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This paper proposes new non-model based partial/conditional association measures for ordinal contingency table where the main interest is the association between two ordinal variables of interest, adjusting for the effect of the covariate(s). We first develop a new type of scores for the ordinal variables,  subcopula scores , taking into account the ordering of the categories of the variables and derive the  subcopula regressions  describing the relationships between the ordinal variables and the covariate(s). The proposed subcopula scores and subcopula regressions are obtained from the subcopula which uniquely links the joint distribution for the ordinal variables with their marginal distributions. We then define the new partial/conditional association measures between two ordinal variables to be the correlations between two sets of subcopula scores for them adjusted by the subcopula regressions of two response variables on the covariate(s). We theoretically investigate the properties of the proposed partial/conditional measures and their corresponding estimators. Finally, the performance of the proposed measures are evaluated by simulation studies and real-data examples.

On partial and conditional association measures for ordinal contingency tables