• Communications for Statistical Applications and Methods
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• 제27권3호
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• pp.301-311
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• 2020

Schwarz's Bayesian information criterion (BIC) is one of the most popular criteria for model selection, that was derived under the assumption of independent and identical distribution. For correlated data in longitudinal studies, Jones (Statistics in Medicine, 30, 3050-3056, 2011) modified the BIC to select the best linear mixed effects model based on the effective sample size where the number of parameters in covariance structure was not considered. In this paper, we propose an extended Jones' modified BIC by considering covariance parameters. We conducted simulation studies under a variety of parameter configurations for linear mixed effects models. Our simulation study indicates that our proposed BIC performs better in model selection than Schwarz's BIC and Jones' modified BIC do in most scenarios. We also illustrate an example of smoking data using a longitudinal cohort of cancer patients.

• Journal of Periodontal and Implant Science
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• 제45권1호
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• pp.2-7
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• 2015

A fundamental problem in analyzing complex multilevel-structured periodontal data is the violation of independency among the observations, which is an assumption in traditional statistical models (e.g., analysis of variance and ordinary least squares regression). In many cases, aggregation (i.e., mean or sum scores) has been employed to overcome this problem. However, the aggregation approach still exhibits certain limitations, such as a loss of power and detailed information, no cross-level relationship analysis, and the potential for creating an ecological fallacy. In order to handle multilevel-structured data appropriately, mixed effects models have been introduced and employed in dental research using periodontal data. The use of mixed effects models might account for the potential bias due to the violation of the independency assumption as well as provide accurate estimates.

• 응용통계연구
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• 제28권2호
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• pp.289-294
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• 2015

생동성 시험과 같은 임상약리학분야의 연구는 일반적으로 한 개체 내에서 반복하여 측정된 자료구조를 사용하므로 선형혼합모형을 이용하여 분석하는 것이 보편적이다. 이러한 모형에서 랜덤효과는 개체 내 관측 자료 사이의 상관관계를 설명하고, 공분산행렬은 개체-내 변동을 설명한다. 생동성 분석은 두 약물의 약동학적 변수인 Cmax와 AUC의 기하평균비에 대한 90% 신뢰구간이 동등성 한계인 [0.8, 1.25] 범위에 드는지 알아보는 분석으로, 고정효과에는 시기, 순서군, 치료효과를, 랜덤효과에는 개체효과를 가지는 선형혼합모형을 이용하여 분석한다. 이러한 분석이 적용된 실제 예를 살펴보기 위하여 레보플록사신 연구의 자료를 활용하였다.

• Communications for Statistical Applications and Methods
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• 제20권3호
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• pp.235-240
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• 2013

Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.

• 응용통계연구
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• 제23권6호
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• pp.1169-1178
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• 2010

본 논문은 불균형 자료에서 선형혼합모형에 적용되는 Akaike Information Criterion(AIC)의 효율에 대한 연구이다. Vaida와 Balanchard (2005)에 의해 제안된 cAIC(conditional AIC)는 mAIC(marginal AIC)가 임의효과의 예측에 대한 불확실성을 모형선택에서 반영하지 못하는 단점을 극복할 수 있는 방법이다. cAIC에 대한 이론적인 성질과 확장은 Liang 등 (2008)과 Greven과 Kneib (2010)에 의하여 연구되었다. cAIC의 형태는 자료의 구조에 영향을 받지는 않지만 선형혼합모형에서 모수의 추정 효율은 자료의 불균형의 정도에 따라 많은 영향을 받는 것이 알려져 있다. 기존의 연구에서 실시한 모든 모의실험이 자료가 균형인 경우에만 실행되어 자료의 불균형이 AIC에 근거한 혼합모형 선택 방법의 효율에 어떤 영향을 미치는지 알려져 있지 않다. 본 논문은 자료의 불균형이 모형선택 방법의 효율에 미치는 영향을 모의실험을 통하여 알아보았다. 자료의 불균형이 심해짐에 따라 AIC에 근거한 모형선택방법은 복잡한 모형을 선택하는 경향이 낮아짐을 보였다.

• 응용통계연구
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• 제25권6호
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• 응용통계연구
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• 제31권3호
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• pp.353-366
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• 2018

영상에 의한 인체의 운동 분석에서 발생하는 오차 중 가장 큰 부분을 차지하는 것은 피부와 같은 연조직의 골격에 대한 상대운동이며 이를 STA라 한다. 본 연구의 목적은 고관절 운동 중 대퇴에서 발생하는 STA를 선형혼합모형을 이용하여 예측하는 것이다. 모형에 포함되어 있는 고정효과는 고관절 회전중심과 마커의 위치로 대퇴 골격에 의한 운동의 효과, 임의효과는 고관절 중심으로부터 각 마커의 편차로 STA에 의한 효과로 각각 가정하였다. 이를 위하여 근골격계 질환 경력이 없는 다섯 명의 남성 피험자를 선정하여 대퇴에 아홉 개의 마커를 부착하여 고관절의 기능적 운동을 수행하였다. 동시에 고속카메라를 이용하여 마커의 3차원 좌표를 얻었다. 이 3차원 위치벡터에 선형혼합모형을 적용하여 임의효과를 예측하였다. 분석결과 다섯 명의 피험자는 비슷한 패턴을 보였다. 고관절에 가까운 지점의 STA가 큰 것으로 나타났으며 작은 크기를 보인 부분은 원위 대퇴의 전방이다.

• Communications for Statistical Applications and Methods
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• 제16권6호
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• pp.971-978
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• 2009

Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.

• 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.

• 한국의류학회지
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• 제44권1호
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• pp.84-95
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• 2020

Wearing ease is a critical factor when designing special uniforms such as flight pilot's garment and should reflect occupational properties for better performance. This study measured skin surface on 31 areas in seven postures that refer to the pilot's occupational postures as well as made six prediction models including linear mixed model (LMM) for each body part to find the best fit model. Skin surface measured from 3D body scanned images of 11 male pilot participants. There were significantly positive and negative changes in various areas from standing posture (P1) to dynamic postures (P2-P7). Six models were designed in various compositions using stature and chest circumference as fixed effects and subject and posture as random effects. The best models were linear mixed models with one fixed effect (chest circumference or stature, varies with body parts) and two random effects (subject and posture). The results of this study provide reference data to set wearing ease for pilot's garment and suggests a new methodology in this research area, but verifying the effect of diverse independent variables is left for future studies.