, smaller sample sizes and zero-inflation known to affect the performance of traditional statistical methods. Further validation work is now required.

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Song, Chao, Yaqian He, Yanchen Bo, Jinfeng Wang, Zhoupeng Ren, and Huibin Yang. "Risk Assessment and Mapping of Hand, Foot, and Mouth Disease at the County Level in Mainland China Using Spatiotemporal Zero-Inflated Bayesian Hierarchical Models." International Journal of Environmental Research and Public Health 15, no. 7 (2018): 1476. http://dx.doi.org/10.3390/ijerph15071476.

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Hand, foot, and mouth disease (HFMD) is a worldwide infectious disease, prominent in China. China’s HFMD data are sparse with a large number of observed zeros across locations and over time. However, no previous studies have considered such a zero-inflated problem on HFMD’s spatiotemporal risk analysis and mapping, not to mention for the entire Mainland China at county level. Monthly county-level HFMD cases data combined with related climate and socioeconomic variables were collected. We developed four models, including spatiotemporal Poisson, negative binomial, zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) models under the Bayesian hierarchical modeling framework to explore disease spatiotemporal patterns. The results showed that the spatiotemporal ZINB model performed best. Both climate and socioeconomic variables were identified as significant risk factors for increasing HFMD incidence. The relative risk (RR) of HFMD at the local scale showed nonlinear temporal trends and was considerably spatially clustered in Mainland China. The first complete county-level spatiotemporal relative risk maps of HFMD were generated by this study. The new findings provide great potential for national county-level HFMD prevention and control, and the improved spatiotemporal zero-inflated model offers new insights for epidemic data with the zero-inflated problem in environmental epidemiology and public health.

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Asmarian, Naeimehossadat, Seyyed Mohammad Taghi Ayatollahi, Zahra Sharafi, and Najaf Zare. "Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran." International Journal of Environmental Research and Public Health 16, no. 22 (2019): 4460. http://dx.doi.org/10.3390/ijerph16224460.

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Hierarchical Bayesian log-linear models for Poisson-distributed response data, especially Besag, York and Mollié (BYM) model, are widely used for disease mapping. In some cases, due to the high proportion of zero, Bayesian zero-inflated Poisson models are applied for disease mapping. This study proposes a Bayesian spatial joint model of Bernoulli distribution and Poisson distribution to map disease count data with excessive zeros. Here, the spatial random effect is simultaneously considered into both logistic and log-linear models in a Bayesian hierarchical framework. In addition, we focus on the BYM2 model, a re-parameterization of the common BYM model, with penalized complexity priors for the latent level modeling in the joint model and zero-inflated Poisson models with different type of zeros. To avoid model fitting and convergence issues, Bayesian inferences are implemented using the integrated nested Laplace approximation (INLA) method. The models are compared according to the deviance information criterion and the logarithmic scoring. A simulation study with different proportions of zero exhibits INLA ability in running the models and also shows slight differences between the popular BYM and BYM2 models in terms of model choice criteria. In an application, we apply the fitting models on male breast cancer data in Iran at county level in 2014.

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Pho, Kim-Hung, and Buu-Chau Truong. "Comparison of the Performance of the Gradient and Newton-Raphson Method to Estimate Parameters in Some Zero-Inflated Regression Models." Journal of Advanced Engineering and Computation 4, no. 4 (2020): 227. http://dx.doi.org/10.25073/jaec.202044.297.

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This paper compares the performance of the gradient and Newton-Raphson (N-R) method to estimate parameters in some zero-inflated (ZI) regression models such as the zero-inflated Poisson (ZIP) model, zero-inflated Bell (ZIBell) model, zero-inflated binomial (ZIB) model and zero-inflated negative binomial (ZINB) model. In the present work, firstly, we briefly present the approach of the gradient and N-R method. We then introduce the origin, formulas and applications of the ZI models. Finally, we compare the performance of two investigated approaches for these models through the simulation studies with numerous sample sizes and several missing rates. A real data set is investigated in this study. Specifically, we compare the results and the execution time of the R code for two methods. Moreover, we provide some important notes on these two approaches and some scalable research directions for future work.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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