To assess the adequacy of a nonreplicated linear regression model, Christensen introduced the concepts of orthogonal between- and within-cluster lack of fit with corresponding optimal tests. However, the properties of these tests depend on the choice of near-replicate clusters. In this paper, a graph theoretic framework is presented to represent candidate clusterings. A clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a specified graph on the predictor settings. Examples are given to illustrate the methodology.
"Maximin clusters for near-replicate regression lack of fit tests." Ann. Statist. 26 (4) 1411 - 1433, August 1998. https://doi.org/10.1214/aos/1024691249