• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.761-770
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• 2012

We frequently encounter outcomes of count that have extra variation. This paper considers several alternative models for overdispersed count responses such as a quasi-Poisson model, zero-inflated Poisson model and a negative binomial model with a special focus on a generalized linear mixed model. We also explain various goodness-of-fit criteria by discussing their appropriateness of applicability and cautions on misuses according to the patterns of response categories. The overdispersion models for counts data have been explained through two examples with different response patterns.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.829-843
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• 2010

To test for the serial dependence in time series of counts data, Jung and Tremayne (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning, iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by Jung and Tremayne (2003) on serial dependence in time series of counts data are affected by overdispersion.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.55-72
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• 2009

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = c + 1 are misclassified as x = c with probability $\alpha$, is defined. We obtain its recurrence relations among the raw moments, the central moments and the factorial moments. Discussion of the effect of the misclassification on the variance is considered. To illustrate the situation under consideration some of its particular cases like the size-biased generalized negative binomial (SBGNB), the size-biased generalized Poisson (SBGP) and sizebiased Borel distributions are included. Finally, an example is presented for the size-biased generalized Poisson distribution to illustrate the results.

• 응용통계연구
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• 제25권6호
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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.

• Communications for Statistical Applications and Methods
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• 제25권1호
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• pp.61-70
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• 2018

Modeling of the random effects covariance matrix in generalized linear mixed models (GLMMs) is an issue in analysis of longitudinal categorical data because the covariance matrix can be high-dimensional and its estimate must satisfy positive-definiteness. To satisfy these constraints, we consider the autoregressive and moving average Cholesky decomposition (ARMACD) to model the covariance matrix. The ARMACD creates a more flexible decomposition of the covariance matrix that provides generalized autoregressive parameters, generalized moving average parameters, and innovation variances. In this paper, we analyze longitudinal count data with overdispersion using GLMMs. We propose negative binomial loglinear mixed models to analyze longitudinal count data and we also present modeling of the random effects covariance matrix using the ARMACD. Epilepsy data are analyzed using our proposed model.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1327-1334
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• 2008

Mixed effect binomial regression models are widely used for analysis of correlated count data in which the response is the result of a series of one of two possible disjoint outcomes. In this paper, we consider kernel extensions with nonparametric 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.

• 응용통계연구
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• 제22권2호
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• pp.271-280
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• 2009

급내/급간상관이 동시에 존재하는 이변량 이항자료에 대한 모형으로 Danaher과 Hardie (2005)는 베타이항분포를 제안한바 있다. 그러나 이 모형은 베타분포에 따르는 성공확률을 통해 급내 상관을 묘사하므로 그 적용범위가 양의 급내상관을 가지는 자료에 제한된다. 이 연구에서는 보다 더 넓은 범위의 급내 상관에 대해 유용성을 가지는 일반화가법/승법이항모형과 확장베타이항모형 등에 Sarmanov형식의 이변량 확장을 고려하고 이들을 기존 모형과 적합도의 측면에서 비교한다. 실제자료인 주식자료와 소비자패널자료에 이변량 일반화이항모형들을 적용한 결과, B-mB와 B-ebB의 성능이 우수한 것으로 나타나며, 그 중 상대적으로 넓은 허용범위의 급내상관을 가지는 B-mB가 선호된다고 할 수 있다.

• 응용통계연구
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• 제23권3호
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• pp.585-594
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• 2010

본 연구에서는 제로절단된 이변량 일반화 포아송 분포에서 두 반응변수간 산포모수의 효과에 대하여 연구하였다. 모의실험 결과 두 반응변수가 서로 다른 산포를 갖는 경우 이를 무시하는 이변량 포아송 분포나 이변량 음이항 분포에 의한 모형적합은 효율성이 떨어지는 것으로 나타났다. 아울러 본 연구에서는 이와 같은 상이한 산포의 존재유무에 대한 가설검정에서 스코어 검정을 유도하고 우도비 검정과 효율성을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제18권2호
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• pp.219-227
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• 2011

본 연구에서는 두 반응변수의 이질적 산포를 허용하는 좀 더 일반적인 형태의 이변량 음이항 회귀모형을 삼각소거법(trivariate reduction technique)을 이용하여 제안하였다. 이 분포에서 산포의 동일성에 대한 스코어 검정과 LR 검정을 유도하고 모의실험을 통하여 각 검정법의 효율성을 비교하였다. 모의실험 결과 스코어 검정과 LR 검정 모두 명목유의수준을 제대로 유지하고 검정력도 높게 나타나 산포의 동일성을 검정하는데 효율적인 검정법으로 나타났다. 하지만 스코어 검정은 LR 검정에 비하여 계산이 간편하다는 장점이 존재하고 모의실험을 통하여 스코어 검정이 LR 검정보다 약간 나은 효율을 보였으므로 산포의 동일성에 대한 검정에서 스코어 검정의 사용을 제안하고자 한다. 더불어 실제 사례에 두 검정법을 적용하고 그 결과를 제시하였다.