• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.231-239
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• 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.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.923-932
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• 2014

The Hurdle model can to analyze zero-inflated count data. This model is a mixed model of the logit model for a binary component and a truncated Poisson model of a truncated count component. We propose a new hurdle model with a general heterogeneous random effects covariance matrix to analyze longitudinal zero-inflated count data using modified Cholesky decomposition. This decomposition factors the random effects covariance matrix into generalized autoregressive parameters and innovation variance. The parameters are modeled using (generalized) linear models and estimated with a Bayesian method. We use these methods to carefully analyze a real dataset.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.16 no.4
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• pp.64-75
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• 2017

Previous count models using fixed parameter can not consider the unobserved heterogeneity, as the standard error of the count value is underestimated, excessive t-values are derived thereby reducing the reliability of the model. Also, the study of unsignalized intersections are inadequate because of the difficulty of collecting data and statistical limits for accurate analytical processes compared to the signalized intersections. The purpose of this study is to analyze the factors affecting traffic accidents by constructing the count model using random parameters, and it aimed to distinguish between existing studies based on the rural unsignalized intersections. As a result of the analysis, 7 variables were presented as significant variables, and 2 variables(presence of crosswalk, speed limit) were presented as random parameter.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.61-71
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• 1996

Kim and Song(1995)과 Kim and Lee(1996)는 하나의 이지공변량(binary covariate)을 갖는 가산위험모형(additive risk model)의 적합도검정법(goodness-of-fit test)을 제안했다. 전자는 모수의 가중추정량들의 차에 기초한 검정법이며 후자는 마팅게일잔차(martingale residual)에 기초한 검정법이다. 본 논문에서는 모의실험을 통하여 두 검정법을 비교하였다.

• 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.9 no.1
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• pp.75-89
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• 1996

This paper proposes a goodness-of-fit test for checking the adequacy of the additive risk model with a binary covariate. The test statistic is based on martingale residuals, which is the extended form of Wei(1984)'s test. The proposed test is shown to be consistent and asymptotically normally distributed under the regularity conditions. Furthermore, the test procedure is illustrated with two set of real data and the results are discussed.

• Environmental and Resource Economics Review
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• v.23 no.2
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• pp.331-347
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• 2014

The purpose of this study is to estimate the economic value of the recreational sea fishing in the Yellow Sea using count data model. For estimating consumer surplus, we used several count data model of travel cost recreation demand such as a poisson model(PM), a negative binomial model(NBM), a truncated poisson model(TPM), and a truncated negative binomial model(TNBM). Model results show that there is no exist the over-dispersion problem and a NBM was statistically more suitable than the other models. All parameters estimated are statistically significant and theoretically valid. The NBM was applied to estimate the travel demand and consumer surplus. The consumer surplus pre trip was estimated to be 254,453won, total consumer surplus per person and per year 1,536,896won.

• Journal of Korean Society of Transportation
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• v.21 no.3
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• pp.15-22
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• 2003

In general, the linear regression model has been used to estimate trip generation in the travel demand forecasting procedure. However, the model suffers from several methodological limitations. First, trips as a dependent variable with non-negative integer show discrete distribution but the model assumes that the dependent variable is continuously distributed between -$\infty$ and +$\infty$. Second, the model may produce negative estimates. Third, even if estimated trips are within the valid range, the model offers only forecasted trips without discrete probability distribution of them. To overcome these limitations, a poisson model with a assumption of equidispersion has frequently been used to analyze count data such as trip frequencies. However, if the variance of data is greater than the mean. the poisson model tends to underestimate errors, resulting in unreliable estimates. Using overdispersion test, this study proved that the poisson model is not appropriate and by using Vuong test, zero inflated negative binomial model is optimal. Model reliability was checked by likelihood test and the accuracy of model by Theil inequality coefficient as well. Finally, marginal effect of the change of socio-demographic characteristics of households on trips was analyzed.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1459-1473
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• 2016

Both longitudinal data and survival data are collected simultaneously in longitudinal data which are observed throughout the passage of time. In this case, the effect of the independent variable becomes biased (provided that sole use of longitudinal data analysis does not consider the relation between both data used) if the missing that occurred in the longitudinal data is non-ignorable because it is caused by a correlation with the survival data. A joint model of longitudinal data and survival data was studied as a solution for such problem in order to obtain an unbiased result by considering the survival model for the cause of missing. In this paper, a joint model of the longitudinal zero-inflated count data and survival data is studied by replacing the longitudinal part with zero-inflated count data. A hurdle model and proportional hazards model were used for each longitudinal zero inflated count data and survival data; in addition, both sub-models were linked based on the assumption that the random effect of sub-models follow the multivariate normal distribution. We used the EM algorithm for the maximum likelihood estimator of parameters and estimated standard errors of parameters were calculated using the profile likelihood method. In simulation, we observed a better performance of the joint model in bias and coverage probability compared to the separate model.

• 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.