Identifying All Connected Subsets in a Two-Way Classification Without Interaction

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Abstract
Animal breeding applications often require determining connectedness of data for statistical or computational reasons. A method is presented for iden- tifying all connected subsets in a two- way classification without interactions. An example of a sire evaluation model with fixed herd-year-seasons and genetic groups and random sires nested within genetic groups is used to describe the algorithm. The method involves four steps for each herd-year-season. The re- sult is a vector, and elements with the same number correspond to connected genetic groups. The algorithm is simple computationally and does not require matrix storage; thus, it can be used when the number of classes of each main effect is large. Applications include identifying estimable contrasts involving fixed effects and obtaining a set of linearly indepen- dent equations from the normal equations.