Families of Generalized Quasisymmetry Models: A ϕ-Divergence Approach

Symmetry

Maria Kateri¹ 

[1] Institute of Statistics, RWTH Aachen University, 52062 Aachen, Germany;

关键词: square contingency table;    ordinal variables;    generalized odds ratios;    log-linear models;    association models;   

DOI  :  10.3390/sym13122297

来源: DOAJ

【 摘 要 】

The quasisymmetry ($QS$) model for square contingency tables is revisited, highlighting properties and features on the basis of its alternative definitions. More parsimonious $QS$-type models, such as the ordinal QS model for ordinal classification variables and models based on association models (AMs) with homogeneous row and column scores, are discussed. All these models are linked to the local odds ratios (LOR). $QS$-type models and AMs were extended in the literature for generalized odds ratios other than LOR. Furthermore, in an information-theoretic context, they are expressed as distance models from a parsimonious reference model (the complete symmetry for $QS$ and the independence for AMs), while they satisfy closeness properties with respect to Kullback–Leibler (KL) divergence. Replacing the KL by $\varphi$ divergence, flexible classes of $QS$-type models for LOR, AMs for LOR, and AMs for generalized odds ratios were generated. However, special $QS$-type models that are based on homogeneous AMs for LOR have not been extended to $\varphi$-divergence-based classes so far, or the $QS$-type models for generalized odds ratios. In this work, we develop these missing extensions, and discuss $QS$-type models and their generalizations in depth. These flexible families enrich the modeling options, leading to models of better fit and sound interpretation, as illustrated by representative examples.

【 授权许可】

Unknown