• Communications for Statistical Applications and Methods
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• v.19 no.6
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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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• v.30 no.3
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• pp.291-309
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• 2023

Longitudinal count data has been widely collected in biomedical research, public health, and clinical trials. These repeated measurements over time on the same subjects need to account for an appropriate dependency. The Poisson regression model is the first choice to model the expected count of interest, however, this may not be an appropriate when data exhibit over-dispersion or under-dispersion. Recently, Conway-Maxwell-Poisson (CMP) distribution is popularly used as the distribution offers a flexibility to capture a wide range of dispersion in the data. In this article, we propose a Bayesian CMP regression model to accommodate over and under-dispersion in modeling longitudinal count data. Specifically, we develop a regression model with random intercept and slope to capture subject heterogeneity and estimate covariate effects to be different across subjects. We implement a Bayesian computation via Hamiltonian MCMC (HMCMC) algorithm for posterior sampling. We then compute Bayesian model assessment measures for model comparison. Simulation studies are conducted to assess the accuracy and effectiveness of our methodology. The usefulness of the proposed methodology is demonstrated by a well-known example of epilepsy data.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1459-1473
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• 2016

Both longitudinal data and survival data are collected simultaneously in longitudinal data which are observed throughout the passage of time. In this case, the effect of the independent variable becomes biased (provided that sole use of longitudinal data analysis does not consider the relation between both data used) if the missing that occurred in the longitudinal data is non-ignorable because it is caused by a correlation with the survival data. A joint model of longitudinal data and survival data was studied as a solution for such problem in order to obtain an unbiased result by considering the survival model for the cause of missing. In this paper, a joint model of the longitudinal zero-inflated count data and survival data is studied by replacing the longitudinal part with zero-inflated count data. A hurdle model and proportional hazards model were used for each longitudinal zero inflated count data and survival data; in addition, both sub-models were linked based on the assumption that the random effect of sub-models follow the multivariate normal distribution. We used the EM algorithm for the maximum likelihood estimator of parameters and estimated standard errors of parameters were calculated using the profile likelihood method. In simulation, we observed a better performance of the joint model in bias and coverage probability compared to the separate model.

• Annals of Laboratory Medicine
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• v.38 no.6
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• pp.503-511
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• 2018

Background: Sampling a healthy reference population to generate reference intervals (RIs) for complete blood count (CBC) parameters is not common for pediatric and geriatric ages. We established age- and sex-specific RIs for CBC parameters across pediatric, adult, and geriatric ages using secondary data, evaluating patterns of changes in CBC parameters. Methods: The reference population comprised 804,623 health examinees (66,611 aged 3-17 years; 564,280 aged 18-59 years; 173,732 aged 60-99 years), and, we excluded 22,766 examinees after outlier testing. The CBC parameters (red blood cell [RBC], white blood cell [WBC], and platelet parameters) from 781,857 examinees were studied. We determined statistically significant partitions of age and sex, and calculated RIs according to the CLSI C28-A3 guidelines. Results: RBC parameters increased with age until adulthood and decreased with age in males, but increased before puberty and then decreased with age in females. WBC and platelet counts were the highest in early childhood and decreased with age. Sex differences in each age group were noted: WBC count was higher in males than in females during adulthood, but platelet count was higher in females than in males from puberty onwards (P <0.001). Neutrophil count was the lowest in early childhood and increased with age. Lymphocyte count decreased with age after peaking in early childhood. Eosinophil count was the highest in childhood and higher in males than in females. Monocyte count was higher in males than in females (P <0.001). Conclusions: We provide comprehensive age- and sex-specific RIs for CBC parameters, which show dynamic changes with both age and sex.

• 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.

• Journal of Korean Society of Transportation
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• v.17 no.5
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• pp.123-135
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• 1999

The rapid increase of Passenger cars which is caused by the discomfort of Public transit and the Preference of automobiles is the major factor of increasing traffic congestions in Seoul With the point that leading the automobilists to the Public transit can be the most important Policy to ease these traffic congestions, this study focuses on the behavioral aspects of company employees and university students and investigates factors influencing bus ridership. To be brief, by estimating bus ridership through count models, this study investigates factors which influence bus ridership and elicits Political suggestions which lead automobilists to Public transit. The Purpose in this study is the application of appropriate count data model. The count data models have been widely applied to the economic area from the middle of the 1980s and to transportation aspect mainly in the foreign countries from the latter half of the 1980s. Even though a few studies in this country employed count data model to count data. all of them were Poisson regression models without suitable tests for the importance of the model specification. In the end, as the result of statistical test, negative binomial regression model which is suitable for overdispersed data was found to be appropriate for the data of weekly bus ridership. To emphasize the importance of model specification, both of poisson regression model and negative binomial regression model were estimated and the results were compared.

• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.569-579
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• 2013

In the field of single-molecule spectroscopy, it is essential to analyze luminescence Intensity changes that result from a single molecule. With the CdSe/ZnS core-shell structured quantum dot photon emission data Bayesian multiple change-point estimation is done with the gamma prior for Poisson parameters and truncated Poisson distribution for the number of change-points.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.927-936
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• 2017

To analyze longitudinal count data, Poisson linear mixed models are commonly used. In the models the random effects covariance matrix explains both within-subject variation and serial correlation of repeated count outcomes. When the random effects covariance matrix is assumed to be misspecified, the estimates of covariates effects can be biased. Therefore, we propose reasonable and flexible structures of the covariance matrix using autoregressive and moving average Cholesky decomposition (ARMACD). The ARMACD factors the covariance matrix into generalized autoregressive parameters (GARPs), generalized moving average parameters (GMAPs) and innovation variances (IVs). Positive IVs guarantee the positive-definiteness of the covariance matrix. In this paper, we use the ARMACD to model the random effects covariance matrix in Poisson loglinear mixed models. We analyze epileptic seizure data using our proposed model.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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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 Korea Society of Computer and Information
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• v.14 no.1
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• pp.217-228
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• 2009

Data analysis applications typically aggregate data across many dimensions looking for unusual patterns in data. Even though such applications are usually possible with standard structured query language (SQL) queries, the queries may become very complex. A complex query may result in many scans of the base table, leading to poor performance. Because online analytical processing (OLAP) queries are usually complex, it is desired to define a new operator for aggregation, called the data cube or simply cube. Data cube supports OLAP tasks like aggregation and sub-totals. Many aggregate functions can be used to construct a data cube. Those functions can be classified into three categories, the distributive, the algebraic, and the holistic. It has been thought that the distributive functions such as SUM, COUNT, MAX, and MIN can be used to construct a data cube, and also the algebraic function such as AVG can be used if the function is replaced to an intermediate function. It is believed that even though AVG is not distributive, but the intermediate function (SUM, COUNT) is distributive, and AVG can certainly be computed from (SUM, COUNT). In this paper, however, it is found that the intermediate function (SUM COUNT) cannot be applied to OLAP cubes, and consequently the function leads to erroneous conclusions and decisions. The objective of this study is to identify some problems in applying aggregate function AVG to OLAP cubes, and to design a process for solving these problems.