Estimation in the general incomplete block design with applications to the analysis of mating structures

Models for analysing data for two commonly used sampling schemes involving inbreeding and environmental effects is considered. The general incomplete block model is utilized where mating types are equated to incomplete blocks. The models allow for varying degrees of inbreeding within mating types and between mating types. The analysis is such as to remove some of the confounding of inbreeding and environmental effects. The models are formulated in matrix notation utilizing pseudoinverses of matrices. Intrablock and interblock estimates of environmental effects or treatment effects are obtained with a suggestion as how one might combine the two estimates. An example is presented to demonstrate the computations.