TY - JOUR
T1 - Two-factor saturated designs
T2 - Cycles, gini index, and state polytopes
AU - Fontana, Roberto
AU - Rapallo, Fabio
AU - Rogantin, Maria Piera
PY - 2014/1/2
Y1 - 2014/1/2
N2 - 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.
AB - 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.
KW - Estimability
KW - Gini index
KW - State polytope
KW - Universal Markov basis
UR - http://www.scopus.com/inward/record.url?scp=84891276407&partnerID=8YFLogxK
U2 - 10.1080/15598608.2014.840518
DO - 10.1080/15598608.2014.840518
M3 - Article
SN - 1559-8608
VL - 8
SP - 66
EP - 82
JO - Journal of Statistical Theory and Practice
JF - Journal of Statistical Theory and Practice
IS - 1
ER -