• Title, Summary, Keyword: Poisson Regression Analysis

### Semiparametric Kernel Poisson Regression for Longitudinal Count Data

• Hwang, Chang-Ha;Shim, Joo-Yong
• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.1003-1011
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• 2008
• Mixed-effect Poisson regression models are widely used for analysis of correlated count data such as those found in longitudinal studies. In this paper, we consider kernel extensions with semiparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method based on kernel trick and our focus is on the efficient computation and the effective hyperparameter selection. For the selection of hyperparameters, cross-validation techniques are employed. Examples illustrating usage and features of the proposed method are provided.

### Optimal designs for small Poisson regression experiments using second-order asymptotic

• Mansour, S. Mehr;Niaparast, M.
• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.527-538
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• 2019
• This paper considers the issue of obtaining the optimal design in Poisson regression model when the sample size is small. Poisson regression model is widely used for the analysis of count data. Asymptotic theory provides the basis for making inference on the parameters in this model. However, for small size experiments, asymptotic approximations, such as unbiasedness, may not be valid. Therefore, first, we employ the second order expansion of the bias of the maximum likelihood estimator (MLE) and derive the mean square error (MSE) of MLE to measure the quality of an estimator. We then define DM-optimality criterion, which is based on a function of the MSE. This criterion is applied to obtain locally optimal designs for small size experiments. The effect of sample size on the obtained designs are shown. We also obtain locally DM-optimal designs for some special cases of the model.

### 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
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• v.25 no.5
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• pp.859-864
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• 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.

### Developing Accident Models of Rotary by Accident Occurrence Location (로터리 사고발생 위치별 사고모형 개발)

• Na, Hee;Park, Byung-Ho
• International Journal of Highway Engineering
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• v.14 no.4
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• pp.83-91
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• 2012
• PURPOSES : This study deals with Rotary by Accident Occurrence Location. The purpose of this study is to develop the accident models of rotary by location. METHODS : In pursuing the above, this study gives particular attentions to developing the appropriate models using multiple linear, Poisson and negative binomial regression models and statistical analysis tools. RESULTS : First, four multiple linear regression models which are statistically significant(their $R^2$ values are 0.781, 0.300, 0.784 and 0.644 respectively) are developed, and four Poisson regression models which are statistically significant(their ${\rho}^2$ values are 0.407, 0.306, 0.378 and 0.366 respectively) are developed. Second, the test results of fitness using RMSE, %RMSE, MPB and MAD show that Poisson regression model in the case of circulatory roadway, pedestrian crossing and others and multiple linear regression model in the case of entry/exit sections are appropriate to the given data. Finally, the common variable that affects to the accident is adopted to be traffic volume. CONCLUSIONS : 8 models which are all statistically significant are developed, and the common and specific variables that are related to the models are derived.

### Bayesian Analysis of a Zero-inflated Poisson Regression Model: An Application to Korean Oral Hygienic Data (영과잉 포아송 회귀모형에 대한 베이지안 추론: 구강위생 자료에의 적용)

• Lim, Ah-Kyoung;Oh, Man-Suk
• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.505-519
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• 2006
• We consider zero-inflated count data, which is discrete count data but has too many zeroes compared to the Poisson distribution. Zero-inflated data can be found in various areas. Despite its increasing importance in practice, appropriate statistical inference on zero-inflated data is limited. Classical inference based on a large number theory does not fit unless the sample size is very large. And regular Poisson model shows lack of St due to many zeroes. To handle the difficulties, a mixture of distributions are considered for the zero-inflated data. Specifically, a mixture of a point mass at zero and a Poisson distribution is employed for the data. In addition, when there exist meaningful covariates selected to the response variable, loglinear link is used between the mean of the response and the covariates in the Poisson distribution part. We propose a Bayesian inference for the zero-inflated Poisson regression model by using a Markov Chain Monte Carlo method. We applied the proposed method to a Korean oral hygienic data and compared the inference results with other models. We found that the proposed method is superior in that it gives small parameter estimation error and more accurate predictions.

### Poisson Regression Trees for Analysis of Lung Cancer Mortality with Extra Variation (폐암 사망수 분석시 과분산을 보정한 Poisson regression tree 적용)

• Choi Yun-Hee;Ahn Hong-Shik;Yoo Keun-Young
• 대한예방의학회:학술대회논문집
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• pp.202-203
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• 2002

### Bayesian analysis for the bivariate Poisson regression model: Applications to road safety countermeasures

• Choe, Hyeong-Gu;Lim, Joon-Beom;Won, Yong-Ho;Lee, Soo-Beom;Kim, Seong-W.
• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.851-858
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• 2012
• We consider a bivariate Poisson regression model to analyze discrete count data when two dependent variables are present. We estimate the regression coefficients as sociated with several safety countermeasures. We use Markov chain and Monte Carlo techniques to execute some computations. A simulation and real data analysis are performed to demonstrate model fitting performances of the proposed model.

### Marginal Likelihoods for Bayesian Poisson Regression Models

• Kim, Hyun-Joong;Balgobin Nandram;Kim, Seong-Jun;Choi, Il-Su;Ahn, Yun-Kee;Kim, Chul-Eung
• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.381-397
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• 2004
• The marginal likelihood has become an important tool for model selection in Bayesian analysis because it can be used to rank the models. We discuss the marginal likelihood for Poisson regression models that are potentially useful in small area estimation. Computation in these models is intensive and it requires an implementation of Markov chain Monte Carlo (MCMC) methods. Using importance sampling and multivariate density estimation, we demonstrate a computation of the marginal likelihood through an output analysis from an MCMC sampler.

### Statistical Analysis of K-League Data using Poisson Model

• Kim, Yang-Jin
• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.775-783
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• 2012
• Several statistical models for bivariate poisson data are suggested and used to analyze 2011 K-league data. Our interest is composed of two purposes: The first purpose is to exploit potential attacking and defensive abilities of each team. Particular, a bivariate poisson model with diagonal inflation is incorporated for the estimation of draws. A joint model is applied to estimate an association between poisson distribution and probability of draw. The second one is to investigate causes on scoring time of goals and a regression technique of recurrent event data is applied. Some related future works are suggested.

### Analysis on Creep of Concrete under Multiaxial Stresses Using Microplane Model (미세평면 모델을 적용한 다축응력 상태의 콘크리트 크리프 분석)

• Kwon Seung-Hee;Kim Yun-Yong;Kim Jin-Keun
• Journal of the Korea Concrete Institute
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• v.16 no.2
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• pp.195-204
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• 2004
• Poisson's ratio due to multiaxial creep of concrete reported by existing experimental works was controversial. Poisson's ratio calculated from measured strain is very sensitive to small experimental error. This sensitivity make it difficult to find out whether the Poisson's ratio varies with time or remain constant, and whether the Poisson's ratio has different value with stress states or not. A new approach method is needed to resolve the discrepancy and obtain reliable results. This paper presents analytical study on multiaxial creep test results. Microplane model as a new approach method is applied to optimally fitting the test data extracted from experimental studies on multiaxial creep of concrete. Double-power law is used as a model to present volumetric and deviatoric creep evolutions on a microplane. Six parameters representing the volumetric and deviatoric compliance functions are determined from regression analysis and the optimum fits accurately describe the test data. Poisson's ratio is calculated from the optimum fits and its value varies with time. Regression analysis is also performed assuming that Poisson's ratio remains constant with time. Four parameters are determined for this condition, and the error between the optimum fits and the test data is slightly larger than that for six parameter regression results. The constant Poisson's ratio with time is obtained from four parameter analysis results and the constant value can be used in practice without serious error.