• 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.

• 응용통계연구
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• 제28권2호
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• pp.211-219
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• 2015

일반화 선형혼합모델은 일반적으로 경시적 범주형 자료를 분석하는데 사용된다. 이 모델에서 임의효과는 반복 측정치들의 시간에 따른 의존성을 설명한다. 임의효과 공분산행렬의 추정은 여러가지 제약조건들 때문에 쉽지 않은 문제이다. 제약조건으로는 행렬의 모수들의 수가 많으며, 또한 추정된 공분산행렬은 양정치성을 만족하여야 한다. 이러한 제한을 극복하기 위해, 임의효과 공분산행렬의 모형화를 위한 여러가지 방법이 제안되었다: 수정 단냠레스키분해, 이동평균 단냠레스키분해와 부분 자기상관행렬을 이용한 방법이 있다. 이 논문에서 위의 제안된 방법들을 소개한다.

• 응용통계연구
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• 제30권1호
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• pp.103-117
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• 2017

경시적 자료분석에서 공변량 효과를 추정할 때 반복 측정된 결과들의 상관성은 고려되어야 한다. 따라서 공분산 행렬을 모형화하는 것은 매우 중요하다. 그러나 공분산 행렬의 추정은 모수들의 수가 많고 추정된 공분산행렬이 양정치성을 만족해야 하므로 쉽지 않은 문제이다. 이러한 제한을 극복하기 위해, 공분산행렬의 모형화를 위한 여러가지 방법을 제안하였다: 자기회귀/이동평균/자기회귀-이동평균 구조를 각각 적용한 수정 콜레스키분해 (Pourahmadi, 1999), 이동평균 콜레스키분해 (Zhang과 Leng, 2012)와 자기회귀-이동평균 콜레스키 분해 (Lee 등, 2017) 이들 구조를 가지는 공분산 행렬의 특징을 비교연구하고자 한다. 이 세 가지 모형의 성능을 비교하기 위한 모의실험을 실시한다.

• Communications for Statistical Applications and Methods
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• 제25권1호
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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 Korean Data and Information Science Society
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• 제28권4호
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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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• 제23권6호
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• pp.575-585
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• 2016

Longitudinal studies repeatedly measure outcomes over time. Therefore, repeated measurements are serially correlated from same subject (within-subject variation) and there is also variation between subjects (between-subject variation). The serial correlation and the between-subject variation must be taken into account to make proper inference on covariate effects (Diggle et al., 2002). However, estimation of the covariance matrix is challenging because of many parameters and positive definiteness of the matrix. To overcome these limitations, we propose autoregressive moving average Cholesky decomposition (ARMACD) for the linear mixed models. The ARMACD allows a class of flexible, nonstationary, and heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the random effects covariance matrix. We analyze a real dataset to illustrate our proposed methods.