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

2016 ◽  
Vol 14 (1) ◽  
pp. 195-204
Author(s):  
Serpil Aktaş
Keyword(s):  
Contingency Table ◽  
Contingency Tables ◽  
Ordered Categories ◽  
Square Contingency Table

AbstractThis paper suggests several models that describe the symmetry and asymmetry structure of each subdimension for the multiway square contingency table with ordered categories. A classical three-way categorical example is examined to illustrate the model results. These models analyze the subsymmetric and asymetric structure of the table.

scholarly journals Collapsed Double Symmetry Model and Its Decomposition for Square Contingency Tables

2016 ◽  
Vol 5 (4) ◽  
pp. 31
Author(s):  
Kouji Yamamoto ◽  
Yuya Matsuda ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Table ◽  
Occupational Mobility ◽  
Contingency Tables ◽  
Square Contingency Table ◽  
Mobility Data ◽  
Symmetry Model ◽  
New Models ◽  
Original Table ◽  
Double Symmetry ◽  
Square Tables

For a square contingency table with ordinal categories, there may be a case that one wants to analyze several collapsed tables obtained by combining some adjacent categories of the original table. This paper proposes some new models which indicate double symmetry, quasi double symmetry and marginal double symmetry for the collapsed square tables. It also gives a decomposition of the double symmetry model for collapsed tables. Two kinds of occupational mobility data are analyzed using new models.

scholarly journals Boolean Monte Carlo Method

2019 ◽  
Author(s):  
Takuma Usuzaki ◽  
Minoru Shimoyama ◽  
Shuji Chiba ◽  
Naoko Mori
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Contingency Table ◽  
Contingency Tables ◽  
Medical Test ◽  
Frequentist Approach ◽  
Large Numbers ◽  
Result Analysis ◽  
Variable Analysis

A medical test and accuracy of diagnosis are often discussed with contingency tables. However, it is difficult to apply a contingency table to multivariate cases because the number of possible categories increases exponentially. We hypothesize that randomly assigning Boolean operators and focusing on frequencies of Boolean operators could explain the outcome correctly, obtain the tendencies of operators, and overcome difficulties in analyzing large numbers of variables and categories. The aims of this paper are introducing a method to obtain tendencies of Boolean operators and expanding 2 by 2 contingency tables to multivariate cases. To test this method, we construct two types of data: 1) when variables and outcome were randomly determined and 2) when the outcome depends on one variable. Analysis of the first type of data by this method showed that there was no significant result. Analysis of the second type of data reflected the bias of the data. As far as we know, this is the first attempt to use a frequentist approach to randomly assigned Boolean operators.

A Decomposition of the Marginal Homogeneity Model for Square Contingency Tables with Ordered Categories

1993 ◽  
Vol 43 (1-2) ◽  
pp. 123-126 ◽  
Author(s):  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Short Note ◽  
Monotonic Function ◽  
Ordered Categories ◽  
Marginal Homogeneity ◽  
Statist Assoc

For square contingency tables, with ordered categories, this short note decomposes the marginal homogeneity (MH) model into an extended MH model and the model of equality of expectation of monotonic function of row and column variables. This decomposition is a generalization of the decomposition of the MH model which was earlier considered by Tomizawa (1991, Cal. Statist. Assoc. Bull., 41, 201-207).

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