Ordinal invariant measures for individual and group changes in ordered categorical data

Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank-invariant properties of such data are well know n, and there are various statistical approaches to the analysis and modelli ng of ordinal data. This paper focuses on the non-additive property of orde red categorical data in the analysis of change. A rank-invariant non-parame tric method of analysis is presented that is valid regardless of the number of response categories. The unique feature of this method is the augmented ranking approach that is related to the joint distribution of paired obser vations. This approach makes it possible to measure separately the individu al order-preserved categorical changes, which are attributable to the group change, and the individual categorical changes that are not consistent wit h the pattern of group change. The method is applied to analysis of change in a three-point scale and in a visual analogue scale of continuous ordinal responses. (C) 1998 John Wiley & Sons, Ltd.