Dual Scaling

This is a method for multidimensional quantification of categorical data in a two-way table (e.g., a contingency table, an examinees-by-questions table of multiple-choice responses). The word “dual” reflects its symmetric scaling of rows and columns of a table. Dual scaling determines weights for options of multiple-choice items in such a way that scores of the subjects, given by weighted sums of weights of chosen options, attain greatest discriminability, hence, maximal internal consistency; in turn, those option weights are expressed as weighted sums of scores of the examinees who chose the options. This property is often referred to as Louis Guttman's principle of internal consistency. Frederic M. Lord verified that such a weighting scheme as this maximizes the internal consistency reliability of the derived scores.