• Title/Summary/Keyword: overdispersion in Poisson models

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Effects of Overdispersion on Testing for Serial Dependence in the Time Series of Counts Data

  • Kim, Hee-Young;Park, You-Sung
    • Communications for Statistical Applications and Methods
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    • v.17 no.6
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    • pp.829-843
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    • 2010
  • To test for the serial dependence in time series of counts data, Jung and Tremayne (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning, iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by Jung and Tremayne (2003) on serial dependence in time series of counts data are affected by overdispersion.

Overdispersion in count data - a review (가산자료(count data)의 과산포 검색: 일반화 과정)

  • 김병수;오경주;박철용
    • The Korean Journal of Applied Statistics
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    • v.8 no.2
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    • pp.147-161
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    • 1995
  • The primary objective of this paper is to review parametric models and test statistics related to overdspersion of count data. Poisson or binomial assumption often fails to explain overdispersion. We reviewed real examples of overdispersion in count data that occurred in toxicological or teratological experiments. We also reviewed several models that were suggested for implementing experiments. We also reviewed several models that were suggested for implementing the extra-binomial variation or hyper-Poisson variability, and we noted how these models were generalized and further developed. The approaches that have been suggested for the overdispersion fall into two broad categories. The one is to develop a parametric model for it, and the other is to assume a particular relationship between the variance and the mean of the response variable and to derive a score test staistics for detecting the overdispersion. Recently, Dean(1992) derived a general score test statistics for detecting overdispersion from the exponential family.

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A Comparative Study on Estimation Models for the Value of Access to a Natural Recreation Site: Focusing on the Estuary Area of Yeongsan River (자연휴양지 방문편익 추정모형의 비교 연구 - 영산강 하구를 대상으로)

  • Shin, Youngchul
    • Environmental and Resource Economics Review
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    • v.21 no.4
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    • pp.981-998
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    • 2012
  • In this paper, several count data model of travel cost recreation demand with Poisson and negative binominal specification are applied to estimate the value of access to the estuary area of Yeongsan river from visitor survey data. The results show that the negative binomial model that accounts for truncation and overdispersion provides the better goodness-of-fit, and therefore the value per visit(i.e. consumer surplus) is 89,350 won for resident of Jeolla province and 432,526 won for that of other provinces. If don't correct overdispersion by relying on Poisson estimates, the consumer surplus will be underestimated. Whereas the consumer surplus will be overestimated unless correct truncation by using estimates of untruncated models. As a result, the truncated negative binomial model should be applied to estimate the travel demand and the consumer surplus per visit by using survey data from single site visitors.

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Developing Rear-End Collision Models of Roundabouts in Korea (국내 회전교차로의 추돌사고 모형 개발)

  • Park, Byung Ho;Beak, Tae Hun
    • Journal of the Korean Society of Safety
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    • v.29 no.6
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    • pp.151-157
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    • 2014
  • This study deals with the rear-end collision at roundabouts. The purpose of this study is to develop the accident models of rear-end collision in Korea. In pursuing the above, this study gives particular attention to developing the appropriate models using Poisson, negative binomial model, ZAM, multiple linear and nonlinear regression models, and statistical analysis tools. The main results are as follows. First, the Vuong statistics and overdispersion parameters indicate that ZIP is the most appropriate model among count data models. Second, RMSE, MPB, MAD and correlation coefficient tests show that the multiple nonlinear model is the most suitable to the rear-end collision data. Finally, such the independent variables as traffic volume, ratio of heavy vehicle, number of circulatory roadway lane, number of crosswalk and stop line are adopted in the optimal model.

On the Extension of Test Statistics for Detecting Negative Binomial Departures from the Poisson Assumption (포아송으로부터 부의 이항분포로의 이탈에 대한 검정통계량의 확장)

  • 이선호
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.171-190
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    • 1993
  • 포아송분포로부터 부의 이항분포로의 이탈을 검색하는 통계량들이 자료의 형태에 따라 여러가지 제시되었다. 그런데 대립가설인 부의 이항분포의 모수화 방법에 따라 분산과 평균의 구조가 변하고 국소 최적 검정 통계량도 달라진다는 것이 알려졌다. 본 논문에서는 대립가설을 일반적인 포아송 혼합분포로까지 확장시키고, 일반적인 형태의 분산과 평균의 구조에도 검정 가능한 새로운 통계량 L을 소개하고 있다. 또한 L 통계량은 포아송 분포로부터 부의 이항분포로의 이탈을 다루는 기존의 여러 통계량들의 일반화된 형태임을 보였다. 점근적 상대효율과 모의 실험을 통하여 L 통계량과 기존의 통계량들을 비교한 결과 분산과 평균사이의 구조에 상관없이 L 통계량이 우수한 것임을 입증하였다.

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A Study on the Socio-economic Characteristics of the Angler Population and the Estimation of A Fishing Frequency Function (유어낚시인구의 사회경제학적 특성과 출조빈도함수의 추정에 관한 연구)

  • Park Cheol-Hyung
    • The Journal of Fisheries Business Administration
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    • v.36 no.1 s.67
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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.

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Development of the U-turn Accident Model at 4-Legged Signalized Intersections in Urban Areas (도시부 4지 신호교차로 유턴 사고모형 개발)

  • Kang, JongHo;Kim, KyungWhan;Ha, ManBok;Kim, SeongMun
    • International Journal of Highway Engineering
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    • v.16 no.2
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    • pp.119-129
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    • 2014
  • PURPOSES : The purpose of this study is to develop the U-turn accident model at 4-legged signalized intersections in urban areas. METHODS : In order to analyze the characteristics of the accidents which are associated with U-turn operation at 4-legged signalized intersections in urban areas and develop an U-turn accident model by regression analysis, the tests of overdispersion and zero-inflation are conducted about the dependent variables of number of accidents and EPDO (Equivalent Property Damage Only). RESULTS : As their results, the Poisson model fits best for number of accident and the ZIP (Zero Inflated Poisson) fits best for EPOD, the variables of conflict traffic, width of opposing road, traffic passing speed are adopted as independent variable for both models. The variables of number of bus berths and rate of U-turn signal time at which the U-turn is permitted are adopted as independent variable only for EPDO. CONCLUSIONS : These study results suggest that U-turn would be permitted at the intersection where the width of opposing road is wider than 11.9 meters, the passing vehicle speed is not high and U-turn operation is not hindered by the buses stopping at bus stops.

A Study on the Evaluation of Economic Value of the Gulf of Mexico Recreational Red Grouper Fishery (여행비용모형 분석을 통한 유어(遊漁)활동의 경제적 가치 추정 -미국 멕시코만 Red Grouper 유어부문을 대상으로 -)

  • Kim, Do-Hoon
    • The Journal of Fisheries Business Administration
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    • v.36 no.2 s.68
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    • pp.121-134
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    • 2005
  • In order to evaluate the effectiveness of management measures and to provide policy suggestions for the allocation of total allowable catch between recreational and commercial sectors, the economic value of red grouper recreational fishery in the United States Gulf of Mexico was estimated using a Travel Cost Method(TCM), Due to the characteristic of count data, a Poisson model(PM) and a Negative binomial model(NBM) were used in the TCM. Results of models showed that the NBM was statistically more suitable than the PM since the overdispersion problem occurred in the PM. Results also indicated all signs of the estimated parameters were as expected and were significant, except for a Boat parameter in both models. Based on the results of NBM, the total economic value of the recreational red grouper fishery was estimated to be $\$698.6$ and the value per trip was $\$179.5$. In addition, the total changes in expected consumer surplus due to changes in catch rates was $ \$42.3$.

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Effects on Regression Estimates under Misspecified Generalized Linear Mixed Models for Counts Data

  • Jeong, Kwang Mo
    • The Korean Journal of Applied Statistics
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    • v.25 no.6
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    • pp.1037-1047
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    • 2012
  • The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

Using the corrected Akaike's information criterion for model selection (모형 선택에서의 수정된 AIC 사용에 대하여)

  • Song, Eunjung;Won, Sungho;Lee, Woojoo
    • The Korean Journal of Applied Statistics
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    • v.30 no.1
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    • pp.119-133
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    • 2017
  • Corrected Akaike's information criterion (AICc) is known to have better finite sample properties. However, Akaike's information criterion (AIC) is still widely used to select an optimal prediction model among several candidate models due to of a lack of research on benefits obtained using AICc. In this paper, we compare the performance of AIC and AICc through numerical simulations and confirm the advantage of using AICc. In addition, we also consider the performance of quasi Akaike's information criterion (QAIC) and the corrected quasi Akaike's information criterion (QAICc) for binomial and Poisson data under overdispersion phenomenon.