Quasi-diagonal exponent symmetry model for square contingency tables with ordered categories

Iki, Kiyotaka; Yamamoto, Keiji; Tomizawa, Sadao

doi:10.1016/j.spl.2014.04.029

Cited by 4 publications

(9 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The smallest value for both AIC and BIC is obtained for Model (8). Note that Model (8) and Model (9) are the conditional models that collapsed the baseline variable. Recall that Model (8) In this model representation, "Baseline" is the control variable therefore it is not included in the parameters.…”

Section: Numerical Examplementioning

confidence: 96%

“…The Models (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) proposed here attampt to analyze what is the relationship between X, Y and Z taking "Baseline" as the control.…”

Section: Numerical Examplementioning

confidence: 99%

“…Some examples for these kind of tables are: for instance, when the subjects are measured at two di erent points in time (e.g., responses before and after experiments); the decisions of two experts are measured on the same set of subjects (e.g., the grading of the same cancer tumors by two specialists); two similar units in a sample are measured (e.g., the grades of vision of the left and the right eyes); matched pair experiments (e.g., social status of the fathers and sons) [1]. For square contingency tables, several models have been proposed (see, for example [2][3][4][5][6][7][8] but the models of symmetry (S), quasi-symmetry (QS), marginal homogeneity (MH) are classical and well known models [9,10] and the applicability of the these models is straightforward. The QS is less restrictive model than the S model [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

Aktaş

2016

Open Mathematics

View full text Add to dashboard Cite

show abstract

Section: Numerical Examplementioning

confidence: 96%

“…The Models (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) proposed here attampt to analyze what is the relationship between X, Y and Z taking "Baseline" as the control.…”

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

Aktaş

2016

Open Mathematics

View full text Add to dashboard Cite

show abstract

“…, R − k). Iki, Yamamoto & Tomizawa (2014) considered the quasi-diagonal exponent symmetry (QDES) model defined by…”

Section: The Global Symmetry (Gs) Model Is Defined Bymentioning

confidence: 99%

“…We define the mean equality (ME) model as E(X) = E(Y). Iki et al (2014) gave the theorem that the DES model holds if and only if both the QDES and ME models hold. Other symmetry and asymmetry models have been described in Tahata & Tomizawa (2014).…”

Section: The Global Symmetry (Gs) Model Is Defined Bymentioning

confidence: 99%

Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories

Iki¹,

Shibuya²,

Tomizawa³

2016

IJSP

Self Cite

View full text Add to dashboard Cite

For square contingency tables with ordered categories, this article proposes new models which indicate that in addition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table, the expected frequency has an exponential form along every subdiagonal of the table. Also it gives the new three kinds of decompositions using the proposed model and proves the orthogonality of the test statistics.

show abstract

Visualising Departures from Symmetry and Bowker’s X2 Statistic

Beh

Lombardo²

2022

Symmetry

View full text Add to dashboard Cite

Sometimes, the same categorical variable is studied over different time periods or across different cohorts at the same time. One may consider, for example, a study of voting behaviour of different age groups across different elections, or the study of the same variable exposed to a child and a parent. For such studies, it is interesting to investigate how similar, or different, the variable is between the two time points or cohorts and so a study of the departure from symmetry of the variable is important. In this paper, we present a method of visualising any departures from symmetry using correspondence analysis. Typically, correspondence analysis uses Pearson’s chi-squared statistic as the foundation for all of its numerical and visual features. In the case of studying the symmetry of a variable, Bowker’s chi-squared statistic, presented in 1948, provides a simple numerical means of assessing symmetry. Therefore, this paper shall discuss how a correspondence analysis can be performed to study the symmetry (or lack thereof) of a categorical variable when Bowker’s statistic is considered. The technique presented here provides an extension to the approach developed by Michael Greenacre in 2000.

show abstract

Quasi-diagonal exponent symmetry model for square contingency tables with ordered categories

Cited by 4 publications

References 14 publications

Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

Subsymmetry and asymmetry models for multiway square contingency tables with ordered categories

Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories

Visualising Departures from Symmetry and Bowker’s X2 Statistic

Contact Info

Product

Resources

About