HANDLING ORDINAL VARIABLES IN 3-WAY ANALYSIS OF QUANTIFICATION MATRICES FOR VARIABLES OF MIXED MEASUREMENT LEVELS

For the analysis of variables of mixed measurement levels a class of m ethods can be used that is based on three-way analysis of quantificati on matrices for nominal or quantitative variables. This class of metho ds incorporates some well-known techniques but also offers a series of interesting new alternatives for the analysis of nominal or quantitat ive variables. Ordinal variables have received hardly any attention in this class of methods, and are usually treated as if they are quantit ative variables. In the present paper this gap is filled by constructi ng quantification matrices for ordinal variables via optimal scaling o f the ordinal variables, thus yielding optimal quantification matrices for these variables. Algorithms for this optimal scaling procedure ar e developed, and the optimal scaling procedures are compared to optima l scaling of ordinal variables in the context of principal components analysis and multidimensional scaling.