• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.31-39
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• 2015

This paper deals with a method for estimating variance components on the basis of projections under the assumption of random effects model. It discusses how to use projections for getting sums of squares to estimate variance components. The use of projections makes the vector subspace generated by the model matrix to be decomposed into subspaces that are orthogonal each other. To partition the vector space by the model matrix stepwise procedure is used. It is shown that the suggested method is useful for obtaining Type I sum of squares requisite for the ANOVA method.

• The Korean Journal of Applied Statistics
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• v.29 no.2
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• pp.291-299
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• 2016

This paper discusses how to establish estimable functions when there are fixed and random effects in design models. It proves that estimable functions of mixed models are not related to random effects. A fitting constants method is used to obtain sums of squares due to random effects and Hartley's synthesis is used to calculate coefficients of variance components. To test about the fixed effects the degrees of freedom associated with divisor are determined by means of the Satterthwaite approximation.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.4
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• pp.525-530
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• 2020

Objective: The purpose of this study was i) to identify the characteristics of carcass traits in Chikso by gender, region, age at slaughter, and coat color using the carcass data collected from the nationwide pedigree information and coat color investigation, and ii) to estimate genetic parameters for breed improvement. Methods: A linear model was used to analyze the environmental effects on the carcass traits and to estimate genetic parameters. Analysis of variance was performed using TYPE III sum of squares for the unbalanced data provided by the general linear model procedure. Variance components for genetic parameters was estimated using REMLF90 of the BLUPF90 family programs. Results: Phenotypic performance of carcass weight (CW), eye muscle area (EMA), and backfat thickness (BF) in Chikso were lower than those of Hanwoo. This is a natural outcome because Hanwoo have undergone significant efforts for improvement at the national level, a phenomenon not observed in Chikso. Another factor influencing the above outcome was the smaller population size of Chikso compared to that of Hanwoo's. The heritabilities of CW, EMA, BF, and marbling score in Chikso were estimated as 0.50, 0.37, 0.35, and 0.53, respectively, which were was higher than those of Hanwoo. Conclusion: Based on the genetic parameters that were estimated in this study, it is expected that the carcass traits will improve when the livestock research institutes at each province conduct small-scale performance tests and the semen is provided to farmers after selecting proven bulls using the state-of-art selection technique such as genomic selection.