Generalised quasi‐symmetry models for ordinal contingency tables

Kateri, Maria; Gottard, Anna; Tarantola, Claudia

doi:10.1111/anzs.12194

Cited by 4 publications

(12 citation statements)

References 29 publications

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“…The indexes φ and ϕ can measure the degree of departure from the QS model corresponding to the EQS model since these indexes are expressed as the function of γ under the EQS model. On the contrary, Kateri et al (2017) proposed the conditional QS (CQS) model as another extension of the QS model. The reader may be interested in measuring the degree of departure from the QS model corresponding to the CQS model, which is a matter to be considered in future studies.…”

Section: Discussionmentioning

confidence: 99%

“…The QS model is a typical model among many models for the square contingency table. The issues related to the QS model have been analyzed in many studies, for example, Kateri and Papaioannou (1997), Kateri and Agresti (2007), Saigusa, Tahata, and Tomizawa (2015), Kateri, Gottard, and Tarantola (2017), Altun (2019), Tahata (2019), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

Ando

2021

AJS

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This study proposes a bivariate index vector to concurrently analyze both the degree and direction of departure from the quasi-symmetry (QS) model for ordinal square contingency tables. The QS model and extended QS (EQS) models identify the symmetry and asymmetry between the probabilities of normal circulation and reverse circulation when the order exists for arbitrary three categories. The asymmetry parameter of the EQS model implies the degree of departure from the QS model; the EQS model is equivalent to the QS model when the asymmetry parameter equals to one. The structure of the EQS model differs depending on whether the asymmetry parameter approaches zero or infinity. Thus, the asymmetry parameter of the EQS model also implies the direction of departure from the QS model. The proposed bivariate index vector is constructed by combining existing and original sub-indexes that represent the degree of departure from the QS model and its direction. These sub-indexes are expressed as functions of the asymmetry parameter under the EQS model. We construct an estimator of the proposed bivariate index vector and an approximate confidence region for the proposed bivariate index vector. Using real data, we show that the proposed bivariate index vector is important to compare degrees of departure from the QS model for plural data sets.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

Ando

2021

AJS

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“…Motivated by the definition of QS through the symmetric LOR, the authors in [15] introduced generalized QS-type models for generalized odds ratios other than the LOR. In this context, the classical QS model that applies on the LOR would be denoted by QS L , while analogously to (6), the QS property for the GOR is defined by…”

Section: Generalized Qs Modelsmentioning

confidence: 99%

“…Moving from LOR to generalized odds ratios, e.g., global odds ratios (GOR), QS models were also considered for modeling the symmetry of generalized odds ratios ( [15]). AMs for generalized odds ratios ( [16]) were extended to a broader family through the φ-divergence ( [17]).…”

Section: Introductionmentioning

confidence: 99%

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Families of Generalized Quasisymmetry Models: A ϕ-Divergence Approach

Kateri¹

2021

Symmetry

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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 ϕ 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 ϕ-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.

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Marginal Continuation odds Ratio Model and Decomposition of Marginal Homogeneity Model for Multi-way Contingency Tables

et al. 2020

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For square contingency tables with ordered categories, the marginal homogeneity model is represented by various expressions, and some extensions of the marginal homogeneity model were proposed. Herein we consider the marginal continuation-ratio to examine a new expression of the marginal homogeneity model. We also propose an extension of the marginal homogeneity model using the ratio of marginal continuation-ratios; namely, the marginal continuation odds ratio. The proposed model can be interpreted in various ways. Additionally, we propose a generalization of it, and decompose the marginal homogeneity model using the generalized model. Furthermore, we extend the models and decompositions into multi-way contingency tables.

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Generalised quasi‐symmetry models for ordinal contingency tables

Cited by 4 publications

References 29 publications

A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

Families of Generalized Quasisymmetry Models: A ϕ-Divergence Approach

Marginal Continuation odds Ratio Model and Decomposition of Marginal Homogeneity Model for Multi-way Contingency Tables

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