Journal articles: 'Zero inflated poisson regression'

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Jeong, Kwang Mo. "A Study on Tests for Zero-Inflated Poisson Regression." Korean Data Analysis Society 21, no. 6 (2019): 2737–49. http://dx.doi.org/10.37727/jkdas.2019.21.6.2737.

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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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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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Famoye, Felix, and John S. Preisser. "Marginalized zero-inflated generalized Poisson regression." Journal of Applied Statistics 45, no. 7 (2017): 1247–59. http://dx.doi.org/10.1080/02664763.2017.1364717.

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Lee, Dong-Hee, and Byoung Cheol Jung. "A Study on the Effect of Dispersion Parameter in a Zero-inflated Generalized Poisson Regression Model." Korean Data Analysis Society 27, no. 1 (2025): 105–15. https://doi.org/10.37727/jkdas.2025.27.1.105.

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In this study, we examine the influence of overdispersion on statistical inference in a zero-inflated generalized Poisson regression model by simulation experiments and real data analysis. In the simulation study, simulated data are generated from the zero-inflated generalized Poisson regression model, and the regression coefficients in the zero-inflated Poisson regression and the zero-inflated generalized Poisson regression models are estimated. The simulation experiment results show that the regression coefficient estimates for the mean and zero-inflation probability of the zero-inflated Poisson regression to ignore overdispersion underestimate the true value when overdispersion exists, and this underestimation problem becomes more severe as the overdispersion increases. In addition, the standard errors of the regression coefficient estimates of the zero-inflated Poisson regression model are more underestimated as the overdispersion increased. Ultimately, the zero-inflated Poisson regression model, which ignores the overdispersion despite its existence, shows a larger nominal significance level in the hypothesis test for the true value of the regression coefficient, and this problem of the nominal significance level becomes more severe as the overdispersion increased. The results of this simulation experiment could be confirmed through the analysis of real data on the number of boat trips to Lake Somerville in eastern Texas in the United States in 1980.

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Zamani, Hossein, and Noriszura Ismail. "Score test for testing zero-inflated Poisson regression against zero-inflated generalized Poisson alternatives." Journal of Applied Statistics 40, no. 9 (2013): 2056–68. http://dx.doi.org/10.1080/02664763.2013.804904.

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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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Azad, Abdulhafedh. "Incorporating Zero-Inflated Poisson (ZIP) Regression Model in Crash Frequency Analysis." International Journal of Novel Research in Interdisciplinary Studies 10, no. 1 (2023): 6–18. https://doi.org/10.5281/zenodo.7632596.

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Abstract: This paper addresses the Zero-inflated Poisson (ZIP) regression model as an effective way to handle the excess zeros that usually exist in vehicle crash data and to allow for possible overdispersion in the data. The ZIP model is based on a zero-inflated probability distribution, that allows for frequent zero-valued observations. When the number of zeros is large that the data do not fit standard distributions (e.g., normal, Poisson, binomial, negative-binomial, and beta), the data is referred to as zero inflated. A dual state crash system is assumed in the ZIP model, in which one state is the zero crash state that can be regarded as virtually safe during the observation period, while the other state is the non-zero crash state. This paper starts by applying a multiple linear regression model, a Poisson regression model, a Negative Binomial regression model and then introduces the ZIP model to analyze the 2013-2015 crash data for the Interstate I-94 in the State of Minnesota in the US. Results show that the ZIP model overperformed the other models by fitting the crash data much better and was able to capture almost all the independent variables in the model and make them statistically significant in the analysis after being insignificant by the other models. Keywords: Zero-Inflated Poisson Regression, ZIP model, Crash Frequency, Multiple Linear Regression, Poisson Regression, Negative Binomial Regression. Title: Incorporating Zero-Inflated Poisson (ZIP) Regression Model in Crash Frequency Analysis Author: Azad Abdulhafedh International Journal of Novel Research in Interdisciplinary Studies ISSN 2394-9716 Vol. 10, Issue 1, January 2023 - February 2023 Page No: 6-18 Novelty Journals Website: www.noveltyjournals.com Published Date: 11-February-2022 DOI: https://doi.org/10.5281/zenodo.7632596 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/Incorporating%20Zero-Inflated-11022023-2.pdf

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Weni Utomo, Candra Rezzing, Achmad Efendi, and Ni Wayan S. Wardhani. "Simulation Study of Bayesian Zero Inflated Poisson Regression." CAUCHY: Jurnal Matematika Murni dan Aplikasi 10, no. 1 (2025): 213–23. https://doi.org/10.18860/cauchy.v10i1.30207.

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Bayesian merupakan salah satu metode estimasi parameter yang dapat diaplikasikan pada ukuran sampel yang kecil. Zero Inflated Poisson merupakan salah satu metode untuk menganalisis data Poisson yang mengalami overdispersion. Tujuan dari penelitian ini adalah untuk mengevaluasi kinerja analisis Zero Inflated Poisson Regression menggunakan Bayesian. Data yang digunakan adalah jumlah kasus campak di Jawa Timur. Campak merupakan penyakit menular yang berpotensi menjadi wabah di berbagai daerah, termasuk Jawa Timur. Terdapat empat variabel prediktor yang digunakan yaitu Jumlah Penduduk (X1), Persentase Vaksinasi (X2), Persentase Penduduk Miskin (X3), dan Persentase Sanitasi Layak (X4), serta satu variabel respon yaitu Jumlah Kasus Campak. Hasil penelitian ini menunjukkan bahwa estimasi model Zero Inflated Poisson (ZIP) menggunakan Bayesian lebih baik dibandingkan estimasi model Zero Inflated Poisson (ZIP) menggunakan MLE. Hal ini dikarenakan data yang digunakan dalam penelitian memiliki sampel yang kecil sehingga estimasi MLE cenderung kurang baik digunakan dalam estimasi parameter. Pemilihan model terbaik dilakukan dengan menggunakan metode Deviance Information Criteria (DIC). Model terbaik ditunjukkan dengan nilai DIC terkecil pada ukuran sampel 100 dan proporsi nol 0,8.

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Chakraborty, Sukanta, and Soma Chowdhury Biswas. "MODELLING ZERO-INFLATED OVER DISPERSED DENGUE DATA VIA ZERO-INFLATED POISSON INVERSE GAUSSIAN REGRESSION MODEL: A CASE STUDY OF BANGLADESH." Acta Scientifica Malaysia 8, no. 1 (2024): 11–14. https://doi.org/10.26480/asm.01.2024.11.14.

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Bangladesh has been noted for experiencing some of the most susceptible dengue outbreaks in Asia; the country’s location, dense population, and changing environment all play major roles in this. Determining the correlation between meteorological conditions and case count is critical for predicting about the characteristics of the DENV outbreak. Certain widely used models, such as the Poisson regression model or the negative binomial regression model, are insufficient to adequately predict dengue fever since many of these datasets are of the over-dispersed, long-tail variety, and zero-inflated. In this study, the Zero-inflated negative binomial regression model is compared with the Zero-inflated Poisson inverse Gaussian regression model. Depending on AIC and BIC criteria Zero-inflated Poisson inverse-Gaussian regression model is proposed. Then Zero-inflated Poisson inverse Gaussian regression model is used to model the dataset containing confirmed positive cases of dengue fever and seven meteorological variables. The proposed model shows that all the meteorological variables are significantly associated with the confirmed positive cases of dengue fever. That’s why modeling a dengue-fever dataset with a Zero-inflated Poisson-inverse Gaussian regression model is suggested in this study.

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HALL, DANIEL B., and JING SHEN. "Robust Estimation for Zero-Inflated Poisson Regression." Scandinavian Journal of Statistics 37, no. 2 (2009): 237–52. http://dx.doi.org/10.1111/j.1467-9469.2009.00657.x.

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Hasan, M. Tariqul, and Gary Sneddon. "Zero-Inflated Poisson Regression for Longitudinal Data." Communications in Statistics - Simulation and Computation 38, no. 3 (2009): 638–53. http://dx.doi.org/10.1080/03610910802601332.

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Loeys, Tom, Beatrijs Moerkerke, Olivia De Smet, and Ann Buysse. "The analysis of zero-inflated count data: Beyond zero-inflated Poisson regression." British Journal of Mathematical and Statistical Psychology 65, no. 1 (2011): 163–80. http://dx.doi.org/10.1111/j.2044-8317.2011.02031.x.

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Ressa Nuryaningsih, Ani, and Nusar Hajarisman. "Perbandingan Model Regresi Zero Inflated Poisson (ZIP) dan Hurdle Poisson (HP) pada Kasus Kematian Balita di Kota Bandung Tahun 2021." Bandung Conference Series: Statistics 3, no. 2 (2023): 538–47. http://dx.doi.org/10.29313/bcss.v3i2.8522.

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Abstract. In this study, the response variable is assumed to be Poisson-distributed enumeration data. However, in the Poisson regression model, the enumerated data often deviates from the Poisson distribution because of the proportion of excess zero values in the response variable (excess zero), resulting in a larger variance than the average of the observed variables (overdispersion). Therefore, this study aims to model the data with Zero Inflated Poisson (ZIP) and Hurdle Poisson regression. Based on the results of the study by comparing the ZIP and Hurdle Poisson regression models using the Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC) values, it is found that the Hurdle Poisson regression model is more appropriate for modeling child mortality data in the city of Bandung in 2021 or in other words the Hurdle Poisson regression model is better at dealing with overdispersion and excess zeros problems compared to the Zero Inflated Poisson (ZIP) regression model. Abstrak. Pada penelitian ini variabel respon diasumsikan merupakan data cacahan yang berdistribusi Poisson. Namun, pada model regresi Poisson data cacah seringkali menyimpang dari distribusi Poisson karena proporsi nilai nol yang berlebih pada variabel respon (excess zero), sehingga menghasilkan varian yang lebih besar dari rata-rata variabel yang diamati (overdispersi). Maka dari itu, penelitian ini bertujuan untuk memodelkan data dengan regresi Zero Inflated Poisson (ZIP) dan Hurdle Poisson. Berdasarkan hasil penelitian dengan membandingkan model regresi ZIP dan Hurdle Poisson menggunakan nilai Akaike Information Criterion (AIC) dan Bayesian Information Criteria (BIC), maka diperoleh bahwa model regresi Hurdle Poisson lebih tepat digunakan untuk memodelkan data kematian balita di Kota Bandung tahun 2021 atau dengan kata lain model regresi Hurdle Poisson lebih baik dalam menangani masalah overdispersi dan excess zeros dibandingkan dengan model regresi Zero Inflated Poisson (ZIP).

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NARANAMMAL, N., and S. R. KRISHNA PRIYA. "Weather based forewarning model for cotton pests using zero-inflated and hurdle regression models." Journal of Agrometeorology 26, no. 4 (2024): 485–90. https://doi.org/10.54386/jam.v26i4.2744.

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Early forewarning of crop pest based on weather variables provides lead time to manage impending pest attacks that minimize crop loss, decrease the cost of pesticides and enhance the crop yield. This paper is an attempt to forewarn incidence of Cotton pests using weather variables. The pest incidence data from 2015 to 2023 for Aphids, Jassids, Thrips, and Whiteflies has been used for the study. The pest incidence being count variable, different count regression models such as zero inflated Poisson & negative binomial, hurdle Poisson & negative binomial, negative binomial and generalized Poisson regression models have been developed for forewarning of pests. Results indicated that zero inflated Poisson regression model outperformed the other models with improved performance of nearly 30 to 75%. Thus, the zero inflated Poisson regression model is a reliable tool in prediction of cotton pests, thereby aiding towards better pest management strategies.

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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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Sarumpaet, Mey Yanti, Sigit Nugroho, and Ramya Rachmawati. "HANDLING OF OVERDISPERSION CASES IN MORBIDITY DATA IN SELUMA REGENCY." MEDIA STATISTIKA 16, no. 2 (2024): 206–14. http://dx.doi.org/10.14710/medstat.16.2.206-214.

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The problem of overdispersion as a violation of the assumption of equidispersion in Poisson regression is generally caused by sources of unobserved heterogeneity, missing observations on predictor variables, outliers in the data, errors in the specification of the bridging function, and many observed values that are zero. The purpose of this study is to find out the right model and the variables that affect data that occurs overdispersion and excess zero in the case of the number of days of disruption at work, school, or other daily activities due to health complaints. The methods used were Poisson Regression, Negative Binomial Regression, Hurdle Poisson Regression, Zero Inflated Poisson Regression, Zero Inflated Negative Binomial Regression, and Hurdle Negative Binomial Regression. The data used were morbidity taken from data on the number of days of disruption at work, school or other daily activities due to health complaints in Seluma district, Bengkulu Province. It was found that the best model is Zero Inflated Negative Poisson with the smallest Akaike Information Criterion (AIC) value of 1620.609 and the variables that have a significant effect on the log model and the logit model are marital status and work variables.

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Dai, Lin, and Ying Zi Fu. "Statistical Inference for Zero-Inflated Poisson Regression Models with Excess Zeros." Applied Mechanics and Materials 367 (August 2013): 253–58. http://dx.doi.org/10.4028/www.scientific.net/amm.367.253.

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In this paper, we deal with a class of zero-inflated Poisson regression models and propose a score test procedure for assessing whether there exists zero-inflation or not. The sampling distribution and the power of the score test statistic are investigated by a limited simulation study. Furthermore, a Bayesian inference procedure is also presented for comparison. Finally, a data set of fire accident is used to illustrate our methodology and our numerical results show that our approach is useful and appealing for the analysis of count data with zero-inflation.

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Dwivedi, Alok K., Sherif E. Elhanafi, Mohamed O. Othman, and Marc J. Zuckerman. "Zero-inflated models for the evaluation of colorectal polyps in colon cancer screening studies—a value-based biostatistics practice." PeerJ 13 (May 26, 2025): e19504. https://doi.org/10.7717/peerj.19504.

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Background Colon cancer screening studies are needed for the early detection of colorectal polyps to reduce the risk of colorectal cancer. Unfortunately, the data generated on colon polyps are typically analyzed in their dichotomized form and sometimes with standard count models, which leads to potentially inaccurate findings in research studies. A more appropriate approach for evaluating colon polyps is zero-inflated models, considering undetected existing polyps at colonoscopy screening. Method We demonstrated the application of the zero-inflated and hurdle models including zero-inflated Poisson (ZIP), zero-inflated robust Poisson (ZIRP), zero-inflated negative binomial (ZINB), zero-inflated generalized Poisson (ZIGP), zero hurdle Poisson (ZHP), and zero hurdle negative binomial (ZHNB) models, and compared them with standard approaches including logistic regression (LR), Poisson regression (PR), robust Poisson (RP), and negative binomial (NB) regression for the evaluation of colorectal polyps using datasets from two randomized studies and one observational study. We also facilitated a step-by-step approach for selecting appropriate models for analyzing polyp data. Results All datasets yielded a significant amount of no polyps and therefore inflated or hurdle models performed best over single distribution models. We showed that cap-assisted colonoscopy yielded significantly more colon polyps (risk ratio [RR] = 1.38; 95% confidence interval [CI] [1.05–1.81]) compared with the standard colonoscopy by using the ZIP analysis. However, these findings were missed by standard analytic methods, including LR (odds ratio [OR] = 0.90; 95% CI [0.59–1.37]), PR (RR = 1.14; 95% CI [0.93–1.41]), and NB (RR = 1.16; 95% CI [0.89–1.51]) for evaluating colon polyps. The standard approaches, such as LR, PR, RP, or NB regressions for analyzing polyp data, produced potentially inaccurate findings compared to zero-inflated models in all example datasets. Furthermore, simulation studies also confirmed the superiority of ZIRP over alternative models in a range of datasets differing from the case studies. ZIRP was found to be the optimal method for analyzing polyp data in randomized studies, while the ZINB/ZHNB model showed a better fit in an observational study. Conclusion We suggest colonoscopy studies should jointly use the polyp detection rate and polyp counts as the quality measure. Based on theoretical, empirical, and simulation considerations, we encourage analysts to utilize zero-inflated models for evaluating colorectal polyps in colonoscopy screening studies for proper clinical interpretation of data and accurate reporting of findings. A similar approach can also be used for analyzing other types of polyp counts in colonoscopy studies.

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Nketia, Kojo, and Dziedzom K. de Souza. "Using zero-inflated and hurdle regression models to analyze schistosomiasis data of school children in the southern areas of Ghana." PLOS ONE 19, no. 7 (2024): e0304681. http://dx.doi.org/10.1371/journal.pone.0304681.

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Background Schistosomiasis is a neglected disease prevalent in tropical and sub-tropical areas of the world, especially in Africa. Detecting the presence of the disease is based on the detection of the parasites in the stool or urine of children and adults. In such studies, typically, data collected on schistosomiasis infection includes information on many negative individuals leading to a high zero inflation. Thus, in practice, counts data with excessive zeros are common. However, the purpose of this analysis is to apply statistical models to the count data and evaluate their performance and results. Methods This is a secondary analysis of previously collected data. As part of a modelling process, a comparison of the Poisson regression, negative binomial regression and their associated zero inflated and hurdle models were used to determine which offered the best fit to the count data. Results Overall, 94.1% of the study participants did not have any schistosomiasis eggs out of 1345 people tested, resulting in a high zero inflation. The performance of the negative binomial regression models (hurdle negative binomial (HNB), zero inflated negative binomial (ZINB) and the standard negative binomial) were better than the Poisson-based regression models (Poisson, zero inflated Poisson, hurdle Poisson). The best models were the ZINB and HNB and their performances were indistinguishable according to information-based criteria test values. Conclusion The zero-inflated negative binomial and hurdle negative binomial models were found to be the most satisfactory fit for modelling the over-dispersed zero inflated count data and are recommended for use in future statistical modelling analyses.

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Mouatassim, Younès, and El Hadj Ezzahid. "Poisson regression and Zero-inflated Poisson regression: application to private health insurance data." European Actuarial Journal 2, no. 2 (2012): 187–204. http://dx.doi.org/10.1007/s13385-012-0056-2.

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Sari, Fitri Mudia, and Pardomuan Robinson Sihombing. "PEMODELAN PENYAKIT DIFTERI DI SUMATERA BARAT MENGGUNAKAN REGRESI ZERO INFLATED DAN REGRESI HURDLE." EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 15, no. 1 (2021): 66. http://dx.doi.org/10.20527/epsilon.v15i1.3676.

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Data that states the number of events in a certain period of time is called count data. Poisson regression is one of the regression models included in the application of GLM that can be used to model the count data. In Poisson regression, there are assumptions that must be met, namely the mean and variance of the response variables must be the same (equidispersion). Several models that are able to overcome overdispersion due to excess zero are the Zero Inflated model and the Hurdle model. This study examines the characteristics of parameter estimation in the modeling of quantified data that is overdispersed due to excess zero using the Zero Inflated Poisson (ZIP), Zero Inflated Negative Binomial (ZINB), Hurdle Poisson (HP) model and the Hurdle Negative Binomial (HNB) model in cases of diphtheria. in West Sumatra in 2018. Based on individual parameter testing and AIC values, the HP model provides better performance than the ZIP, ZINB, and HNB models. So the Hurdle Poisson model is better used in this case than other models

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Azagi, Ilham. "Measles Disease Analysis in Bengkulu Province Using Zero Inflated Poisson Regression and Zero Inflated Negative Binomial Regression." Journal of Statistics and Data Science 1, no. 2 (2022): 1–9. http://dx.doi.org/10.33369/jsds.v1i2.24028.

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Zero Inflated Poisson regression (ZIP) and Zero Inflated Negative Binomial (ZINB) regression were used if there was overdispersion and no multicollinearity in the data. This study aims to analyze measles in Bengkulu Province using the ZIP and ZINB regression models. Among them are selecting the best model, seeing the influential variables from the best model, and predicting the results of the best model. The data used is one dependent variable, namely the number of measles cases (Y) in each puskesmas and six independent variables (X) namely the percentage of measles immunization, the amount of malnutrition, the percentage of exclusive breastfeeding, the percentage of vitamin A, the percentage of proper sanitation, and the percentage of healthy house. The results of this study, the ZIP regression model formed is a discrete model for , namely ln()=-5.042-0.007X1-0.014X3+0.094X4 and a zero inflation model for , namely logit()= -3.656+0.101X4-0.054X6, while the ZINB regression model formed is a discrete model for , namely ln()=-9,289+0.120X4 and a zero inflation model for , namely logit()=- 17.841+0.205X4. The AIC value of the ZINB regression model is 255.249, which is smaller than the AIC value of the ZIP regression model of 331.467, so the ZINB regression model is better to use. The influential variable in this study is the percentage of vitamin A administered. There is not much difference between predicted results and the actual data.

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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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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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Santi, Vera Maya, Defina Ambarwati, and Bagus Sumargo. "Zero Inflated Poisson Regression Analysis in Maternal Death Cases on Java Island." Pattimura International Journal of Mathematics (PIJMath) 1, no. 2 (2022): 59–68. http://dx.doi.org/10.30598/pijmathvol1iss2pp59-68.

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The basic regression model used to analyze the count data is the Poisson regression.. However, applying the Poisson regression model is unsuitable for excess zero data because it can cause overdispersion where the variance data is greater than its mean. One of the developments of the Poisson regression model can overcome this condition, Zero Inflated Poisson Regression (ZIP). In the health sector, the death of pregnant women on the Java island is an event that still rarely occurs and forms an excess zero data structure. However, the analysis of cases of maternal mortality using ZIP regression has never been studied in more depth. In this article, the maternal mortality cases in Java were modelled using ZIP regression to specify the variables that had a significant effect. The initial analysis results indicated the occurrence of overdispersion due to excess zero where there are 52% zero values in the data. The ZIP regression applied in this research provides enhancements to the Poisson regression based on the Vuong test. The results showed that the variables that had a significant effect on the maternal death cases in Java in the count model are the percentage of maternal health service coverage and the percentage of coverage of postpartum visit coverage, while in the zero-inflation model, the percentage of deliveries in health facilities and the percentage of obstetric complications treatment

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Algamal, Zakariya Yahya, Adewale F. Lukman, Mohamed R. Abonazel, and Fuad A. Awwad. "Performance of the Ridge and Liu Estimators in the zero-inflated Bell Regression Model." Journal of Mathematics 2022 (September 13, 2022): 1–15. http://dx.doi.org/10.1155/2022/9503460.

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The Poisson regression model is popularly used to model count data. However, the model suffers drawbacks when there is overdispersion—when the mean of the Poisson distribution is not the same as the variance. In this situation, the Bell regression model fits well to the data. Also, there is a high tendency of excess zeros in the count data. In this case, the zero-inflated Bell regression model is an alternative to the Bell regression model. The parameters of the zero-inflated Bell regression model are mostly estimated using the method of maximum likelihood. Linear dependency is a threat in a real-life application when modeling the relationship between the response variable and two or more explanatory variables in a generalized linear model such as the zero-inflated Bell regression model. It reduced the efficiency of the maximum likelihood estimator. Therefore, we developed the ridge and Liu estimators for the zero-inflated Bell regression model to deal with this issue. The simulation and application results support the dominance of the proposed methods over the conventional maximum likelihood estimator.

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Santana, Rogério A., Katiane S. Conceição, Carlos A. R. Diniz, and Marinho G. Andrade. "Type I multivariate zero‐inflated COM–Poisson regression model." Biometrical Journal 64, no. 3 (2021): 481–505. http://dx.doi.org/10.1002/bimj.202000249.

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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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Xie, Feng-chang, Jin-guan Lin, and Bo-cheng Wei. "Score tests for zero-inflated double poisson regression models." Acta Mathematicae Applicatae Sinica, English Series 33, no. 4 (2017): 851–64. http://dx.doi.org/10.1007/s10255-017-0702-1.

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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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David, I. J., P. O. Ikwuoche, and R. L. Kolo. "Zero-Inflated Poisson Regression Modeling of Plant Protein Consumption." Biometrical Letters 60, no. 2 (2023): 149–57. http://dx.doi.org/10.2478/bile-2023-0010.

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Summary This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–χ 2 and scaled Pearson–χ 2 statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect.

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Altun, Emrah, Hana Alqifari, and Mohamed S. Eliwa. "A novel approach for zero-inflated count regression model: Zero-inflated Poisson generalized-Lindley linear model with applications." AIMS Mathematics 8, no. 10 (2023): 23272–90. http://dx.doi.org/10.3934/math.20231183.

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<abstract>Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.</abstract>

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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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Alomair, Gadir. "Predictive performance of count regression models versus machine learning techniques: A comparative analysis using an automobile insurance claims frequency dataset." PLOS ONE 19, no. 12 (2024): e0314975. https://doi.org/10.1371/journal.pone.0314975.

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Accurate forecasting of claim frequency in automobile insurance is essential for insurers to assess risks effectively and establish appropriate pricing policies. Traditional methods typically rely on a Poisson distribution for modeling claim counts; however, this approach can be inadequate due to frequent zero-claim periods, leading to zero inflation in the data. Zero inflation occurs when more zeros are observed than expected under standard Poisson or negative binomial (NB) models. While machine learning (ML) techniques have been explored for predictive analytics in other contexts, their application to zero-inflated insurance data remains limited. This study investigates the utility of ML in improving forecast accuracy under conditions of zero-inflation, a data characteristic common in automobile insurance. The research involved a comparative evaluation of several models, including Poisson, NB, zero-inflated Poisson (ZIP), hurdle Poisson, zero-inflated negative binomial (ZINB), hurdle negative binomial, random forest (RF), support vector machine (SVM), and artificial neural network (ANN) on an insurance dataset. The performance of these models was assessed using mean absolute error. The results reveal that the SVM model outperforms others in predictive accuracy, particularly in handling zero-inflation, followed by the ZIP and ZINB models. In contrast, the traditional Poisson and NB models showed lower predictive capabilities. By addressing the challenge of zero-inflation in automobile claim data, this study offers insights into improving the accuracy of claim frequency predictions. Although this study is based on a single dataset, the findings provide valuable perspectives on enhancing prediction accuracy and improving risk management practices in the insurance industry.

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Dona, Febri Rahmat, and Hendro Permadi. "Zero-inflated poisson regression untuk memodelkan faktor-faktor yang mempengaruhi terjadinya kebakaran di kabupaten Sidoarjo." Jurnal MIPA dan Pembelajarannya 2, no. 11 (2023): 6. http://dx.doi.org/10.17977/um067v2i112022p6.

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The purpose of this research is determine the factors that affect the rate of fires in Sidoarjo using analysis Zero-Inflated Poisson (ZIP) regression. The procedure in this research through the steps are detecting the distribution of a variable number of fire (Y), identified cases multikolinearitas, establishing models Poison regression, testing overdispersi or underdispersi, establishing models ZIP regression, testing coefficient simultaneously and partially, and choose a suitable model. The independent variable used are population density (X_1), the number of factories (X_2), sugarcane and paddy land area (X_3), vacant land that overgrown with weeds (X_4), and year (X_5) Based on the regression model Zero-Inflated Poisson (ZIP) obtained best model of rate of fires that affected by the population density (X_1), sugarcane and paddy land area (X_3), and the year (X_5) to distinguish the difference the incidence of fires in every year. The model has a value of AIC (257,4) and the smallest value of R^2 (70,86).

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SEKARMINI, NI MADE, I. KOMANG GDE SUKARSA, and I. GUSTI AYU MADE SRINADI. "PENERAPAN REGRESI ZERO-INFLATED NEGATIVE BINOMIAL (ZINB) UNTUK PENDUGAAN KEMATIAN ANAK BALITA." E-Jurnal Matematika 2, no. 4 (2013): 11. http://dx.doi.org/10.24843/mtk.2013.v02.i04.p052.

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One method of regression analysis used to analyze the count data is Poisson regression. Poisson regression requires that the mean value equal to the value of variance (equidispersion). However, sometimes the data is going overdispersion the state variance values ??greater than the mean value. One of the causes overdispersion is the excessive number of zero values ??on the response variable (excess zeros). One method of analysis that can be used on data that had overdispersion due to excess zeros is regression Zero-Inflated Negative Binomial (ZINB). The data that can be analyzed using the ZINB regression is the early childhood mortality in the province of Bali because much of the data is zero. The analysis showed that the data had overdispersion on Poisson regression, so the ZINB regression analysis was used. From the results of the ZINB regression can overcome overdispersion so it was better than the Poisson Regression Model.

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YILDIRIM, Gizem, Selahattin KAÇIRANLAR, and Hasan YILDIRIM. "Poisson and negative binomial regression models for zero-inflated data: an experimental study." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (2022): 601–15. http://dx.doi.org/10.31801/cfsuasmas.988880.

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Count data regression has been widely used in various disciplines, particularly health area. Classical models like Poisson and negative binomial regression may not provide reasonable performance in the presence of excessive zeros and overdispersion problems. Zero-inflated and Hurdle variants of these models can be a remedy for dealing with these problems. As well as zero-inflated and Hurdle models, alternatives based on some biased estimators like ridge and Liu may improve the performance against to multicollinearity problem except excessive zeros and overdispersion. In this study, ten different regression models including classical Poisson and negative binomial regression with their variants based on zero-inflated, Hurdle, ridge and Liu approaches have been compared by using a health data. Some criteria including Akaike information criterion, log-likelihood value, mean squared error and mean absolute error have been used to investigate the performance of models. The results show that the zero-inflated negative binomial regression model provides the best fit for the data. The final model estimations have been obtained via this model and interpreted in detail. Finally, the experimental results suggested that models except the classical models should be considered as powerful alternatives for modelling count and give better insights to the researchers in applying statistics on working similar data structures.

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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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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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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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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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Auty, David, Alexis Achim, Pierre Bédard, and David Pothier. "StatSAW: modelling lumber product assortment using zero-inflated Poisson regression." Canadian Journal of Forest Research 44, no. 6 (2014): 638–47. http://dx.doi.org/10.1139/cjfr-2013-0500.

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Realistic forestry value chain simulations require accurate representations of each component. For primary processing, this is complicated by the fact that a single raw material is converted into a wide range of lumber products. The aim of this study was to develop statistical models for predicting lumber product assortment from tree size information, while taking into account the high proportion of zeros in the data. Lumber recovery was simulated from a database of 1013 laser-scanned Picea mariana (Mill.) Britton, Sterns & Poggenb. and Abies balsamea (L.) Mill. stems using the sawing simulator Optitek. The number of boards per stem of specific products was modelled with zero-inflated Poisson regression using stem diameter and height as covariates. The number of boards per stem was strongly related to both diameter and height, but also changed according to input prices for lumber products. Zero-inflated models outperformed ordinary Poisson regression in all cases. The developed models will be integrated into simulation tools designed to optimize processes along the entire forest value chain from forest to end user.

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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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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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Xie, Feng-Chang, Bo-Cheng Wei, and Jin-Guan Lin. "Score tests for zero-inflated generalized Poisson mixed regression models." Computational Statistics & Data Analysis 53, no. 9 (2009): 3478–89. http://dx.doi.org/10.1016/j.csda.2009.02.017.

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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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Sathitvudh, Samach, Piyada Wongwiwat, and Wikanda Phaphan. "Enhancing Tourist Forecasting in Thailand’s." WSEAS TRANSACTIONS ON ENVIRONMENT AND DEVELOPMENT 21 (April 15, 2025): 284–92. https://doi.org/10.37394/232015.2025.21.25.

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This article focuses on predicting the number of tourists visiting Thailand’s national parks using count data models. Given the discrete and overdispersed nature of the tourist count data, traditional Poisson regression models were extended to include Negative Binomial (NB) and Zero-Inflated models. Using data from 2016 to 2022, we evaluated four model types: Poisson, Negative Binomial, Zero-Inflated Poisson, and Zero-Inflated Negative Binomial (ZINB). Model performance was assessed using the Akaike Information Criterion (AIC), log-likelihood values, and the Vuong test. Findings reveal that the ZINB model best fits the data, addressing both overdispersion and excess zeros, resulting in more accurate predictions. This model is thus recommended for similar count data applications in tourism and environmental studies. Future work may focus on optimizing the model by reducing complexity and improving outlier handling.

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Channouf, Nabil, Marc Fredette, and Brenda MacGibbon. "Power and sample size calculations for Poisson and zero-inflated Poisson regression models." Computational Statistics & Data Analysis 72 (April 2014): 241–51. http://dx.doi.org/10.1016/j.csda.2013.09.029.

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Affleck, David LR. "Poisson mixture models for regression analysisof stand-level mortality." Canadian Journal of Forest Research 36, no. 11 (2006): 2994–3006. http://dx.doi.org/10.1139/x06-189.

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Periodic stand-level mortality data from permanent plots tend to be highly variable, skewed, and frequently contain many zero observations. Such data have commonly been modeled using nonlinear mortality functions fitted by least squares, and more recently by a two stage approach incorporating a logistic regression step. This study describes a set of nonlinear regression models that structure stochastic variation about a mortality function according to basic probability distributions appropriate for non-negative count data, including the Poisson, negative binomial (NB), and generalized Poisson (GP). Also considered are zero-inflated and hurdle modifications of these basic models. The models are developed and fit to mortality data from a loblolly pine (Pinus taeda L.) spacing trial with a conspicuous mode at 0. The sample data exhibit more variability than can be accommodated by a Poisson or modified Poisson model; the NB and GP models incorporate the extra-Poisson dispersion and offer an improved fit. A hurdle NB model best describes this sample, but, like the zero-inflated models and two-stage approach, modifies the interpretation of the mean structure and raises the question of overfitting. Considering both data-model agreement and the biological relevance of these models' components, the analysis suggests that the NB model offers a more compelling and credible inferential basis for fitting stand-level mortality functions.

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Journal articles on the topic 'Zero inflated poisson regression'

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