• Title/Summary/Keyword: Zero-Inflated Negative Binomial Model

Search Result 37, Processing Time 0.025 seconds

Safety Performance Functions for Central Business Districts Using a Zero-Inflated Model (영과잉을 고려한 중심상업지구 교통사고모형 개발에 관한 연구)

  • Lee, Sang Hyuk;Woo, Yong Han
    • International Journal of Highway Engineering
    • /
    • v.18 no.4
    • /
    • pp.83-92
    • /
    • 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.

Traffic Crash Prediction Models for Expressway Ramps (고속도로 연결로의 교통사고예측모형 개발)

  • Choi, Yoon-Hwan;Oh, Young-Tae;Choi, Kee-Choo;Lee, Choul-Ki;Yun, Il-Soo
    • International Journal of Highway Engineering
    • /
    • v.14 no.5
    • /
    • pp.133-143
    • /
    • 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.

A Bayesian zero-inflated negative binomial regression model based on Pólya-Gamma latent variables with an application to pharmaceutical data (폴랴-감마 잠재변수에 기반한 베이지안 영과잉 음이항 회귀모형: 약학 자료에의 응용)

  • Seo, Gi Tae;Hwang, Beom Seuk
    • The Korean Journal of Applied Statistics
    • /
    • v.35 no.2
    • /
    • pp.311-325
    • /
    • 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.

A simple zero inflated bivariate negative binomial regression model with different dispersion parameters

  • Kim, Dongseok
    • Journal of the Korean Data and Information Science Society
    • /
    • v.24 no.4
    • /
    • pp.895-900
    • /
    • 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.

Zero In ated Poisson Model for Spatial Data (영과잉 공간자료의 분석)

  • Han, Junhee;Kim, Changhoon
    • The Korean Journal of Applied Statistics
    • /
    • v.28 no.2
    • /
    • pp.231-239
    • /
    • 2015
  • A Poisson model is the first choice for counts data. Quasi Poisson or negative binomial models are usually used in cases of over (or under) dispersed data. However, these models might be unsuitable if the data consist of excessive number of zeros (zero inflated data). For zero inflated counts data, Zero Inflated Poisson (ZIP) or Zero Inflated Negative Binomial (ZINB) models are recommended to address the issue. In this paper, we further considered a situation where zero inflated data are spatially correlated. A mixed effect model with random effects that account for spatial autocorrelation is used to fit the data.

Bivariate Zero-Inflated Negative Binomial Regression Model with Heterogeneous Dispersions (서로 다른 산포를 허용하는 이변량 영과잉 음이항 회귀모형)

  • Kim, Dong-Seok;Jeong, Seul-Gi;Lee, Dong-Hee
    • Communications for Statistical Applications and Methods
    • /
    • v.18 no.5
    • /
    • pp.571-579
    • /
    • 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.

Modelling Count Responses with Overdispersion

  • Jeong, Kwang Mo
    • Communications for Statistical Applications and Methods
    • /
    • v.19 no.6
    • /
    • pp.761-770
    • /
    • 2012
  • We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

Developing the Accident Models of Cheongju Arterial Link Sections Using ZAM Model (ZAM 모형을 이용한 청주시 간선가로 구간의 사고모형 개발)

  • Park, Byung-Ho;Kim, Jun-Yong
    • International Journal of Highway Engineering
    • /
    • v.12 no.2
    • /
    • pp.43-49
    • /
    • 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.

Analysis of Food Poisoning via Zero Inflation Models

  • Jung, Hwan-Sik;Kim, Byung-Jip;Cho, Sin-Sup;Yeo, In-Kwon
    • The Korean Journal of Applied Statistics
    • /
    • v.25 no.5
    • /
    • pp.859-864
    • /
    • 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.

An Analysis on the Determinants of Employed Labour Quantity in the Fishing Industry (어가의 고용량 결정요인 분석)

  • Kim, Tae-Hyun;Park, Cheol-Hyung;Nam, Jongoh
    • Environmental and Resource Economics Review
    • /
    • v.27 no.3
    • /
    • pp.545-567
    • /
    • 2018
  • This study applied and compared Poisson model, negative binomial model, zero inflated Poisson model, and zero inflated negative binomial model to estimate determinants of employed labour quantity. To estimate each of models, this study used fisheries census data which were obtained at microdata integrated service running by Statistics Korea. The study selected zero inflated negative binomial model according to the Vuong test and Likelihood-ratio test. In addition, the study estimated fishing village's practical changes on employed labour quantity as analyzing changes from 2010 to 2015. The results showed that the household with fishing vessels and high selling price had a significant effect on decrease of the labour quantities. Meanwhile, the longer work experience of the household, the more significant the increase in the labour quantities. In conclusion, this study presented that capitalized fishing household and the acceleration of aging had a significant impact on the change in the labour quantities.