A Comparative Study of Scores for Correspondence Analysis with Ordered Categories

Ordered categorical data can be analysed using correspondence analysis with the ordered categories taken into consideration. Such an analysis was proposed by Beh (1997) and uses orthogonal polynomials which require the input of a scoring scheme to reflect the ordered structure of the categories. This method of correspondence analysis visualises the relationship between the categories, in terms of the location, dispersion and higher order components. The impact of the scoring method on the orthogonal polynomials, and hence upon the correspondence plot and other output of the analysis should therefore be considered. This paper aims at identifying this impact by considering four scoring schemes: integer valued (natural) scores, midrank scores, Nishisato scores and singular vectors from the classical correspondence analysis of the data. It is shown that while the latter two maximise the location component, generally there is little difference when comparing them with the output of the former two scoring schemes. A simple comparative study of profile co-ordinates using different scoring schemes is also discussed.