Variances of Variance Components: III. Third Moments in a Balanced Single Classification

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...

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...

Smoothing Balanced Single-Error-Term Analysis of Variance

We present an approach to smoothing balanced, single–error term analysis of variance (ANOVA), descended from Smith, that also allows spatial, temporal, or spatiotemporal smoothing. The approach addresses unreplicated designs, masked contrasts in effects with many degrees of freedom, and subgroup analysis, demonstrated using a study of denture-lining materials. Our approach is Bayesian but can b...

Credible and Confidence Sets for the Ratio of Variance Components in the Balanced One-way Model

Classical confidence intervals for the ratio of variance components can degenerate to a single point with positive probability, leaving no allowance for error. An alternative method is considered which avoids this problem, but maintains the frequentist coverage probability. The alternative intervals are compared to Bayesian credible intervals, derived from a non-informative prior; and the Bayes...

Variance Components