• Communications for Statistical Applications and Methods
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• 제24권1호
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• pp.81-96
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• 2017

Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
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• pp.1-6
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• 2006

We consider the issue of Bayesian prediction of the unobservable random effects, And we characterize priors that ensure approximate frequentist validity of posterior quantiles of unobservable random effects. Finally we show that the probability matching criteria for prediction of unobservable random effects in one-way random ANOVA model.

• 한국ITS학회 논문지
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• 제16권1호
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• pp.26-37
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• 2017

본 연구는 random effects Tobit 회귀모형을 이용하여 도심지 교차로에 대한 교통사고모형을 개발하여 교통사고와 요인간의 상관관계를 파악하는 것이 목적이다. Random effects Tobit 회귀모형의 적용성을 비교 분석하기 위하여 fixed effect Tobit 회귀모형을 산정하였다. 산정결과, 교통량, 제한속도, 차로수, 토지이용, 우회전차로, 전방신호등이 유효한 변수로 나타났으며, 총 교통사고율에 대한 random effects 모형의 모형 적합도(결정계수: 0.418, 로그-우도함수값: -3210.103, 우도비: 0.056)와 모형 설명력(MAD: 19.533, MAPE: 75.725, RMSE: 26.886)은 fixed effects 모형의 모형 적합도 (결정계수: 0.298, 로그-우도함수값: -3276.138, 우도비: 0.037)와 모형 설명력(MAD: 20.725, MAPE: 82.473, RMSE: 27.267)보다 우수한 것으로 나타났으며, 부상교통사고율에 대한 교통사고모형에서도 총 교통사고율의 산정결과와 동일하게 나타나 두 모형에서 random effects Tobit 회귀모형이 다소 우수한 것으로 분석되었다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.193-200
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• 2000

Modelling the dependence via random effects in censored multivariate survival data has recently received considerable attention in the biomedical literature. The random effects models model not only the conditional survival times but also the conditional hazard rate. Systematic likelihood inference for the models with random effects is possible using Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). The purpose of this presentation is to introduce Ha et al.'s (2000a,b) inferential methods for the random effects models via the h-likelihood, which provide a conceptually simple, numerically efficient and reliable inferential procedures.

• Journal of the Korean Data and Information Science Society
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• 제27권3호
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• pp.815-825
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• 2016

Marginalized random effects models (MREMs) are often used to analyze longitudinal categorical data. The models permit direct estimation of marginal mean parameters and specify the serial correlation of longitudinal categorical data via the random effects. However, it is not easy to estimate the random effects covariance matrix in the MREMs because the matrix is high-dimensional and must be positive-definite. To solve these restrictions, we introduce two modeling approaches of the random effects covariance matrix: partial autocorrelation and the modified Cholesky decomposition. These proposed methods are illustrated with the real data from Korean genomic epidemiology study.

• Communications for Statistical Applications and Methods
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• 제27권2호
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• pp.201-210
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• 2020

Baseline-category logit random effects models have been used to analyze longitudinal nominal data. The models account for subject-specific variations using random effects. However, the random effects covariance matrix in the models needs to explain subject-specific variations as well as serial correlations for nominal outcomes. In order to satisfy them, the covariance matrix must be heterogeneous and high-dimensional. However, it is difficult to estimate the random effects covariance matrix due to its high dimensionality and positive-definiteness. In this paper, we exploit the modified Cholesky decomposition to estimate the high-dimensional heterogeneous random effects covariance matrix. Bayesian methodology is proposed to estimate parameters of interest. The proposed methods are illustrated with real data from the McKinney Homeless Research Project.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.169-181
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• 2014

Marginalized random effects models (MREM) are commonly used to analyze longitudinal categorical data when the population-averaged effects is of interest. In these models, random effects are used to explain both subject and time variations. The estimation of the random effects covariance matrix is not simple in MREM because of the high dimension and the positive definiteness. A relatively simple structure for the correlation is assumed such as a homogeneous AR(1) structure; however, it is too strong of an assumption. In consequence, the estimates of the fixed effects can be biased. To avoid this problem, we introduce one approach to explain a heterogenous random effects covariance matrix using a modified Cholesky decomposition. The approach results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The interpretation of the parameters is sensible. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using this method.

• Journal of the Korean Data and Information Science Society
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• 제25권6호
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• pp.1263-1272
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• 2014

경시적 범주형자료 (longitudinal categorical data)는 의학, 보건학, 그리고 사회과학에서 많이 발생하는 자료이다. 이러한 자료는 반복측정으로 인한 결과치들의 상관관계를 설명하면서 공변량의 효과를 설명해야 한다. 이 논문에서 모집단에 대한 공변량의 효과를 추정하면서 우도함수에 기초한 모형인 주변화 변량효과모형 (marginalized random effects model)을 소개하고, 그 모형의 어떻게 발전했는지를 고찰한다. 그리고 실제 자료를 이용하여 제시된 모형을 설명한다.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.123-130
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• 2006

This paper discusses about how to build up a mixed-effects model using cumulative logits when some factors are fixed and others are random. Location effects are considered as random effects by choosing them randomly from a population of locations. Estimation procedure for the unknown parameters in a suggested model is also discussed by an illustrated example.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.203-209
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• 2009

Frailty models are useful for the analysis of correlated and/or heterogeneous survival data. However, the inferences of fixed parameters, rather than random effects, have been mainly studied. The prediction (or estimation) of random effects is also practically useful to investigate the heterogeneity of the hospital or patient effects. In this paper we propose how to extend the prediction method for random effects in HGLMs (hierarchical generalized linear models) to log-normal semiparametric frailty models with nonparametric baseline hazard. The proposed method is demonstrated by a simulation study.