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Ordinal invariant measures for individual and group changes in ordered categorical data
Author(s) -
Svensson Elisabeth
Publication year - 1998
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19981230)17:24<2923::aid-sim104>3.0.co;2-#
Subject(s) - categorical variable , ordinal data , ordinal scale , mathematics , ordinal regression , invariant (physics) , statistics , ranking (information retrieval) , computer science , artificial intelligence , mathematical physics
Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank‐invariant properties of such data are well known, and there are various statistical approaches to the analysis and modelling of ordinal data. This paper focuses on the non‐additive property of ordered categorical data in the analysis of change. A rank‐invariant non‐parametric 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 observations. This approach makes it possible to measure separately the individual order‐preserved categorical changes, which are attributable to the group change, and the individual categorical changes that are not consistent with 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. © 1998 John Wiley & Sons, Ltd.