• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.205-213
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• 2007

In this paper, the normal mixture model subjected to general linear restriction for component-means based on linear regression is proposed, and its fitting method by EM algorithm and Lagrange multiplier is provided. This model is applied to gene clustering of microarray expression data, which demonstrates it has very good performances for real data set. This model also allows to obtain the clusters that an analyst wants to find out in the fashion that the hypothesis for component-means is represented by the design matrices and the linear restriction matrices.

• Journal of the Korean Statistical Society
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• 제28권3호
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• pp.325-336
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• 1999

Collinearity among independent variables can have severe effects on the precision of response estimation for some region of interest in the experiments with mixture. A method of finding optimal linear restriction on regression parameter in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• 대한원격탐사학회지
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• 제23권6호
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• pp.537-546
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• 2007

초분광영상의 분석 기법 중 하나인 선형혼합분석기법은 각 화소를 구성하는 구성물질과 구성 비율을 추정하는데 매우 유용하게 사용되고 있다. 선형혼합모델은 지질 및 광물분포와 관련된 분야에서는 비교적 성공적으로 시도되고 있으나, 산림이나 여러 인공물들로 구성된 도시와 같은 상대적으로 복잡한 구조를 가진 혼합체에서는 그 정확도가 떨어진다. 본 연구에서는 식물과 토양의 혼합체를 대상으로 선형혼합모델을 적용하여 계산된 혼합체의 반사값과 실제 이 혼합체들을 분광측정기로 측정한 반사값과의 비교를 통해, 선형혼합모델의 오차를 계산하였다. 이를 통해 선형혼합모델의 오차 원인인 구성 물질간의 분광적 상호작용이 어느 경우 발생 혹은 증가하는지를 분석하고, 또한 파장대별 상호작용의 정도 차이가 있는지를 분석하였다. 연구 결과, 선형혼합모델은 혼합체를 구성하는 구성물질의 구성비율이 비슷한 경우, 각 구성 물질간의 상호작용이 증가하여 선형혼합모델의 오차가 가장 커지는 것을 알 수 있었다. 결과적으로 선형혼합모델의 오차 원인인 구성 물질간 상호작용의 발생 정도는 혼합체를 구성하는 성분의 종류, 반사 특성, 구성비율, 파장대와 구성 성분의 배열 상태에 따라 다르게 나타나는 것을 알 수 있었다. 향후 선형혼합모델의 정확도를 높이기 위해서는 이러한 혼합체의 특징들이 구성 물질간의 상호작용에 끼치는 영향을 정량적으로 분석하여야 할 것이다.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.239-250
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• 1998

A method of finding optimal linear restriction on regression parameters in linear model for mixture experiments in the sense of minimizing integrated mean squared error is studied. We use the formulation of optimal restrictions on regression parameters for estimating responses proposed by Park(1981) by transforming mixture components to mathematically independent variables.

• International Journal of Reliability and Applications
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• 제6권2호
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• pp.101-115
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• 2005

This article provides a new class of multivariate linear failure rate distributions where every component is a mixture of linear failure rate distribution. The new class includes several multivariate and bivariate models including Marslall and Olkin type. The approach in this paper is based on the introducing a linear failure rate distributed latent random variable. The distribution of minimum in a competing risk model is discussed.

• Communications for Statistical Applications and Methods
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• 제13권1호
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• pp.113-123
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• 2006

Normal mixture model(NMM) frequently used to cluster genes on microarray gene expression data. In this paper some of component means of NMM are modelled by a linear regression model so that its design matrix presents the pattern between sample classes in microarray matrix. This modelling for the component means by given design matrices certainly has an advantage that we can lead the clusters that are previously designed. However, it suffers from 'overfitting' problem because in practice genes often are highly dimensional. This problem also arises when the NMM restricted by the linear model for component-means is fitted. To cope with this problem, in this paper, the use of the factor analyzer NMM restricted by linear model is proposed to cluster genes. Also several design matrices which are useful for clustering genes are provided.

• 응용통계연구
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• 제25권3호
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• pp.415-422
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• 2012

For statistical microarray data analysis, clustering analysis is a useful exploratory technique and offers the promise of simultaneously studying the variation of many genes. However, most of the proposed clustering methods are not rigorously solved for a time-course microarray data cluster and for a fitting time covariate; therefore, a statistical method is needed to form a cluster and represent a linear trend of each cluster for each gene. In this research, we developed a modified hierarchical mixture of an experts model to suggest clustering data and characterize each cluster using a linear mixed effect model. The feasibility of the proposed method is illustrated by an application to the human fibroblast data suggested by Iyer et al. (1999).

• Journal of the Korean Statistical Society
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• 제27권4호
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• pp.407-420
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• 1998

This paper is concerned with selecting covariates to be included in building linear random effects models designed to analyze clustered response normal data. It is based on a Bayesian approach, intended to propose and develop a procedure that uses probabilistic considerations for selecting premising subsets of covariates. The approach reformulates the linear random effects model in a hierarchical normal and point mass mixture model by introducing a set of latent variables that will be used to identify subset choices. The hierarchical model is flexible to easily accommodate sign constraints in the number of regression coefficients. Utilizing Gibbs sampler, the appropriate posterior probability of each subset of covariates is obtained. Thus, In this procedure, the most promising subset of covariates can be identified as that with highest posterior probability. The procedure is illustrated through a simulation study.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.625-637
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• 2015

We develop a Bayesian clustering procedure based on a Dirichlet process prior with cluster specific random effects. Gibbs sampling of a normal mixture of linear mixed regressions with a Dirichlet process was implemented to calculate posterior probabilities when the number of clusters was unknown. Our approach (unlike its counterparts) provides simultaneous partitioning and parameter estimation with the computation of the classification probabilities. A Monte Carlo study of curve estimation results showed that the model was useful for function estimation. We find that the proposed Dirichlet process mixture model with cluster specific random effects detects clusters sensitively by combining vague edges into different clusters. Examples are given to show how these models perform on real data.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.589-598
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• 2015

In longitudinal studies missing data are common and require a complicated analysis. There are two popular modeling frameworks, pattern mixture model (PMM) and selection models (SM) to analyze the missing data. We focus on the PMM and we also propose Bayesian pattern mixture models using generalized linear mixed models (GLMMs) for longitudinal binary data. Sensitivity analysis is used under the missing not at random assumption.