Asymmetry Models Based on Non-integer Scores for Square Contingency Tables

Square contingency tables with ordinal classifications are used in many disciplines that include but are not limited to data science, engineering, and medical research. This study proposes two original asymmetry models based on non-integer scores for the analysis of square contingency tables. The ordinal quasi-symmetry model applies to data sets that can be assigned to known ordered scores for all categories. When we assign the equally spaced score for categories, the ordinal quasi-symmetry model is equivalent to the linear diagonals-symmetry model. The ordinal quasi-symmetry model, however, is not applicable to data sets that cannot be assigned the known ordered scores for all categories. This study addresses this issue. The proposed models apply to data sets that: (i) can be assigned the known ordered scores for all except one category and (ii) cannot be assigned the known ordered scores for all categories. These two models provide a better fit than existing models for real-world data.