• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.129-134
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• 1995

The ordinary least square estimator of the disturbance variance in the pooled cross-sectional and time series regression model is shown to be asymptotically unbiased without any restrictions on the regressor matrix when the disturbances follow an equicorrelated error component models.

• Asian-Australasian Journal of Animal Sciences
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• 제21권9호
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• pp.1227-1232
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• 2008

Carcass characteristics data of Hanwoo (N = 1,084) were collected from two stations of the National Livestock Institute of Animal Science (NIAS), Korea and records from thirteen individual cow-calf operators were analyzed to estimate variance and covariance components and the effect of different slaughter endpoints. Carcass traits analyzed were cold carcass weight (CWT, kg), REA (rib eye area, cm2), back fat thickness (mm) and marbling score (1-7). Four different models were examined. All models included sex and contemporary group as fixed effects and the animal's direct genetic potential and environment as random effects. The first model fitted a linear covariate of age at slaughter. The second model fitted both linear and quadratic covariates of age at slaughter. The third model fitted a linear covariate of body weight at slaughter. The fourth model fitted both linear covariates of age at slaughter and body weight at slaughter. Variance components were estimated using the REML procedure with Gibb's sampler. Heritability estimate of CWT was in the range of 0.08-0.11 depending on the model applied. Heritability estimates of BF, REA and MS were in the ranges of 0.23-0.28, 0.19-0.26, and 0.44-0.45, respectively. Genetic correlations between CWT and BF, between CWT and REA, and between CWT and MS were in the ranges of -0.33 - -0.14, 0.73-0.84, and -0.01- 0.11, respectively. Genetic correlations between REA and BF, between MS and BF and between REA and MS were in the ranges of -0.82 ~ -0.72, 0.04~0.28 and -0.08 ~ -0.02, respectively. Variance and covariance components estimated varied by model with different slaughter endpoints. Body weight endpoint was more effective for direct selection in favor of yield traits and body weight endpoints affected more of the correlated response to selection for the traits of yield and quality of edible portion of beef.

• Journal of the Korean Statistical Society
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• 제31권2호
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• pp.177-198
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• 2002

The estimation of variance components or variance ratios in linear model is an important issue in plant or animal breeding fields, and various estimation methods have been devised to estimate variance components or variance ratios. However, many traits of economic importance in those fields are observed as dichotomous or polychotomous outcomes. The usual estimation methods might not be appropriate for these cases. Recently threshold linear model is considered as an important tool to analyze discrete traits specially in animal breeding field. In this note, we consider a hierarchical Bayesian method for the threshold animal model. Gibbs sampler for making full Bayesian inferences about random effects as well as fixed effects is described to analyze jointly discrete traits and continuous traits. Numerical example of the model with two discrete ordered categorical traits, calving ease of calves from born by heifer and calving ease of calf from born by cow, and one normally distributed trait, birth weight, is provided.

• Genomics & Informatics
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• 제20권3호
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• pp.34.1-34.11
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• 2022

Multilevel analysis is an appropriate and powerful tool for analyzing hierarchical structure data widely applied from public health to genomic data. In practice, however, we may lose the information on multiple nesting levels in the multilevel analysis since data may fail to capture all levels of hierarchy, or the top or intermediate levels of hierarchy are ignored in the analysis. In this study, we consider a multilevel linear mixed effect model (LMM) with single imputation that can involve all data hierarchy levels in the presence of missing top or intermediate-level clusters. We evaluate and compare the performance of a multilevel LMM with single imputation with other models ignoring the data hierarchy or missing intermediate-level clusters. To this end, we applied a multilevel LMM with single imputation and other models to hierarchically structured cohort data with some intermediate levels missing and to simulated data with various cluster sizes and missing rates of intermediate-level clusters. A thorough simulation study demonstrated that an LMM with single imputation estimates fixed coefficients and variance components of a multilevel model more accurately than other models ignoring data hierarchy or missing clusters in terms of mean squared error and coverage probability. In particular, when models ignoring data hierarchy or missing clusters were applied, the variance components of random effects were overestimated. We observed similar results from the analysis of hierarchically structured cohort data.

• 응용통계연구
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• 제28권6호
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• pp.1093-1101
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• 2015

본 논문은 요인들의 처리구조와 실험단위들의 설계구조에서 지분이 발생하는 경우의 지분계획모형에서 분산성분을 구하는 방법을 다루고 있다. 지분구조의 고정효과와 확률효과 그리고 실험단위들의 지분구조에 따른 오차성분을 포함하는 지분계획모형을 제안하고 있다. 모형내 확률효과의 분산성분과 다수의 오차항에 따른 분산성분을 추정하는 방법으로 상수적합법을 이용하고 있다. 상수적합법에 의한 제1종 제곱합의 계산은 모형의 단계별 적합에서 주어지는 모형행렬의 사영을 이용하고 구하고 있다. 사영을 이용한 변동요인별 제1종 제곱합의 기댓값 계산에 Hartley의 합성법이 이용된다. 단계별 방법에 의한 모형의 순차적 적합은 모형행렬로의 사영공간을 나타내는 사영행렬의 구조를 파악할 수 있는 이점이 있다.

• Asian-Australasian Journal of Animal Sciences
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• 제14권7호
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• pp.910-914
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• 2001

The teat number of a sow plays an important role for weaning pigs and has been utilized in selection of swine breeding stock. Various linear models have been employed for genetic analyses of teat number although the teat number can be considered as a count trait. Theoretically, Poisson error mixed models are more appropriate for count traits than Normal error mixed models. In this study, the two models were compared by analyzing data simulated with Poisson error. Considering the mean square errors and correlation coefficients between observed and fitted values, the Poisson generalized linear mixed model (PGLMM) fit the data better than the Normal error mixed model. Also these two models were applied to analyzing teat numbers in four breeds of swine (Landrace, Yorkshire, crossbred of Landrace and Yorkshire, crossbred of Landrace, Yorkshire, and Chinese indigenous Min pig) collected in China. However, when analyzed with the field data, the Normal error mixed model, on the contrary, fit better for all the breeds than the PGLMM. The results from both simulated and field data indicate that teat numbers of swine might not have variance equal to mean and thus not have a Poisson distribution.

• Journal of the Korean Statistical Society
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• 제10권
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• pp.91-96
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• 1981

The development of Minimum Norm Quadratic Unbiased Estimation (MINQUE) has introduced a unified approach for the estimation of variance components in general linear models. The computational problem has been studied by Liu and Senturia (1977) and Goodnight (1978, setting a-priori values to 0). This paper further simplifies the computation and gives efficient and compact computational algorithm for the MINQUE and dispersion matrix in general linear random model.

• Journal of the Korean Statistical Society
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• 제18권1호
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• pp.4-12
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• 1989

An efficient method for computing minimum norm quadratic unbiased estimates (MINQUE) of variance components in the mixed model is developed. This computing algorithm which used W-matrix saves both storage usage and computing time.

• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.291-301
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• 2017

It is well known in a small sample that the maximum likelihood (ML) approach for variance components in the general linear model yields estimates that are biased downward. The ML estimate of residual variance tends to be downwardly biased. The underestimation of residual variance, which has implications for the estimation of marginal effects and asymptotic standard error of estimates, seems to be more serious in some limited dependent variable models, as shown by some researchers. An alternative frequentist's approach may be restricted or residual maximum likelihood (REML), which accounts for the loss in degrees of freedom and gives an unbiased estimate of residual variance. In this situation, the REML estimator is derived in a censored regression model. A small sample the REML is shown to provide proper inference on regression coefficients.

• 대한산업공학회지
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• 제19권1호
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• pp.61-71
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• 1993

We focus on a way of combining the Monte Calro methods of antithetic variates and control variates to reduce the variance of the estimator of the mean response in a simulation experiment. Combined Method applies antithetic variates (partially) for driving approiate stochastic model components to reduce the vaiance of estimator and utilizes the correlations between the response and control variates. We obtain the variance of the estimator for the response analytically and compare Combined Method with control variates method. We explore the efficiency of this method in reducing the variance of the estimator through the port operations model. Combined Method shows a better performance in reducing the variance of estimator than methods of antithetic variates and control variates in the range from 6% to 8%. The marginal efficiency gain of this method is modest for the example considered. When the effective set of control variates is small, the marginal efficiency gain may increase. Though these results are from the limited experiments, Combined Method could profitably be applied to large-scale simulation models.