• International Journal of Highway Engineering
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• v.18 no.4
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• pp.83-92
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• 2016

PURPOSES : The purpose of this study was to develop safety performance functions (SPFs) that use zero-inflated negative binomial regression models for urban intersections in central business districts (CBDs), and to compare the statistical significance of developed models against that of regular negative binomial regression models. METHODS : To develop and analyze the SPFs of intersections in CBDs, data acquisition was conducted for dependent and independent variables in areas of study. We analyzed the SPFs using zero-inflated negative binomial regression model as well as regular negative binomial regression model. We then compared the results by analyzing the statistical significance of the models. RESULTS : SPFs were estimated for all accidents and injury accidents at intersections in CBDs in terms of variables such as AADT, Number of Lanes at Major Roads, Median Barriers, Right Turn with an Exclusive Turn Lane, Turning Guideline, and Front Signal. We also estimated the log-likelihood at convergence and the likelihood ratio of SPFs for comparing the zero-inflated model with the regular model. In he SPFs, estimated log-likelihood at convergence and the likelihood ratio of the zero-inflated model were at -836.736, 0.193 and -836.415, 0.195. Also estimated the log-likelihood at convergence and likelihood ratio of the regular model were at -843.547, 0.187 and -842.631, 0.189, respectively. These figures demonstrate that zero-inflated negative binomial regression models can better explain traffic accidents at intersections in CBDs. CONCLUSIONS : SPFs that use a zero-inflated negative binomial regression model demonstrate better statistical significance compared with those that use a regular negative binomial regression model.

• International Journal of Highway Engineering
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• v.14 no.5
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• pp.133-143
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• 2012

PURPOSES: Using the collected data for crash, traffic volume, and design elements on ramps between 2007 and 2009, this research effort was initiated to develop traffic crash prediction models for expressway ramps. METHODS: Three negative binomial regression models and three zero-inflated negative binomial regression models were developed for individual ramp types, including direct, semi-direct and loop, respectively. For validating the developed models, authors compared the estimated crash frequencies with actual crash frequencies of twelve randomly selected interchanges, the ramps of which have not been used for model developing. RESULTS: The results show that the negative binomial regression models for direct, semi-direct and loop ramps showed 60.3%, 63.8% and 48.7% error rates on average whereas the zero-inflated negative binomial regression models showed 82.1%, 120.4% and 57.3%, respectively. CONCLUSIONS: Conclusively, the negative binomial regression models worked better in traffic crash prediction than the zero-inflated negative binomial regression models for estimating the frequency of traffic accidents on expressway ramps.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.895-900
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• 2013

In this research, we propose a simple bivariate zero inflated negative binomial regression model with different dispersion for bivariate count data with excess zeros. An application to the demand for health services shows that the proposed model is better than existing models in terms of log-likelihood and AIC.

• The Korean Journal of Applied Statistics
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• v.35 no.2
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• pp.311-325
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• 2022

For count responses, the situation of excess zeros often occurs in various research fields. Zero-inflated model is a common choice for modeling such count data. Bayesian inference for the zero-inflated model has long been recognized as a hard problem because the form of conditional posterior distribution is not in closed form. Recently, however, Pillow and Scott (2012) and Polson et al. (2013) proposed a Pólya-Gamma data-augmentation strategy for logistic and negative binomial models, facilitating Bayesian inference for the zero-inflated model. We apply Bayesian zero-inflated negative binomial regression model to longitudinal pharmaceutical data which have been previously analyzed by Min and Agresti (2005). To facilitate posterior sampling for longitudinal zero-inflated model, we use the Pólya-Gamma data-augmentation strategy.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.859-864
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• 2012

Poisson regression and negative binomial regression are usually used to analyze counting data; however, these models are unsuitable for fit zero-inflated data that contain unexpected zero-valued observations. In this paper, we review the zero-inflated regression in which Bernoulli process and the counting process are hierarchically mixed. It is known that zero-inflated regression can efficiently model the over-dispersion problem. Vuong statistic is employed to compare performances of the zero-inflated models with other standard models.

• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.1087-1097
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• 2017

This study aims to find the best model to fit the number of insurance solicitor's turnovers of life insurance companies using count data regression models such as poisson regression, negative binomial regression, zero-inflated poisson regression, or zero-inflated negative binomial regression. Out of the four models, zero-inflated negative binomial model has been selected based on AIC and SBC criteria, which is due to over-dispersion and high proportion of zero-counts. The significant factors to affect insurance solicitor's turnover found to be a work period in current company, a total work period as financial planner, an affiliated corporation, and channel management satisfaction. We also have found that as the job satisfaction or the channel management satisfaction gets lower as channel management satisfaction, the number of insurance solicitor's turnovers increases. In addition, the total work period as financial planner has positive relationship with the number of insurance solicitor's turnovers, but the work period in current company has negative relationship with it.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.571-579
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• 2011

We propose a new bivariate zero-inflated negative binomial regression model to allow heterogeneous dispersions. To show the performance of our proposed model, Health Care data in Deb and Trivedi (1997) are used to compare it with the other bivariate zero-inflated negative binomial model proposed by Wang (2003) that has a common dispersion between the two response variables. This empirical study shows better results from the views of log-likelihood and AIC.

• Journal of Korean Academy of Nursing
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• v.42 no.6
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• pp.819-832
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• 2012

Purpose: This study was conducted to identify risk factors that influence the probability and severity of elder abuse in community-dwelling older adults. Methods: This study was a cross-sectional descriptive study. Self-report questionnaires were used to collect data from community-dwelling Koreans, 65 and older (N=416). Logistic regression, negative binomial regression and zero-inflated negative binomial regression model for abuse count data were utilized to determine risk factors for elder abuse. Results: The rate of older adults who experienced any one category of abuse was 32.5%. By zero-inflated negative binomial regression analysis, the experience of verbal-psychological abuse was associated with marital status and family support, while the experience of physical abuse was associated with self-esteem, perceived economic stress and family support. Family support was found to be a salient risk factor of probability of abuse in both verbal-psychological and physical abuse. Self-esteem was found to be a salient risk factor of probability and severity of abuse in physical abuse alone. Conclusion: The findings suggest that tailored prevention and intervention considering both types of elder abuse and target populations might be beneficial for preventative efficiency of elder abuse.

• International Journal of Highway Engineering
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• v.12 no.2
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• pp.43-49
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• 2010

This study deals with the traffic accident of the Cheongju arterial link sections. The purpose of the study is to develop the traffic accident model. In pursuing the above, this study gives particular attentions to developing the ZAM(zero-altered model) model using the accident data of arterial roads devided by 322 small link sections. The main results analyzed by ZIP(zero inflated Poisson model) and ZINB(zero inflated negative binomial model) which are the methods of ZAM, are as follows. First, the evaluation of various developed models by the Vuong statistic and t statistic for overdispersion parameter ${\alpha}$ shows that ZINB is analyzed to be optimal among Poisson, NB, ZIP(zero-inflated Poisson) and ZINB regression models. Second, ZINB is evaluated to be statistically significant in view of t, ${\rho}$ and ${\rho}^2$ (0.63) values compared to other models. Finally, the accident factors of ZINB models are developed to be the traffic volume(ADT), number of entry/exit and length of median. The traffic volume(ADT) and the number of entry/exit are evaluated to be the '+' factors and the length of median to be '-' factor of the accident.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.951-961
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• 2011

In this paper, we propose a Bayesian inference using the Markov Chain Monte Carlo(MCMC) method for the zero inflated negative binomial(ZINB) regression model. The proposed model allows the regression model for zero inflation probability as well as the regression model for the mean of the dependent variable. This extends the work of Jang et al. (2010) to the fully defiend ZINB regression model. In addition, we apply the proposed method to a real data example, and compare the efficiency with the zero inflated Poisson model using the DIC. Since the DIC of the ZINB is smaller than that of the ZIP, the ZINB model shows superior performance over the ZIP model in zero inflated count data with overdispersion.