A family of quasisymmetry models. (English) Zbl 1344.05155

Kateri, Maria; Mohammadi, Fatemeh; Sturmfels, Bernd

J. Algebr. Stat. 6, No. 1, 1-16 (2015).

Summary: We present a one-parameter family of models for square contingency tables that interpolates between the classical quasisymmetry model and its Pearsonian analogue. Algebraically, this corresponds to deformations of toric ideals associated with graphs. Our discussion of the statistical issues centers around maximum likelihood estimation.

MSC:

05E40	Combinatorial aspects of commutative algebra
13P25	Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
62H17	Contingency tables

Keywords:

square contingency tables; algebraic statistics; toric models; linear models; maximum likelihood estimation; \(\phi\)-divergence