• 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.

• 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.

• Journal of Korean Society of Transportation
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• v.26 no.2
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• pp.35-46
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• 2008

The purposes of this study are to analyze the characteristics and to develop the models of traffic accidents. In pursuing the above, this study gives particular attentions to developing the models(multiple linear, poisson and negative binomial regression) using the data of Cheongju and Cheongwon signalized intersections. The main results analyzed are as follows. First, the accident characteristics of rural area were defined by factor. Second, 4 accident models which are all statistically significant were developed. Finally, such the variables as $X_2$ and $X_{11}$ were evaluated to be specific variables which reflect the characteristics of rural area.

• Journal of the Korean Society of Safety
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• v.29 no.1
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• pp.54-58
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• 2014

This study deals with the accidents of circular intersections in Korea. The goal is to develop the accident models for 94 circular intersections. In pursuing the above, this study gives particular attentions to collecting the data of geometric structure and accidents, and comparatively analyzing such the models as Poisson and NB regression and multiple regression model using SPSS 17.0 and LIMDEP 3.0. The main results are as follows. First, the negative binomial model among various models was analyzed to be the most appropriate. Second, 3 independent variables was adopted in the model, and these variables was analyzed to have a positive relation to the accident rate. Finally, the reduced width of circulatory roadway, removal of the parking lot within circulatory roadway and appropriate levels of approach lane were required to improve the safety of circular intersection.

• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.485-494
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• 2011

When the observations can take only the non-negative integer values, it is called the count data such as the numbers of car accidents, earthquakes, or insurance coverage. In general, the Poisson regression model has been used to model these count data; however, this model has a weakness in that it is restricted by the equality of the mean and the variance. On the other hand, the count data often tend to be too dispersed to allow the use of the Poisson model in practice because the variance of data is significantly larger than its mean due to heterogeneity within groups. When overdispersion is not taken into account, it is expected that the resulting parameter estimates or standard errors will be inefficient. Since coverage is the main issue for insurance, some accidents may not be covered by insurance, and the number covered by insurance may be zero. This paper considers the zero-inflated model for the count data including many zeros. The performance of this model has been investigated by using of real data with overdispersion and many zeros. The results indicate that the Zero-Inflated Negative Binomial Regression Model performs the best for model evaluation.

• Journal of the Korean Society of Safety
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• v.24 no.2
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• pp.94-99
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• 2009

This study deals with the traffic accidents at the 3-legged signalized intersections in Cheongu. The goals are to analyze the geometric, traffic and operational conditions of intersections and to develop a various functional forms that predict the accidents. The models are developed through the correlation analysis, the multiple linear, the multiple nonlinear, Poisson and negative binomial regression analysis. In this study, two multiple linear, two multiple nonlinear and two negative binomial regression models were calibrated. These models were all analyzed to be statistically significant. All the models include 2 common variables(traffic volume and lane width) and model-specific variables. These variables are, therefore, evaluated to be critical to the accident reduction of Cheongju.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.951-961
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• 2011

In this paper, we propose a Bayesian inference using the Markov Chain Monte Carlo(MCMC) method for the zero inflated negative binomial(ZINB) regression model. The proposed model allows the regression model for zero inflation probability as well as the regression model for the mean of the dependent variable. This extends the work of Jang et al. (2010) to the fully defiend ZINB regression model. In addition, we apply the proposed method to a real data example, and compare the efficiency with the zero inflated Poisson model using the DIC. Since the DIC of the ZINB is smaller than that of the ZIP, the ZINB model shows superior performance over the ZIP model in zero inflated count data with overdispersion.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2023.11a
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• pp.120-121
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• 2023

Recently, there has been a continuous imbalance between the demand and supply in the shipping industry. Consequently, shipping companies are implementing blank sailing to adjust the supply of vessels and achieve a balance between demand and supply. Blank sailing can create negative ripple effects by delaying cargo transportation, so this study uses Poisson regression analysis,

• Journal of the Korean Society of Safety
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• v.29 no.3
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• pp.107-113
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• 2014

The goal of this study is to develop the accident models of motorcycle at roundabouts. In the pursuing the above, this study gives particular attentions to developing the appropriate models using ZAM. The main results are as follows. First, the evaluation of various developed models by the Vuong statistic and over-dispersion parameter shows that ZINB is analyzed to be optimal among Poisson, NB, ZIP(zero-inflated Poisson) and ZINB regression models. Second, the traffic volume, width of central island and width of approach are evaluated to be important variables to the accidents. Finally, the common variables that affect to the accident are selected to be traffic volume and width of approach. This study might be expected to give some implications to the accident research on the roundabout by motorcycle.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.325-336
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• 2019

In this article we extend the discrete Weibull regression model in the presence of missing data. Discrete Weibull regression models can be adapted to various type of dispersion data however, it is not widely used. Recently Yoo (Journal of the Korean Data and Information Science Society, 30, 11-22, 2019) adapted the discrete Weibull regression model using single imputation. We extend their studies by using multiple imputation also with several various settings and compare the results. The purpose of this study is to address the merit of using multiple imputation in the presence of missing data in discrete count data. We analyzed the seventh Korean National Health and Nutrition Examination Survey (KNHANES VII), from 2016 to assess the factors influencing the variable, 1 month hospital stay, and we compared the results using discrete Weibull regression model with those of Poisson, negative Binomial and zero-inflated Poisson regression models, which are widely used in count data analyses. The results showed that the discrete Weibull regression model using multiple imputation provided the best fit. We also performed simulation studies to show the accuracy of the discrete Weibull regression using multiple imputation given both under- and over-dispersed distribution, as well as varying missing rates and sample size. Sensitivity analysis showed the influence of mis-specification and the robustness of the discrete Weibull model. Using imputation with discrete Weibull regression to analyze discrete data will increase explanatory power and is widely applicable to various types of dispersion data with a unified model.