Two-Factor Saturated Designs: Cycles, Gini Index, and State Polytopes
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In this article, we analyze and characterize the saturated fractions of two-factor designs under the simple effect model. Using linear algebra, we define a criterion to check whether a given fraction is saturated or not. We also compute the number of saturated fractions, providing an alternative proof of the Cayley’s formula. Finally, we show how, given a list of saturated fractions, Gini indexes of their margins and the associated state polytopes could be used to classify them.
KeywordsEstimability Gini index State polytope Universal Markov basis
AMS Subject Classification62K15 15B34 05B20 62H17
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