ABSTRACT
Chapter 15 derived a simple form for the restricted likelihood for two-variance models. This also yielded a vector of known linear functions of the data y, the vˆ j, with nice properties: They contain all the information about the two variances and conditional on (σ2s ,σ2e ) they are independent with mean zero and variance σ2s a j +σ2e , where the a j are known functions of the design matrices X and Z. Also, for twovariance models, the re-expressed restricted likelihood is a particular generalized linear model. These facts provided some tools with which we pried open the black box of the restricted likelihood and analyzed it, much as we might analyze a linear model fit.
