• 한국도로학회논문집
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• 제14권5호
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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.

• 한국도로학회논문집
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• 제18권4호
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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.

• Journal of the Korean Data and Information Science Society
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• 제24권4호
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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.

• 한국안전학회지
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• 제30권2호
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• pp.70-76
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• 2015

This study deals with the traffic accident of circular intersections. The purpose of the study is to develop the accident models by traffic violation type. In pursuing the above, this study gives particular attention to analyzing various factors that influence traffic accident and developing such the optimal models as Poisson and Negative binomial regression models. The main results are the followings. First, 4 negative binomial models which were statistically significant were developed. This was because the over-dispersion coefficients had a value greater than 1.96. Second, the common variables in these models were not adopted. The specific variables by model were analyzed to be traffic volume, conflicting ratio, number of circulatory lane, width of circulatory lane, number of traffic island by access road, number of reduction facility, feature of central island and crosswalk.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• 한국도로학회논문집
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• 제17권5호
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• pp.39-46
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• 2015

PURPOSES: The operational characteristics of roundabouts are generally influenced by location as well as traffic volume. The goal of this study is to develop urban and rural roundabout accident models and to discuss safety improvement guidelines based on the model. METHODS : To analyze accidents, count data models are utilized in this study. This study used accident data from 2010 to 2013 for 56 roundabouts collected from the Traffic Accident Analysis System (TASS) of Road Traffic Authority. Poisson and negative binomial regression models were developed for this study using NLOGIT 4.0. RESULTS : The main results are as follows. First, the hypotheses that there are distributional differences in the number of accidents and injuries/fatalities among rural and urban roundabouts were accepted. Second, Poisson and negative binomial regression accident models, which were all statistically significant, were developed. Seven independent variables, which were statistically significant, were adopted. Third, the common variable of models was evaluated to be traffic volume. CONCLUSIONS : This study developed two negative binomial roundabout accident models and suggested some accident reduction strategies. The results are expected to give some implications to the safety improvement of roundabout.

• Communications for Statistical Applications and Methods
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• 제18권5호
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• pp.571-579
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• 2011

본 연구에서는 두 반응 변수에 서로 다른 산포를 허용하는 새로운 이변량 영과잉 음이항 회귀모형을 제안하고, Deb과 Trivedi (1997)에 나타난 헬스케어 자료를 이용하여 두 반응변수가 갖는 서로 다른 산포도를 무시한 Wang (2003)이 제안한 이변량 영과잉 음이항 회귀모형과의 효율성을 로그우도와 AIC의 관점에서 비교 하였다. 모형적합결과, 본 연구에서 제안한 모형이 모형선택기준 관점에서 기존모형에 비하여 월등히 우수한 결과를 보여주었다.

• 대한교통학회지
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• 제25권3호
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• pp.123-135
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• 2007

본 연구에서는 고속도로 트럼펫 인터체인지상에서 연결로 형식별로 일어나는 교통사고와 도로 기하구조 및 교통량등의 교통사고 요인들과의 관계를 분석하기 위해 교통사고의 분포의 특성을 분석하여 적합도 검증을 통해 모형추정시 가장 적절한 분포를 찾은 결과 음이항분포(Negative binomial distribution)가 선택되었다. 선택된 분포에 기반하여 트럼펫 인터체인지 연결로 전체, 연결로 형식별(직결, 준직결, 루프연결로) 각각의 음이항회귀모형 (Negative binomial regression model)을 개발하였다. 총 4개의 모형을 개발하고 그것의 적합도를 판단하는 여러 가지 통계값과 모형에서 예측한 값과 실제 관측값과의 차이를 분석한 결과 예측모형이 적합하게 구축되었음을 보였다. 추정된 모형의 통계적으로 유의한 변수들을 분석하여 교통사고를 설명하는데 유의한 변수들을 판단하고 이러한 변수들을 도로의 설계자가 도로 설계 및 운영에 적용하거나 교통안전계획 수립시 해당도로의 교통특성을 반영한 교통사고 절감 대책 등에 이용할 수 있을 것이다.

• 응용통계연구
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• 제35권2호
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• pp.311-325
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• 2022

0의 값을 과도하게 포함하는 가산자료는 다양한 연구 분야에서 흔히 나타난다. 영과잉 모형은 영과잉 가산자료를 분석하기 위해 가장 일반적으로 사용되는 모형이다. 영과잉 모형에 대한 전통적인 베이지안 추론은 조건부 사후분포의 형태가 폐쇄형 분포로 나타나지 않아 모형 적합 과정이 용이하지 않다는 한계점이 존재했다. 그러나 최근 Pillow와 Scott (2012)과 Polson 등 (2013)이 제안한 폴랴-감마 자료확대전략으로 인해, 로지스틱 회귀모형과 음이항 회귀모형에서 깁스 샘플링을 통한 추론이 가능해지면서, 영과잉 모형에 대한 베이지안 추론이 용이해졌다. 본 논문에서는 베이지안 추론에 기반한 영과잉 음이항 회귀모형을 Min과 Agresti(2005)에서 분석된 약학 연구 자료에 적용해본다. 분석에 사용된 자료는 경시적 영과잉 가산자료로 복잡한 자료 구조를 가지고 있다. 모형 적합 과정에서는 깁스 샘플링을 통한 추론을 수행하기 위해 폴랴-감마 자료확대전략을 사용한다.

• 수산경영론집
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• 제36권1호
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• pp.81-101
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• 2005

This article is to estimate the fishing frequency function in Korean recreational fishery with respect to socio-economic characteristics of anglers. First, the study described the characteristics of the entire angler population on the view points of 9 socio-economic variables. And then, the study divided the total angler population into three groups of in-land, sea, and mixed angler populations in order to investigate the differences in their characteristics. The study could confirm the existence of differences in regions, size of regions, and educational levels between the in - land and the sea angler populations by testing heterogeneity in the frequency table. The fishing frequency function is estimated using Poisson regression model in order to accomodate the count data(non-negative discrete random variable) aspects of the fishing frequency. However, the model specification error is found due to overdispersion of data. The model exhibits the lack of goodness of fit. The negative binomial regression model is adopted to cure the overdispersion of the data as an alternative estimation methodology. Finally, the study can confirm overdispersion does not exist in the model any more and the goodness of fit improved significantly to the reasonable level. The results of estimation of fishing frequency population modeled by the negative binomial regression models are following. The three variables of region, sex, and education have effects on the decision making process of fishing frequency in the case of in-land recreation fishery. On the other hand, the three variables of sex, age, and marriage status do the same job in the case of sea angler population. Among the left-over variables, both income and use of Internet variables now affect on the process in mixed angler population. Finally, the results of whole angler population show that all of the previous variables are proven to be statistically significant due to the summation of data with all three sub-groups of angler population.