• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.1-12
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• 2006

The aim of this study is to analyse a survey data on the number of charitable donations using a mixture of two Poisson regression models. The survey was conducted in 2002 by Volunteer 21, an nonprofit organization, based on Koreans, who were older than 20. The mixture of two Poisson distributions is used to model the number of donations based on the empirical distribution of the data. The mixture of two Poisson distributions implies the whole population is subdivided into two groups, one with lesser number of donations and the other with larger number of donations. We fit the mixture of Poisson regression models on the number of donations to identify significant covariates. The expectation-maximization algorithm is employed to estimate the parameters. We computed 95% bootstrap confidence interval based on bias-corrected and accelerated method and used then for selecting significant explanatory variables. As a result, the income variable with four categories and the volunteering variable (1: experience of volunteering, 0: otherwise) turned out to be significant with the positive regression coefficients both in the lesser and the larger donation groups. However, the regression coefficients in the lesser donation group were larger than those in larger donation group.

• 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.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.