Abstract
For the analysis of square contingency tables with ordered categories, a measure was developed to represent the degree of departure from the conditional symmetry model in which there is an asymmetric structure of the cell probabilities with respect to the main diagonal of the table. The present paper proposes a novel measure for the departure from conditional symmetry based on the cumulative probabilities from the corners of the square table. In a given example, the proposed measure is applied to Japanese occupational status data, and the interpretation of the proposed measure is illustrated as the departure from a proportional structure of social mobility.
Highlights
Symmetry and asymmetry issues frequently arise in square contingency tables with the same row and column classifications from a broad range of scientific fields, for example, medical, social, and geographical sciences [1,2]
Regarding the residuals from the symmetry model, [8] gave the index, which represents the degree of residuals, and [9] considered the correspondence analysis of the residual matrix
The present paper focuses on measuring the degree of departure from an asymmetric structure for cumulative cell probabilities
Summary
Symmetry and asymmetry issues frequently arise in square contingency tables with the same row and column classifications from a broad range of scientific fields, for example, medical, social, and geographical sciences [1,2]. The present paper focuses on measuring the degree of departure from an asymmetric structure for cumulative cell probabilities. Because the CS model can be expressed as (2), we might be interested in measuring the degree to which the cumulative probabilities {Gij} are distant from those with a conditional symmetric structure. The present paper considers a new measure to represent the degree of departure from CS based on the cumulative probabilities {Gij}. Such a new measure may be useful when we determine the structure of the cumulative probabilities underlying the data rather than the structure of cell probabilities.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
