• Communications for Statistical Applications and Methods
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• 제25권3호
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• pp.275-282
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• 2018

This paper discusses the use of projections for the sums of squares in the analyses of variance for two-way nested design data. The model for this data is assumed to only have random effects. Two different sizes of experimental units are required for a given experimental situation, since nesting is assumed to occur both in the treatment structure and in the design structure. So, variance components are coming from the sources of random effects of treatment factors and error terms in different sizes of experimental units. The model for this type of experimental situation is a random effects model with more than one error terms and therefore estimation of variance components are concerned. A projection method is used for the calculation of sums of squares due to random components. Squared distances of projections instead of using the usual reductions in sums of squares that show how to use projections to estimate the variance components associated with the random components in the assumed model. Expectations of quadratic forms are obtained by the Hartley's synthesis as a means of calculation.

• 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.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1429-1440
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• 2008

In a meta-analysis combining the results from different clinical trials, it is important to consider the possible heterogeneity in outcomes between trials. Such variations can be regarded as random effects. Thus, random-effect models such as HGLMs (hierarchical generalized linear models) are very useful. In this paper, we propose a HGLM framework for analyzing the binominal response data which may have variations in the odds-ratios between clinical trials. We also present the prediction intervals for random effects which are in practice useful to investigate the heterogeneity of the trial effects. The proposed method is illustrated with a real-data set on 22 trials about respiratory tract infections. We further demonstrate that an appropriate HGLM can be confirmed via model-selection criteria.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.471-479
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• 2007

This paper discusses about how to build up mixed-effects model for analysing ordinal response data by using cumulative logits. Random factors are assumed to be coming from the designed sampling scheme for choosing observational units. Since the observed responses of individuals are ordinal, a proportional odds model with two random effects is suggested. 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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• 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.

• 응용통계연구
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• 제28권2호
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• pp.269-279
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• 2015

본 논문에서는 임의효과에 대한 추론 문제가 다루어졌으며 이 추론에서 신뢰분포를 사용하는 것이 제안되었다. 신뢰분포를 이용한 방법은 표본의 크기가 작아도 임의절편들이 있는 로지스틱 회귀분석에서 좋은 결과를 보여주었으며, 자료분석을 통해서도 각 개체가 가지는 임의효과들에 대한 세밀한 분석이 가능함을 확인하였다.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.523-542
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• 2007

In this paper we consider semiparametric random effect panel models that contain AR(p) disturbances. We derive the efficient score function and the information bound for estimating the slope parameters. We make minimal assumptions on the distribution of the random errors, effects, and the regressors, and provide semiparametric efficient estimates of the slope parameters. The present paper extends the previous work of Park et al.(2003) where AR(1) errors were considered.

• 응용통계연구
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• 제31권6호
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• pp.801-810
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• 2018

확산은 금융이나 물리적 현상의 모형화에 이용되는 확률과정이다. 반복적으로 관측된 확산과정에 대하여 통계적인 모형을 구축할 때, 확률효과를 고려할 필요가 있다. 이 연구에서는 Ornstein-Uhlenbeck 확산모형과 geometric Brownian motion 확산모형에 대하여 확률효과를 도입한다. 모형모수에 대한 최도우도추정법을 적용하기 위하여, 확률효과에 대한 적절한 분포를 가정하여 닫힌 형태로 우도함수를 얻는 방법을 탐색하였다. 1991년부터 2017년까지 27년간 일일 단위로 기록된 다우존스 산업지수에 대하여 확률효과 모형을 적용하였다.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.1-19
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• 1984

A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

• Journal of the Korean Statistical Society
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• 제31권1호
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• pp.93-107
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• 2002

Random effects generalised linear models are useful for analysing clustered count data in which responses are usually correlated. We propose a Bayesian approach to parameter estimation and variable selection in random effects generalised linear models for count data. A simple Gibbs sampling algorithm for parameter estimation is presented and a simple and efficient variable selection is done by using the Gibbs outputs. An illustrative example is provided.