• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.177-186
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• 2003

The Zero-Inflated Poisson regression is a model for count data with exess zeros. When the correlated response variables are intrested, we have to extend the univariate zero-inflated regression model to multivariate model. In this paper, we study and simulate the multivariate zero-inflated regression model. A real example was applied to this model. Regression parameters are estimated by using MLE's. We also compare the fitness of multivariate zero-inflated Poisson regression model with the decision tree model.

• Journal of Korean Society for Quality Management
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• v.46 no.3
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• pp.509-522
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• 2018

Purpose: The purpose of this study was to propose more accurate mathematical model which can represent result of government quality assurance activity, especially corrective action and flaw. Methods: The collected data during government quality assurance activity was represented through histogram. To find out which distributions (Poisson distribution, Zero-Inflated Poisson distribution) could represent the histogram better, this study applied Pearson's correlation coefficient. Results: The result of this study is as follows; Histogram of corrective action during past 3 years and Zero-Inflated Poisson distribution had strong relationship that their correlation coefficients was over 0.94. Flaw data could not re-parameterize to Zero-Inflated Poisson distribution because its frequency of flaw occurrence was too small. However, histogram of flaw data during past 3 years and Poisson distribution showed strong relationship that their correlation coefficients was 0.99. Conclusion: Zero-Inflated Poisson distribution represented better than Poisson distribution to demonstrate corrective action histogram. However, in the case of flaw data histogram, Poisson distribution was more accurate than Zero-Inflated Poisson distribution.

• 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.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.59-70
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• 2013

The purpose of this study was to develop a zero-inflated Rasch (ZI-Rasch) model, a combination of the Rasch model and the ZIP model. The ZI-Rasch model was considered in this study as an appropriate alternative to the Rasch model for zero-inflated data. To investigate the relative appropriateness of the ZI-Rasch model, several analyses were conducted using PROC NLMIXED procedures in SAS under various simulation conditions. Sets of criteria for model evaluations (-2LL, AIC, AICC, and BIC) and parameter estimations (RMSE, and $r$) from the ZI-Rasch model were compared with those from the Rasch model. In the data-model fit indices, regardless of the simulation conditions, the ZI-Rasch model produced better fit statistics than did the Rasch model, even when the response data were generated from the Rasch model. In terms of item parameter ${\lambda}$ estimations, the ZI-Rasch model produced estimates similar to those of the Rasch model.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.45-53
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• 2003

The Zero-Inflated Poisson regression is a model for count data with exess zeros. When the reponse variables have excess zeros, it is not easy to apply the Poisson regression model. In this paper, we study and simulate the zero-inflated Poisson regression model. An real example was applied to this model. Regression parameters are estimated by using MLE's. We also compare the fitness of zero-inflated Poisson model with the Poisson regression and decision tree model.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.387-394
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• 2004

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

• 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.

• International Journal of Highway Engineering
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• v.18 no.4
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• pp.83-92
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• 2016

PURPOSES : The purpose of this study was to develop safety performance functions (SPFs) that use zero-inflated negative binomial regression models for urban intersections in central business districts (CBDs), and to compare the statistical significance of developed models against that of regular negative binomial regression models. METHODS : To develop and analyze the SPFs of intersections in CBDs, data acquisition was conducted for dependent and independent variables in areas of study. We analyzed the SPFs using zero-inflated negative binomial regression model as well as regular negative binomial regression model. We then compared the results by analyzing the statistical significance of the models. RESULTS : SPFs were estimated for all accidents and injury accidents at intersections in CBDs in terms of variables such as AADT, Number of Lanes at Major Roads, Median Barriers, Right Turn with an Exclusive Turn Lane, Turning Guideline, and Front Signal. We also estimated the log-likelihood at convergence and the likelihood ratio of SPFs for comparing the zero-inflated model with the regular model. In he SPFs, estimated log-likelihood at convergence and the likelihood ratio of the zero-inflated model were at -836.736, 0.193 and -836.415, 0.195. Also estimated the log-likelihood at convergence and likelihood ratio of the regular model were at -843.547, 0.187 and -842.631, 0.189, respectively. These figures demonstrate that zero-inflated negative binomial regression models can better explain traffic accidents at intersections in CBDs. CONCLUSIONS : SPFs that use a zero-inflated negative binomial regression model demonstrate better statistical significance compared with those that use a regular negative binomial regression model.

• 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.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.