• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.319-332
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• 1997

The application of multivariate linear rank statistics to data with item nonresponse is considered. Only a modest extension of the complete data techniques is required when the missing data may be thought of as a random sample, and an appropriate modification of the covariances is derived. A proof of the asymptotic multivariate normality is given. A review of some related results in the literature is presented and applications including longitudinal and repeated measures designs are discussed.

• The Korean Journal of Applied Statistics
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• v.35 no.6
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• pp.703-724
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• 2022

Although longitudinal studies mainly produce multivariate longitudinal data, most of existing statistical models analyze univariate longitudinal data and there is a limitation to explain complex correlations properly. Therefore, this paper describes various methods of modeling the covariance matrix to explain the complex correlations. Among them, modified Cholesky decomposition, modified Cholesky block decomposition, and hypersphere decomposition are reviewed. In this paper, we review these methods and analyze Korean children and youth panel (KCYP) data are analyzed using the Bayesian method. The KCYP data are multivariate longitudinal data that have response variables: School adaptation, academic achievement, and dependence on mobile phones. Assuming that the correlation structure and the innovation standard deviation structure are different, several models are compared. For the most suitable model, all explanatory variables are significant for school adaptation, and academic achievement and only household income appears as insignificant variables when cell phone dependence is a response variable.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.15-35
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• 2020

In research on behavioral studies, significant attention has been paid to the stage-sequential process for multiple latent class variables. We now explore the stage-sequential process of multiple latent class variables using the multivariate latent class profile analysis (MLCPA). A latent profile variable, representing the stage-sequential process in MLCPA, is formed by a set of repeatedly measured categorical response variables. This paper proposes the extended MLCPA in order to explain an association between the latent profile variable and the latent group variable as a form of a two-dimensional contingency table. We applied the extended MLCPA to the National Longitudinal Survey on Youth 1997 (NLSY97) data to investigate the association between of developmental progression of depression and substance use behaviors among adolescents who experienced Authoritarian parental styles in their youth.

• The Korean Journal of Applied Statistics
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• v.33 no.3
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• pp.281-296
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• 2020

Repeated outcomes from the same subjects are referred to as longitudinal data. Analysis of the data requires different methods unlike cross-sectional data analysis. It is important to model the covariance matrix because the correlation between the repeated outcomes must be considered when estimating the effects of covariates on the mean response. However, the modeling of the covariance matrix is tricky because there are many parameters to be estimated, and the estimated covariance matrix should be positive definite. In this paper, we consider analysis of multivariate longitudinal data via two modeling methodologies for the covariance matrix for multivariate longitudinal data. Both methods describe serial correlations of multivariate longitudinal outcomes using a modified Cholesky decomposition. However, the two methods consider different decompositions to explain the correlation between simultaneous responses. The first method uses enhanced linear covariance models so that the covariance matrix satisfies a positive definiteness condition; in addition, and principal component analysis and maximization-minimization algorithm (MM algorithm) were used to estimate model parameters. The second method considers variance-correlation decomposition and hypersphere decomposition to model covariance matrix. Simulations are used to compare the performance of the two methodologies.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.335-342
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• 2015

Joint hierarchical generalized linear models proposed by Molas et al. (2013) extend the simple longitudinal model into multiple models fitted jointly. It can easily handle the correlation of multivariate longitudinal data. In this paper, we apply this method to analyze KoGES cohort dataset. Fixed unknown parameters, random effects and variance components are estimated based on a standard framework of h-likelihood theory. Furthermore, based on the conditional Akaike information criterion the correlated covariance structure of random-effect model is selected rather than an independent structure.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.389-402
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• 2023

Multivariate or clustered failure time data often occur in many medical, epidemiological, and socio-economic studies when survival data are collected from several research centers. If the data are periodically observed as in a longitudinal study, survival times are often subject to various types of interval-censoring, creating multivariate interval-censored data. Then, the event times of interest may be correlated among individuals who come from the same cluster. In this article, we propose a unified linear regression method for analyzing multivariate interval-censored data. We consider a semiparametric multivariate accelerated failure time model as a statistical analysis tool and develop a generalized Buckley-James method to make inferences by imputing interval-censored observations with their conditional mean values. Since the study population consists of several heterogeneous clusters, where the subjects in the same cluster may be related, we propose a generalized estimating equations approach to accommodate potential dependence in clusters. Our simulation results confirm that the proposed estimator is robust to misspecification of working covariance matrix and statistical efficiency can increase when the working covariance structure is close to the truth. The proposed method is applied to the dataset from a diabetic retinopathy study.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.191-202
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• 2024

The goal of this paper is to show how multivariate regression analysis with high-dimensional responses is facilitated by the response dimension reduction. Multivariate regression, characterized by multi-dimensional response variables, is increasingly prevalent across diverse fields such as repeated measures, longitudinal studies, and functional data analysis. One of the key challenges in analyzing such data is managing the response dimensions, which can complicate the analysis due to an exponential increase in the number of parameters. Although response dimension reduction methods are developed, there is no practically useful illustration for various types of data such as so-called large p-small n data. This paper aims to fill this gap by showcasing how response dimension reduction can enhance the analysis of high-dimensional response data, thereby providing significant assistance to statistical practitioners and contributing to advancements in multiple scientific domains.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.295-304
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• 2015

This paper considers the problem of estimation of the Hurst parameter H ${\in}$ (1/2, 1) from longitudinal data with the error term of a fractional Brownian motion with Hurst parameter H that gives the amount of the long memory of its increment. We provide a new estimator of Hurst parameter H using a two scale sampling method based on $A{\ddot{i}}t$-Sahalia and Jacod (2009). Asymptotic behaviors (consistent and central limit theorem) of the proposed estimator will be investigated. For the proof of a central limit theorem, we use recent results on necessary and sufficient conditions for multi-dimensional vectors of multiple stochastic integrals to converges in distribution to multivariate normal distribution studied by Nourdin et al. (2010), Nualart and Ortiz-Latorre (2008), and Peccati and Tudor (2005).

• Genomics & Informatics
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• v.20 no.1
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• pp.8.1-8.14
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• 2022

Despite the success of recent genome-wide association studies investigating longitudinal traits, a large fraction of overall heritability remains unexplained. This suggests that some of the missing heritability may be accounted for by gene-gene and gene-time/environment interactions. In this paper, we develop a Bayesian variable selection method for longitudinal genetic data based on mixed models. The method jointly models the main effects and interactions of all candidate genetic variants and non-genetic factors and has higher statistical power than previous approaches. To account for the within-subject dependence structure, we propose a grid-based approach that models only one fixed-dimensional covariance matrix, which is thus applicable to data where subjects have different numbers of time points. We provide the theoretical basis of our Bayesian method and then illustrate its performance using data from the 1000 Genome Project with various simulation settings. Several simulation studies show that our multivariate method increases the statistical power compared to the corresponding univariate method and can detect gene-time/ environment interactions well. We further evaluate our method with different numbers of individuals, variants, and causal variants, as well as different trait-heritability, and conclude that our method performs reasonably well with various simulation settings.

• 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.