Quasi local odds symmetry model for square contingency table with ordinal categories

Altun, Gökçen

doi:10.1080/00949655.2019.1643347

Cited by 5 publications

(6 citation statements)

References 15 publications

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“…The contingency tables which have the same number of row and column categories are called square contingency tables or 𝑅×𝑅 tables [1,2]. The association models exhibit the association between row and column variables.…”

Section: Association Modelsmentioning

confidence: 99%

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Aktaş

Yılmaz

2021

Mugla Journal of Science and Technology

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The Uniform Association (UA) and Quasi-Uniform Association (QUA) models are used for analysis of two-way square contingency tables with ordered categories. When the QUA model does not fit the data, one wants to measure the degree of departure from the quasi-uniform association model. The degree of the departure from the model is calculated by using the power divergence statistics. In this study, as an alternative to measures in the literature, a measure to estimate the degree of departure from the QUA model is suggested. This suggested measure allows us to compare the several R×R tables in terms of the departure from the model. The measures are compared by the simulation study and discussed by three unaided distance vision data.

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Section: Association Modelsmentioning

confidence: 99%

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Aktaş

Yılmaz

2021

Mugla Journal of Science and Technology

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“…In addition to the existing models introduced in previous sections, we apply the CCOS model and the quasi-local odds symmetry (QLOS) model to the data set in Table 1. The QLOS model recently proposed by Altun (2019) is defined by…”

Section: Application To Real-world Datamentioning

confidence: 99%

Odds‐symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables

Ando

2021

Aus NZ J of Statistics

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For the analysis of square contingency tables, it is necessary to estimate an unknown distribution with high confidence from an obtained observation. For that purpose, we need to introduce a statistical model that fits the data well and has parsimony. This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for all i < j, that an observation will fall in row category i or below, and column category j or above, instead of row category j or above, and column category i or below, depend on only row category i or column category j. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse is not necessarily true. This study also shows that it is necessary to satisfy the extended marginal homogeneity model, in addition to the proposed models, to satisfy the CS model. These decomposition theorems explain why the CS model does not hold. The proposed models provide a better fit for application to a single data set of real-world occupational data for father-and-son dyads.

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“…We point out that the ELA k model is the asymmetry model based on the EQS model. As an extension of the EQS model, Altun [16] recently proposed the quasi local odds symmetry (QLOS) defined by…”

Section: Introductionmentioning

confidence: 99%

Asymmetry Model Based on Quasi Local Odds Symmetry for Square Contingency Tables

Ando

2022

Symmetry

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For the analysis of square contingency tables, the primary objective is to estimate an unknown distribution from presented data. To achieve this objective, we generally use a statistical model that fits the presented data well and has a parsimony. The recently proposed quasi local odds symmetry (QLOS) model was compared to various models that represent the structure of symmetry or asymmetry, and it provided the best fit performance compared with other models for real data. However, the QLOS model has many parameters, that is, the QLOS model is not the parsimonious model. To address this issue, this study proposes a new model that is more parsimonious than the QLOS model. The proposed model is identical to the QLOS model under the specified condition; it is the asymmetry model based on the QLOS model.Moreover, we compare the proposed model with the existing models, including the QLOS model, and show that the proposed model provides better fit performance than the existing models for real datasets.

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Quasi local odds symmetry model for square contingency table with ordinal categories

Cited by 5 publications

References 15 publications

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Departure From Quasi-Uniform Association Model in Ordered Square Contingency Tables

Odds‐symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables

Asymmetry Model Based on Quasi Local Odds Symmetry for Square Contingency Tables

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