For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare wit...For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature,the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.展开更多
混合效应模型是统计模型中非常重要的一类模型,广泛地应用到许多领域.本文比较了该模型下方差分量的两种估计:方差分析(ANOVA)估计和谱分解(SD)估计,借助吴密霞和王松桂[A new method of spectral decomposition of covariance matrix i...混合效应模型是统计模型中非常重要的一类模型,广泛地应用到许多领域.本文比较了该模型下方差分量的两种估计:方差分析(ANOVA)估计和谱分解(SD)估计,借助吴密霞和王松桂[A new method of spectral decomposition of covariance matrix in mixed effects models and its applications,Sci.China,Ser.A,2005,48:1451-1464]协方差矩阵的谱分解结果,给出了ANOVA估计和SD估计相等的两个充分条件及其相应的统计性质,并将以上的结果应用于圆形部件数据模型和混合方差分析模型.展开更多
基金supported by the National Nature Science Foundation of China(Grant No.10271010)the Natural Science Foundation of Bejng(Grant No.1032001)
文摘For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature,the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.
文摘混合效应模型是统计模型中非常重要的一类模型,广泛地应用到许多领域.本文比较了该模型下方差分量的两种估计:方差分析(ANOVA)估计和谱分解(SD)估计,借助吴密霞和王松桂[A new method of spectral decomposition of covariance matrix in mixed effects models and its applications,Sci.China,Ser.A,2005,48:1451-1464]协方差矩阵的谱分解结果,给出了ANOVA估计和SD估计相等的两个充分条件及其相应的统计性质,并将以上的结果应用于圆形部件数据模型和混合方差分析模型.
