Variance component ($V={\sum }_k{\tau }_k^2{Z}_k{Z}_k^T+R$)

A variance component is a nonnegative parameter multiplying a specified covariance contribution. In a Gaussian linear mixed model with independent standardized group effects, ${\tau }_k^2{Z}_k{Z}_k^T$ describes the covariance induced by one set of random effects. Testing whether a component is zero is a variance-component likelihood-ratio test at a boundary; ordinary regular chi-squared likelihood-ratio calibration need not apply.