• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.667-675
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• 2001

The usefulness of analysis of variance(ANOVA) estimates of variance components is impaired by the frequent occurrence of negative values. The probability of such an occurrence is therefore of interest. In this paper, we investigate a variety of reasons for negative estimates under one way random effects model. It can be shown, through simulation, that this probability increases when the number of treatments is too small for fixed total observations, unbalancedness of data is severe, ratio of variance components is too small, and data may contain many outliers.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.121-130
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• 1993

For the One-way random effects model with unbalanced data, the AOV and MINQUE estimates of variance components are frequently found to be negative. The primary objective of present study is placed on the computation of the probability of the main effect variance component, being negative. The probability of negative estimators from AOV and MINQUE can be obtained by theoretical computation under the normality assumption. It is, however, difficult to compute the probability of negative estimates for these estimators under arbitrary distributions, and hence their probabilities of being negative were computed by simulation experiment in this study. It was shown that there was no significant difference between the theoretical probability under normality and calculated probability by simulation experiment, and that probability of negative estimates decreases as sample size, number of levels and the value of increase.

• Asian-Australasian Journal of Animal Sciences
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• v.15 no.8
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• pp.1222-1226
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• 2002

Estimates of genetic correlation between direct and maternal effects for weaning weight of beef cattle are often negative in field data. The biological existence of this genetic antagonism has been the point at issue. Some researchers perceived such negative estimate to be an artifact from poor modeling. Recent studies on sources affecting the genetic correlation estimates are reviewed in this article. They focus on heterogeneity of the correlation by sex, selection bias caused from selective reporting, selection bias caused from splitting data by sex, sire by year interaction variance, and sire misidentification and inbreeding depression as factors contributing sire by year interaction variance. A biological justification of the genetic antagonism is also discussed. It is proposed to include the direct-maternal genetic covariance in the analytical models.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.6
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• pp.772-779
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• 2005

The objectives of this study were to examine problems with using F$_1$ data by simulation, association of marker loci and QTL from crosses of inbred parental lines and to enumerate the preliminary characterization of genetic superiority within inbred parental lines. In this study, the association between markers for QTL used as covariates and estimates of variance components due to effects of lines was investigated through computer simulation. The effects of size of population to develop inbred lines and initial frequencies and magnitudes of effects of QTL were also considered. Results show that estimates of variance components due to line effects are influenced by including marker information as covariates in the model for analysis. Estimates of line variance were increased by adding marker information into the analysis, because negative covariances between effects associated with the markers and the remaining effects associated with other loci existed. However, the fit of the model as indicated by the log likelihood improved by adding more markers as covariates into the analysis. Marker assisted selection will be beneficial when markers explain unexplained genetic difference during selection procedure. Markers can be used to identify QTLs affecting traits, and to select for favorable QTL alleles. To efficiently use genetic markers, location of markers at the genome must be identified. The estimates of variance due to effects of with and without marker information used as covariates in the analysis were investigated. The estimates of line variances were always increased when markers were included as covariates for the model because a negative covariance were existed.

• Asian-Australasian Journal of Animal Sciences
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• v.18 no.7
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• pp.909-914
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• 2005

This study was conducted to estimate phenotypic and genetic parameters of body condition score (BCS) and reproductive traits in Hanwoo cows. DFREML procedures were applied to obtain variance-covariance components and heritability estimates with single or two-trait models. Estimates of phenotypic correlations of BCS at service with BCS at calving was 0.16 and 0.26 with calving interval, 0.08 with gestation length, and 0.06 with number of services per conception, respectively. Estimates of phenotypic correlation of BCS at calving was 0.10 with calving interval, 0.13 with gestation length, and 0.10 with number of services per conception, respectively. Estimates of phenotypic correlation were low and negative, -0.11 between calving interval and gestation length and -0.13 between gestation length and number of services per conception. Estimates of direct genetic correlation were -0.06, between BCS at service and BCS at calving, 0.37 between BCS at service and BCS at weaning, and -0.18 between BCS at calving and BCS at weaning. Estimates of direct genetic correlation of days from calving to the 1st service were 0.17 with number of services per conception and -0.21 with BCS at service. Estimates of direct genetic correlation for BCS at calving were -0.02 with number of services per conception and -0.08 with BCS at service. Estimates of direct genetic correlation for BCS at weaning were 0.02 with number of services per conception and -0.07 with BCS at service. Estimates of direct heritability from single trait analyses were 0.13 for BCS at service, 0.20 for BCS at calving, 0.02 for BCS at weaning, and 0.20 for number of service per conception, respectively. Estimates of direct heritability were 0.20 for birth weight and 0.10 for weaning weight.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.337-346
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• 2019

This paper discusses a method for obtaining nonnegative estimates for variance components in a random effects model. A variance component should be positive by definition. Nevertheless, estimates of variance components are sometimes given as negative values, which is not desirable. The proposed method is based on two basic ideas. One is the identification of the orthogonal vector subspaces according to factors and the other is to ascertain the projection in each orthogonal vector subspace. Hence, an observation vector can be denoted by the sum of projections. The method suggested here always produces nonnegative estimates using projections. Hartley's synthesis is used for the calculation of expected values of quadratic forms. It also discusses how to set up a residual model for each projection.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

• KDI Journal of Economic Policy
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• v.40 no.1
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• pp.67-83
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• 2018

We have hypothesized that nuclear risk is significantly inversely related to the distance from residences to nuclear power plants and that the level of life satisfaction of residents therefore increases with the distance. We empirically explore the relationship between Ulsan citizens' life satisfaction levels and the distance between their residences and the Kori and Wolsong nuclear power plants (NPP) based on the life satisfaction approach (LSA). The dataset we used covers only Ulsan citizens from the biennial Ulsan Statistics on Citizen's Living Condition and Consciousness of 2014 and 2016. Controlling for micro-variables such as education, work satisfaction, gender, marital status, and expenditures, we found a statistically significant relationship between life satisfaction and the distance between the residences and the nuclear power plants. Nuclear negative externalities including (i) health and environmental impact, (ii) radioactive waste disposal, and (iii) the effect of severe accidents can be quantified in terms of LS units and monetary units. We were able to calculate the monetary value of NPP externalities at $277 per kilometer of distance for Kori and $280 per kilometer of distance for Wolsong at constant 2015 prices. These estimates are quite different from the traditional estimates made with the contingent valuation method, whereas they are similar to the findings of LSA studies abroad. Hence, the need to adopt the LSA in South Korea and policy implications are demonstrated.

• Asian-Australasian Journal of Animal Sciences
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• v.10 no.5
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• pp.510-513
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• 1997

This study examined the effects of ignoring inbreeding depression on (co)variance components for weaning weight through the use of Monte Carlo simulation. Weaning weight is of particular interest as a trait for which additive direct and maternal genetic components exist and there then is the potential for a direct-maternal genetic covariance. Ignoring inbreeding depression in the analytical model (.8 kg reduction of phenotypic value per 1% inbreeding) led to biased estimates of all genetic (co) variance components, all estimates being larger than the true values of the parameters. In particular, a negative bias in the direct-maternal genetic covariance was observed in analyses that ignored inbreeding depression. A small spurious sire-by-year interaction variance was also observed.