in Asselin (2002), the expression of the categorical composite indicator of multiple correspondence analysis (qualitative variables) is:
Where K = number of categorical indicators, p = number of categories for indicator k, Wp = the weight of category p, Ip = binary indicator 0/1, which takes on the value 1 when the individu has the category p, and 0 otherwise.
Can i treat Asselin 2002 linear categorical composite indicator of multiple correspondence analysis above as a geometrical function as bellow?
Since in principal component analysis there is a linear aggregation and also geometric aggregation for numerical composite indicator as in OECD 2008 bellow:
for linear aggreagtion:
Where q = number of quantitative variables, Wq = the weight of quantitative variables q, Zq = standardized of quantitative variables q.
and for geometric aggregation:
Where Xq = unstandardized of quantitative variables q.
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