• Asian-Australasian Journal of Animal Sciences
• /
• v.13 no.3
• /
• pp.413-422
• /
• 2000

In the class of models which include random effects, the variance component estimates are important to obtain accurate predictors and estimators. Variance component estimation is straightforward for balanced data but not for unbalanced data. Since orthogonality among factors is absent in unbalanced data, various methods for variance component estimation are available. REML estimation is the most widely used method in animal breeding because of its attractive statistical properties. Recently, Bayesian approach became feasible through Markov Chain Monte Carlo methods with increasingly powerful computers. Furthermore, advances in variance component estimation with complicated models such as generalized linear mixed models enabled animal breeders to analyze non-normal data.

• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.159-164
• /
• 1998

The two-factor nested variance component model with equal numbers in the cells are given by $y_{ijk}\;=\;{\mu}\;+\;A_i\;+\;B_{ij}\;+\;C_{ijk}$ and the confidence intervals for the ratio of variance components, ${\sigma}^{2}_{A}/{\sigma}^{2}_{B}$ are obtained in various forms by many authors. This article shows the probability ranges of these confidence intervals on ${\sigma}^{2}_{A}/{\sigma}^{2}_{B}$ proved by the mathematical computation.

• Korean Journal of Food Science and Technology
• /
• v.26 no.1
• /
• pp.57-61
• /
• 1994

Performance of panelists trained for cooked rice quality was evaluated using analysis of variance, correlation analysis, and principal component analysis. Each method offered different information. Results showed that panleists with high F ratios (p=0.05) did not always have high correlation coefficient (p=0.05) with mean values pooled from whole panel. The results of analysis of variance for the panelists whose performance were extremely good or extremely poor were consistent with those of correlation analysis. Outliers designated by principal component analysis were different from the panelists whose performance was defined as extremely good or extremely poor by analysis of variance and correlation analysis. The results of principal component analysis descriminated the panelists with different scoring range more than different scoring trends depending on the treatments. Our study suggested combination of analysis of variance and correlation analysis provided valid basis for screening panelists.

• Journal of the Korean Statistical Society
• /
• v.18 no.2
• /
• pp.118-124
• /
• 1989

In the one-way random effect model, we often estimate the variance components by the ANOVA method and then estimate the population mean. Whe there are only two distint group sizes, the conventional mean estimator is represented as a weighted average of two normal means with weights being the function of variance component estimators. In this paper, we will study a method which can compute the exact variance of the mean estimator when we set the negative variance component estimate to zero.

• Journal of the Korean Statistical Society
• /
• v.22 no.1
• /
• pp.39-54
• /
• 1993

In the three-factor nested variance component model with equal numbers in the cells given by $y_{ijkm} = \mu + A_i + B_{ij} + C_{ijk} + \varepsilon_{ijkm}$, the exact confidence intervals of the variance component of $\sigma^2_A, \sigma^2_B, \sigma^2_C, \sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_{\varepsilon}, \sigma^2_B/\sigma^2_{\varepsilon}, \sigma^2_C/\sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_C, \sigma^2_B/\sigma^2_C$ and $\sigma^2_A/\sigma^2_B$ are not found out yet. In this paper approximate lower and upper confidence intervals are presented.

• East Asian mathematical journal
• /
• v.5 no.1
• /
• pp.95-110
• /
• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• Communications for Statistical Applications and Methods
• /
• v.12 no.1
• /
• pp.47-59
• /
• 2005

Expected mean square(EMS) is an important part of conducting the analysis of variance in the experimental design problem, especially in mixed or random models. We present a set of EMS rules for balanced factorial designs under no restriction on interaction. Also we point out how to use the variance component of SPSS or SAS procedure to obtain EMS.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.459-471
• /
• 2002

In applications using a linear regression model with nested error structure, one might be interested in making inferences concerning variance components. This article proposes approximate confidence intervals on the variance component of the primary level in a simple linear regression model with an unbalanced nested error structure. The intervals are compared using computer simulation and recommendations are provided for selecting an appropriate interval.

• Journal of the Korean Statistical Society
• /
• v.24 no.2
• /
• pp.407-417
• /
• 1995

The h-plot is a graphical technique for displaying the structure of one population's variance-covariance matrix. This follows the mathematical algorithem of the principle component biplot based on the singular value decomposition. But it is known that the singular value decomposition is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, since the mathematical algorithm of the h-plot is equivalent to that of principal component biplot of Choi and Huh (1994), we derive the resistant h-plot.

• Journal of Animal Science and Technology
• /
• v.55 no.2
• /
• pp.103-107
• /
• 2013

A crucial first step in the planning of any scientific experiment is to evaluate an appropriate sample size to permit sufficient statistical power to detect the desired effect. In this study, we investigated the optimal sample size of quantitative trait locus (QTL) linkage analysis for simple random sibship samples in pedigreed chicken populations, under the variance component framework implemented in the genetic power calculator program. Using the program, we could compute the statistical power required to achieve given sample sizes in variance component linkage analysis in random sibship data. For simplicity, an additive model was taken into account. Power calculations were performed to relate sample size to heritability attributable to a QTL. Under the various assumptions, comparative power curves indicated that the power to detect QTL with the variance component method is highly affected by a function of the effect size of QTL. Hence, more power can be achievable for QTL with a larger effect. In addition, a marked improvement in power could be obtained by increasing the sibship size. Thus, the use of chickens is advantageous regarding the sampling unit issue, since desirable sibship size can be easily obtained compared with other domestic species.