Variances of Variance Components: II. The Unbalanced Single Classification

Running head : Approximate REML sampling variances Approximation of Sampling Variances and Confidence Intervals for Maximum Likelihood Estimates of Variance Components

After reviewing pertinent literature on the estimation of sampling variances and confidence intervals in the maximum likelihood framework, a method to approximate these for individual parameters in a multi-parameter analysis is described. It is based on the profile likelihood, defined as the likelihood for a subset of parameter(s) of interest with the remaining parameters equal to their maximum...

- - , ' Estimation of Ratios of Variance Components in the Unbalanced One Way Random Effects Model

The point estimation of the ratio of variance components and the intraclass correlation coefficient for the unbalanced one way random effects model are considered. ANOVA, REML, ML, MIVQUE, MINQE type, and MU (median unbiased) estimators are compared with respect to their absolute biases and mean squared errors through a simulation study. Explicit, computable expressions with no matrix inversion...

Identification of Factors Causing Heterogeneous Within-Herd Variance Components Using a Structural Model for Variances

Many applications of mixed linear statistical models for genetic evaluation of dairy cattle assume that genetic and residual components of variance are each constant across environments. However, this assumption is violated for production and conformation traits, which can reduce accuracy of selection and cause biases in the proportions of breeding animals chosen from each environment. Best lin...

Efficient moment calculations for variance components in large unbalanced crossed random effects models

Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation, inference and prediction (both space and time) grow at most linearly with sample size. Both traditional maximum likelihood estimation and numerous Markov cha...

Variance Components