• Title/Summary/Keyword: Poisson count data

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Count Data Model for The Estimation of Bus Ridership (Focusing on Commuters and Students in Seoul) (가산자료모형(Count Data Model)을 이용한 버스이용횟수추정에 관한 연구 (서울시 통근.통학자를 대상으로))

  • 문진수;김순관;임강원
    • Journal of Korean Society of Transportation
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    • v.17 no.5
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    • pp.123-135
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    • 1999
  • The rapid increase of Passenger cars which is caused by the discomfort of Public transit and the Preference of automobiles is the major factor of increasing traffic congestions in Seoul With the point that leading the automobilists to the Public transit can be the most important Policy to ease these traffic congestions, this study focuses on the behavioral aspects of company employees and university students and investigates factors influencing bus ridership. To be brief, by estimating bus ridership through count models, this study investigates factors which influence bus ridership and elicits Political suggestions which lead automobilists to Public transit. The Purpose in this study is the application of appropriate count data model. The count data models have been widely applied to the economic area from the middle of the 1980s and to transportation aspect mainly in the foreign countries from the latter half of the 1980s. Even though a few studies in this country employed count data model to count data. all of them were Poisson regression models without suitable tests for the importance of the model specification. In the end, as the result of statistical test, negative binomial regression model which is suitable for overdispersed data was found to be appropriate for the data of weekly bus ridership. To emphasize the importance of model specification, both of poisson regression model and negative binomial regression model were estimated and the results were compared.

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A new sample selection model for overdispersed count data (과대산포 가산자료의 새로운 표본선택모형)

  • Jo, Sung Eun;Zhao, Jun;Kim, Hyoung-Moon
    • The Korean Journal of Applied Statistics
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    • v.31 no.6
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    • pp.733-749
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    • 2018
  • Sample selection arises as a result of the partial observability of the outcome of interest in a study. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. Recently sample selection models for binomial and Poisson response variables have been proposed. Based on the theory of symmetry-modulated distribution, we extend these to a model for overdispersed count data. This type of data with no sample selection is often modeled using negative binomial distribution. Hence we propose a sample selection model for overdispersed count data using the negative binomial distribution. A real data application is employed. Simulation studies reveal that our estimation method based on profile log-likelihood is stable.

Bayesian Analysis for the Zero-inflated Regression Models (영과잉 회귀모형에 대한 베이지안 분석)

  • Jang, Hak-Jin;Kang, Yun-Hee;Lee, S.;Kim, Seong-W.
    • The Korean Journal of Applied Statistics
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    • v.21 no.4
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    • pp.603-613
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    • 2008
  • We often encounter the situation that discrete count data have a large portion of zeros. In this case, it is not appropriate to analyze the data based on standard regression models such as the poisson or negative binomial regression models. In this article, we consider Bayesian analysis for two commonly used models. They are zero-inflated poisson and negative binomial regression models. We use the Bayes factor as a model selection tool and computation is proceeded via Markov chain Monte Carlo methods. Crash count data are analyzed to support theoretical results.

Evaluating the Economic Damages to Anglers of the Marine Recreational Charter due to the Herbei Spirit Vessel Oil Spill (허베이 스피리트호의 기름유출에 따른 바다유어낚시어선 이용객의 경제적 손실평가연구)

  • Pyo, Heedong
    • Ocean and Polar Research
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    • v.36 no.3
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    • pp.289-302
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    • 2014
  • This paper aims to evaluate the indirect economic damages to anglers of the marine recreational charter caused by marine pollution associated with the Herbei Spirit vessel, which spilled 12,547 kl of crude oil in Taean coastal areas in December 2007. In order to evaluate the indirect cost to anglers of the charter fishing, consumer surplus for charter fishing is estimated using a Poisson model (PM), a negative binomial model (NBM), a truncated Poisson model (TPM), and a truncated negative binomial model (TNBM), which account for the characteristics of count data (non-negative discrete data), for individual travel cost method (ITCM). Because of over-dispersion problem in PM and TPM, NBM and TNBM are considered to be more appropriate statistically. All parameters such as income, fishing careers, travel cost and catch that are estimated are statistically significant and theoretically valid. Based on TNBM results, consumer surplus per trip and per person was estimated to be 277 thousand won, total consumer surplus per person and per year about 2.3 million won, and the marginal effect of consumer surplus on % changes in catch rate is about 33 thousand won. The consumer surplus was converted into total indirect economic damages for aggregation which are evaluated to be 125 billion won, reflecting the number of anglers and damage rate.

Estimating Consumer Surplus for Recreational Sea Fishing using Individual Travel Cost Method (개별여행비용법을 이용한 바다 유어 낚시의 소비자 잉여추정)

  • Pyo, Hee-Dong;Park, Cheol-Hyung;Chung, Jin-Ho
    • Ocean and Polar Research
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    • v.30 no.2
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    • pp.141-148
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    • 2008
  • This paper aims at estimating consumer surplus for recreational sea fishing in Tongyeong coastal area using individual travel cost method. A Poisson model (PM), a negative binomial model (NBM), a truncated Poisson model (TPM), and a truncated negative binomial model (TNBM) are applied for individual travel cost method in order to account characteristics of count data (non-negative discrete data.) The survey was conducted for 462 inshore anglers using personal interview method in Tongyeong during July and October 2007. Respondents were asked about how often they do fishing, travel costs, catch, income, and so on. Because of over-dispersion problem in PM and TPM, NBM and TNBM were considered to be more appropriate statistically. All parameters estimated are statistically significant and theoretically valid. As the results based on TNBM, consumer surplus per trip was estimated to be 183,486 won, total consumer surplus per person and per year 3,399,658 won, and the marginal effect of consumer surplus on % changes in catch rate is 185,372 won.

The factors of insurance solicitor's turnovers of life insurance using Poisson regression (포아송회귀 모형을 활용한 생명보험 설계사들의 이직 요인 분석)

  • Chun, Heuiju
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.5
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    • pp.1337-1347
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    • 2016
  • This study investigates factors affecting the number of insurance solicitor's turnovers of life insurance companies based on questionnaire about them. Since the response variable which is the number of insurance solicitor's turnovers is count data, it is analyzed by Poisson regression which is one of generalized regression. When work year in current company, which is direct influential factor on the number of insurance solicitor's turnovers, is controlled, affiliated corporation has been found to be the most influential factor. In addition, age, motivation to work as financial planner, monthly income, a number of average new contract per month, and final education have been identified to be important factors. If insurance solicitor's occupant organization is large company, the number of turnovers becomes small, but if the organization is general agent(GA), it becomes larger. When insurance solicitor's age is high, the number of insurance solicitor's turnovers are reduced. If the motivation to become a financial planner is due to acquaintance such as family and relatives, the number of turnovers becomes small.

Bayesian Methods for Generalized Linear Models

  • Paul E. Green;Kim, Dae-Hak
    • Communications for Statistical Applications and Methods
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    • v.6 no.2
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    • pp.523-532
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    • 1999
  • Generalized linear models have various applications for data arising from many kinds of statistical studies. Although the response variable is generally assumed to be generated from a wide class of probability distributions we focus on count data that are most often analyzed using binomial models for proportions or poisson models for rates. The methods and results presented here also apply to many other categorical data models in general due to the relationship between multinomial and poisson sampling. The novelty of the approach suggested here is that all conditional distribution s can be specified directly so that staraightforward Gibbs sampling is possible. The prior distribution consists of two stages. We rely on a normal nonconjugate prior at the first stage and a vague prior for hyperparameters at the second stage. The methods are demonstrated with an illustrative example using data collected by Rosenkranz and raftery(1994) concerning the number of hospital admissions due to back pain in Washington state.

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A Ppoisson Regression Aanlysis of Physician Visits (외래이용빈도 분석의 모형과 기법)

  • 이영조;한달선;배상수
    • Health Policy and Management
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    • v.3 no.2
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    • pp.159-176
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    • 1993
  • The utilization of outpatient care services involves two steps of sequential decisions. The first step decision is about whether to initiate the utilization and the second one is about how many more visits to make after the initiation. Presumably, the initiation decision is largely made by the patient and his or her family, while the number of additional visits is decided under a strong influence of the physician. Implication is that the analysis of the outpatient care utilization requires to specify each of the two decisions underlying the utilization as a distinct stochastic process. This paper is concerned with the number of physician visits, which is, by definition, a discrete variable that can take only non-negative integer values. Since the initial visit is considered in the analysis of whether or not having made any physician visit, the focus on the number of visits made in addition to the initial one must be enough. The number of additional visits, being a kind of count data, could be assumed to exhibit a Poisson distribution. However, it is likely that the distribution is over dispersed since the number of physician visits tends to cluster around a few values but still vary widely. A recently reported study of outpatient care utilization employed an analysis based upon the assumption of a negative binomial distribution which is a type of overdispersed Poisson distribution. But there is an indication that the use of Poisson distribution making adjustments for over-dispersion results in less loss of efficiency in parameter estimation compared to the use of a certain type of distribution like a negative binomial distribution. An analysis of the data for outpatient care utilization was performed focusing on an assessment of appropriateness of available techniques. The data used in the analysis were collected by a community survey in Hwachon Gun, Kangwon Do in 1990. It was observed that a Poisson regression with adjustments for over-dispersion is superior to either an ordinary regression or a Poisson regression without adjustments oor over-dispersion. In conclusion, it seems the most approprite to assume that the number of physician visits made in addition to the initial visist exhibits an overdispersed Poisson distribution when outpatient care utilization is studied based upon a model which embodies the two-part character of the decision process uderlying the utilization.

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Maximum Likelihood Estimation Using Laplace Approximation in Poisson GLMMs

  • Ha, Il-Do
    • Communications for Statistical Applications and Methods
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    • v.16 no.6
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    • pp.971-978
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    • 2009
  • Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.

Bayesian Approaches to Zero Inflated Poisson Model (영 과잉 포아송 모형에 대한 베이지안 방법 연구)

  • Lee, Ji-Ho;Choi, Tae-Ryon;Wo, Yoon-Sung
    • The Korean Journal of Applied Statistics
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    • v.24 no.4
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    • pp.677-693
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    • 2011
  • In this paper, we consider Bayesian approaches to zero inflated Poisson model, one of the popular models to analyze zero inflated count data. To generate posterior samples, we deal with a Markov Chain Monte Carlo method using a Gibbs sampler and an exact sampling method using an Inverse Bayes Formula(IBF). Posterior sampling algorithms using two methods are compared, and a convergence checking for a Gibbs sampler is discussed, in particular using posterior samples from IBF sampling. Based on these sampling methods, a real data analysis is performed for Trajan data (Marin et al., 1993) and our results are compared with existing Trajan data analysis. We also discuss model selection issues for Trajan data between the Poisson model and zero inflated Poisson model using various criteria. In addition, we complement the previous work by Rodrigues (2003) via further data analysis using a hierarchical Bayesian model.