• 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.

• Proceedings of the KIEE Conference
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• 2006.04a
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• pp.90-92
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• 2006

기존의 Support Vector Data Description (SVDD) 방법은 학습 데이터의 개수가 증가함에 따라 학습 시간이 지수 함수적으로 증가하므로, 대량의 데이터를 학습하는 데에는 한계가 있었다. 본 논문에서는 학습 속도를 빠르게 하기 위해 K-means clustering 알고리즘을 이용하는 SVDD 알고리즘을 제안하고자 한다. 제안된 알고리즘은 기존의 decomposition 방법과 유사하게 K-means clustering 알고리즘을 이용하여 학습 데이터 영역을 sub-grouping한 후 각각의 sub-group들을 개별적으로 학습함으로써 계산량 감소 효과를 얻는다. 이러한 sub-grouping 과정은 hypersphere를 이용하여 학습 데이터를 둘러싸는 SVDD의 학습 특성을 훼손시키지 않으면서 중심점으로 모여진 작은 영역의 학습 데이터를 학습하도록 함으로써, 기존의 SVDD와 비교하여 학습 정확도의 차이 없이 빠른 학습을 가능하게 한다. 다양한 데이터들을 이용한 모의실험을 통하여 그 효과를 검증하도록 한다.

• 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.