• 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.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.31 no.2
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• pp.287-301
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• 2018

It is common to encounter count data with excess zeros in various research fields such as the social sciences, natural sciences, medical science or engineering. Such count data have been explained mainly by zero-inflated Poisson model and extended models. Zero-inflated count data are also often correlated or clustered, in which random effects should be taken into account in the model. Frequentist approaches have been commonly used to fit such data. However, a Bayesian approach has advantages of prior information, avoidance of asymptotic approximations and practical estimation of the functions of parameters. We consider a Bayesian zero-inflated Poisson regression model with random effects for correlated zero-inflated count data. We conducted simulation studies to check the performance of the proposed model. We also applied the proposed model to smoking behavior data from the Regional Health Survey (2015) of the Korea Centers for disease control and prevention.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.363-376
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• 2012

Excessive zeroes are often observed in ordinal categorical response variables. An ordinary ordered Probit model is not appropriate for zero-inflated data especially when there are many different sources of generating 0 observations. In this paper, we apply a two-stage zero-inflated ordered Probit (ZIOP) model which incorporate the zero-flated nature of data, propose a Bayesian analysis of a ZIOP model, and apply the method to alcohol consumption data collected by the National Bureau of Statistics, Korea. In the first stage of a ZIOP model, a Probit model is introduced to divide the non-drinkers into genuine non-drinkers who do not participate in drinking due to personal beliefs or permanent health problems and potential drinkers who did not drink at the time of the survey but have the potential to become drinkers. In the second stage, an ordered probit model is applied to drinkers that consists of zero-consumption potential drinkers and positive consumption drinkers. The analysis results show that about 30% of non-drinkers are genuine non-drinkers and hence the Korean alcohol consumption data has the feature of zero-inflated data. A study on the marginal effect of each explanatory variable shows that certain explanatory variables have effects on the genuine non-drinkers and potential drinkers in opposite directions, which may not be detected by an ordered Probit model.

• 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 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.

• 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.

• The Korean Journal of Applied Statistics
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• v.30 no.6
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• pp.917-929
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• 2017

Korean income data obtained from Korea Labor Panel Survey shows excessive zeros, which may not be properly explained by the Tobit model. In this paper, we analyze the data using a zero-inflated Tobit model to incorporate excessive zeros. A zero-inflated Tobit model consists of two stages. In the first stage, individuals with 0 income are divided into two groups: genuine zero group and random zero group. Individuals in the genuine zero group did not participate labor market since they have no intention to do so. Individuals in the random zero group participated labor market but their incomes are very low and truncated at 0. In the second stage, the Tobit model is assumed to a subset of data combining random zeros and positive observations. Regression models are employed in both stages to obtain the effect of explanatory variables on the participation of labor market and the income amount. Markov chain Monte Carlo methods are applied for the Bayesian analysis of the data. The proposed zero-inflated Tobit model outperforms the Tobit model in model fit and prediction of zero frequency. The analysis results show strong evidence that the probability of participating in the labor market increases with age, decreases with education, and women tend to have stronger intentions on participating in the labor market than men. There also exists moderate evidence that the probability of participating in the labor market decreases with socio-economic status and reserved wage. However, the amount of monthly wage increases with age and education, and it is larger for married than unmarried and for men than women.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.583-592
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• 2015

Zero-inflation has recently attracted much attention in integer-valued time series. This article deals with conditional variance (volatility) modeling for the zero-inflated count time series. We incorporate zero-inflation property into integer-valued GARCH (INGARCH) via conditional Poisson and negative binomial marginals. The Cholera frequency time series is analyzed as a data application. Estimation is carried out using EM-algorithm as suggested by Zhu (2012).

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.1-9
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• 1998

In case of Zero-Inflated Poisson model with a change-point, likelihood ratio test statistic was used for testing hypothesis for a change-point. A change-point and several interesting parameters were estimated by using the method of moments and maximum likelihood. In order to compare the estimators, empirical mean-square-error was used. Real data for the Zero-Inflated Poisson model with a change-point and Poisson model without a change-point were examined.