Partial cumulative correspondence analysis

Partial correspondence analysis (Yanai, in: Diday, Escoufier, Lebart, Pages, Schektman, Thomassone (eds) Data analysis and informatics IV, North-Holland, Amsterdam, pp 193-207, 1986, in: Hayashi, Jambu, Diday, Osumi (eds) Recent developments in clustering and data analysis, Academic Press, Boston, pp 259-266, 1988) has been introduced in statistical literature to eliminate the effects of an ancillary criterion variable on the relationship between two categorical characters. It is well known that partial and classical correspondence analyses do not perform well if one (or both) of the variables forming the contingency table presents an ordinal structure. Cumulative correspondence analysis is a method that considers the information included in the ordinal variable(s). Nevertheless, in this case, a third categorical variable (ancillary) could also influence the existing relation. In this paper, we extend Yanai's partial approach to cumulative correspondence analysis and, by using suitable orthogonal projectors, we obtain some properties. Finally, we present two real case studies.